Continued increases in the emission of greenhouse gases by passenger ve<span style="font-family:Verdana;">hicles ha</span><span style="font-family:Verdana;">ve</span><spa...Continued increases in the emission of greenhouse gases by passenger ve<span style="font-family:Verdana;">hicles ha</span><span style="font-family:Verdana;">ve</span><span style="font-family:;" "=""><span style="font-family:Verdana;"> accelerated the production of hybrid electric vehicles. With this increase in production, there has been a parallel demand for continuously improving strategies of hybrid electric vehicle control. The goal of an ideal control strategy is to maximize fuel economy while minimizing emissions. Methods exist by which the globally optimal control strategy may be found. However, these methods are not applicable in real-world driving applications since these methods require </span><i><span style="font-family:Verdana;">a</span></i> <i><span style="font-family:Verdana;">priori</span></i><span style="font-family:Verdana;"> knowledge of the upcoming drive cycle. Real-time control strategies use the global optimal as a benchmark against which performance can be evaluated. The goal of this work is to use a previously defined strategy that has been shown to closely approximate the global optimal and implement a radial basis function (RBF) artificial neural network (ANN) that dynamically adapts the strategy based on past driving conditions. The strate</span><span style="font-family:Verdana;">gy used is the Equivalent Consumption Minimization Strategy (ECMS),</span><span style="font-family:Verdana;"> which uses an equivalence factor to define the control strategy and the power train </span><span style="font-family:Verdana;">component torque split. An equivalence factor that is optimal for a single</span><span style="font-family:Verdana;"> drive cycle can be found offline</span></span><span style="font-family:;" "=""> </span><span style="font-family:;" "=""><span style="font-family:Verdana;">with </span><i><span style="font-family:Verdana;">a</span></i> <i><span style="font-family:Verdana;">priori</span></i><span style="font-family:Verdana;"> knowledge of the drive cycle. The RBF-ANN is used to dynamically update the equivalence factor by examining a past time window of driving characteristics. A total of 30 sets of training data (drive cycles) are used to train the RBF-ANN. For the majority of drive cycles examined, the RBF-ANN implementation is shown to produce fuel economy values that are within ±2.5% of the fuel economy obtained with the optimal equivalence factor. The advantage of the RBF-ANN is that it does not require </span><i><span style="font-family:Verdana;">a</span></i> <i><span style="font-family:Verdana;">priori</span></i><span style="font-family:Verdana;"> drive cycle knowledge and is able to be implemented in real-time while meeting or exceeding the performance of the optimal ECMS. Recommendations are made on how the RBF-ANN could be improved to produce better results across a greater array of driving conditions.</span></span>展开更多
The introduction of fully controlled devices to build hybrid line commutated converter(H-LCC)has become a new idea to solve the commutation failure.However,existing H-LCC has not considered the implementation of a tar...The introduction of fully controlled devices to build hybrid line commutated converter(H-LCC)has become a new idea to solve the commutation failure.However,existing H-LCC has not considered the implementation of a targeted firing angle control strategy during AC faults,with the objective of enhancing their power transmission and fault response performance.For this reason,this paper proposes an optimized control method for firing angle of H-LCC,designated as flexible virtual firing(FVF).This method first analyzes the influence of alterations in firing angle on reactive power,commutation process and associated action paths.By combining prediction and dynamic search,it optimizes the natural commutation process through the utilization of dynamic boundary and minimum commutation area difference.This can mitigate the impact of AC faults on H-LCC and DC system,thereby improving power transmission and defense to commutation failure,which is beneficial for improving the stability of AC/DC power grids.Finally,the simulation results in PSCAD/EMTDC verify the effectiveness of the proposed method.展开更多
This paper presents an optimized shared control algorithm for human–AI interaction, implemented through a digital twin framework where the physical system and human operator act as the real agent while an AI-driven d...This paper presents an optimized shared control algorithm for human–AI interaction, implemented through a digital twin framework where the physical system and human operator act as the real agent while an AI-driven digital system functions as the virtual agent. In this digital twin architecture, the real agent acquires an optimal control strategy through observed actions, while the AI virtual agent mirrors the real agent to establish a digital replica system and corresponding control policy. Both the real and virtual optimal controllers are approximated using reinforcement learning(RL) techniques. Specifically, critic neural networks(NNs) are employed to learn the virtual and real optimal value functions, while actor NNs are trained to derive their respective optimal controllers. A novel shared mechanism is introduced to integrate both virtual and real value functions into a unified learning framework, yielding an optimal shared controller. This controller adaptively adjusts the confidence ratio between virtual and real agents, enhancing the system's efficiency and flexibility in handling complex control tasks. The stability of the closed-loop system is rigorously analyzed using the Lyapunov method. The effectiveness of the proposed AI–human interactive system is validated through two numerical examples: a representative nonlinear system and an unmanned aerial vehicle(UAV) control system.展开更多
Dear Editor,In this letter,a constrained networked predictive control strategy is proposed for the optimal control problem of complex nonlinear highorder fully actuated(HOFA)systems with noises.The method can effectiv...Dear Editor,In this letter,a constrained networked predictive control strategy is proposed for the optimal control problem of complex nonlinear highorder fully actuated(HOFA)systems with noises.The method can effectively deal with nonlinearities,constraints,and noises in the system,optimize the performance metric,and present an upper bound on the stable output of the system.展开更多
Assessing the impact of anthropogenic volatile organic compounds(VOCs)on ozone(O_(3))formation is vital for themanagement of emission reduction and pollution control.Continuousmeasurement of O_(3)and the major precurs...Assessing the impact of anthropogenic volatile organic compounds(VOCs)on ozone(O_(3))formation is vital for themanagement of emission reduction and pollution control.Continuousmeasurement of O_(3)and the major precursorswas conducted in a typical light industrial city in the YRD region from 1 May to 25 July in 2021.Alkanes were the most abundant VOC group,contributing to 55.0%of TVOCs concentration(56.43±21.10 ppb).OVOCs,aromatics,halides,alkenes,and alkynes contributed 18.7%,9.6%,9.3%,5.2%and 1.9%,respectively.The observational site shifted from a typical VOC control regime to a mixed regime from May to July,which can be explained by the significant increase of RO_(x)production,resulting in the transition of environment from NOx saturation to radical saturation with respect to O_(3)production.The optimal O_(3)control strategy should be dynamically changed depending on the transition of control regime.Under NOx saturation condition,minimizing the proportion of NOx in reduction could lead to better achievement of O_(3)alleviation.Under mixed control regime,the cut percentage gets the top priority for the effectiveness of O_(3)control.Five VOCs sources were identified:temperature dependent source(28.1%),vehicular exhausts(19.9%),petrochemical industries(7.2%),solvent&gasoline usage(32.3%)and manufacturing industries(12.6%).The increase of temperature and radiation would enhance the evaporation related VOC emissions,resulting in the increase of VOC concentration and the change of RO_(x)circulation.Our results highlight determination of the optimal control strategies for O_(3)pollution in a typical YRD industrial city.展开更多
We present a robust quantum optimal control framework for implementing fast entangling gates on ion-trap quantum processors.The framework leverages tailored laser pulses to drive the multiple vibrational sidebands of ...We present a robust quantum optimal control framework for implementing fast entangling gates on ion-trap quantum processors.The framework leverages tailored laser pulses to drive the multiple vibrational sidebands of the ions to create phonon-mediated entangling gates and,unlike the state of the art,requires neither weakcoupling Lamb-Dicke approximation nor perturbation treatment.With the application of gradient-based optimal control,it enables finding amplitude-and phase-modulated laser control protocols that work without the Lamb-Dicke approximation,promising gate speeds on the order of microseconds comparable to the characteristic trap frequencies.Also,robustness requirements on the temperature of the ions and initial optical phase can be conveniently included to pursue high-quality fast gates against experimental imperfections.Our approach represents a step in speeding up quantum gates to achieve larger quantum circuits for quantum computation and simulation,and thus can find applications in near-future experiments.展开更多
This paper addresses the Singular Optimal Control Problem(SOCP)for a surface-to-air missile with limited control,fully considering aerodynamic effects with a parabolic drag polar.This problem is an extension of the ty...This paper addresses the Singular Optimal Control Problem(SOCP)for a surface-to-air missile with limited control,fully considering aerodynamic effects with a parabolic drag polar.This problem is an extension of the typical Goddard problem.First,the classical Legendre-Clebsch condition is applied to derive optimal conditions for the singular angle of attack,revealing that the missile turns by gravity along the singular arc.Second,the higher-order differentiation of the switching function provides the necessary conditions to determine the optimal thrust,expressed as linear functions of the costate variables.The vanishing coefficient determinant is then employed to decouple the control and costate variables,yielding the singular thrust solely dependent on state variables and identifying the singular surface.Moreover,the analytical singular control can be regarded as path constraints subject to the typical Optimal Control Problem(OCP),enabling the GPOPS-Ⅱ,a direct method framework that does not involve the singular condition,to solve the SOCP.Finally,three cases with different structures are presented to evaluate the performance of the proposed method.The results show that it takes a few steps to obtain the numerical optimal solution,which is consistent with the analytical solution derived from the calculus of variations,highlighting its great computational accuracy and effectiveness.展开更多
The electromagnetic levitation system(EMLS)serves as the most important part of any magnetic levitation system.However,its characteristics are defined by its highly nonlinear dynamics and instability.Furthermore,the u...The electromagnetic levitation system(EMLS)serves as the most important part of any magnetic levitation system.However,its characteristics are defined by its highly nonlinear dynamics and instability.Furthermore,the uncertainties in the dynamics of an electromagnetic levitation system make the controller design more difficult.Therefore,it is necessary to design a robust control law that will ensure the system’s stability in the presence of these uncertainties.In this framework,the dynamics of an electromagnetic levitation system are addressed in terms of matched and unmatched uncertainties.The robust control problem is translated into the optimal control problem,where the uncertainties of the electromagnetic levitation system are directly reflected in the cost function.The optimal control method is used to solve the robust control problem.The solution to the optimal control problem for the electromagnetic levitation system is indeed a solution to the robust control problem of the electromagnetic levitation system under matched and unmatched uncertainties.The simulation and experimental results demonstrate the performance of the designed control scheme.The performance indices such as integral absolute error(IAE),integral square error(ISE),integral time absolute error(ITAE),and integral time square error(ITSE)are compared for both uncertainties to showcase the robustness of the designed control scheme.展开更多
The co-infection of corona and influenza viruses has emerged as a significant threat to global public health due to their shared modes of transmission and overlapping clinical symptoms.This article presents a novel ma...The co-infection of corona and influenza viruses has emerged as a significant threat to global public health due to their shared modes of transmission and overlapping clinical symptoms.This article presents a novel mathematical model that addresses the dynamics of this co-infection by extending the SEIR(Susceptible-Exposed-Infectious-Recovered)framework to incorporate treatment and hospitalization compartments.The population is divided into eight compartments,with infectious individuals further categorized into influenza infectious,corona infectious,and co-infection cases.The proposed mathematical model is constrained to adhere to fundamental epidemiological properties,such as non-negativity and boundedness within a feasible region.Additionally,the model is demonstrated to be well-posed with a unique solution.Equilibrium points,including the disease-free and endemic equilibria,are identified,and various properties related to these equilibrium points,such as the basic reproduction number,are determined.Local and global sensitivity analyses are performed to identify the parameters that highly influence disease dynamics and the reproduction number.Knowing the most influential parameters is crucial for understanding their impact on the co-infection’s spread and severity.Furthermore,an optimal control problem is defined to minimize disease transmission and to control strategy costs.The purpose of our study is to identify the most effective(optimal)control strategies for mitigating the spread of the co-infection with minimum cost of the controls.The results illustrate the effectiveness of the implemented control strategies in managing the co-infection’s impact on the population’s health.This mathematical modeling and control strategy framework provides valuable tools for understanding and combating the dual threat of corona and influenza co-infection,helping public health authorities and policymakers make informed decisions in the face of these intertwined epidemics.展开更多
This article presents an adaptive optimal control method for a semi-active suspension system.The model of the suspension system is built,in which the components of uncertain parameters and exogenous disturbance are de...This article presents an adaptive optimal control method for a semi-active suspension system.The model of the suspension system is built,in which the components of uncertain parameters and exogenous disturbance are described.The adaptive optimal control law consists of the sum of the optimal control component and the adaptive control component.First,the optimal control law is designed for the model of the suspension system after ignoring the components of uncertain parameters and exogenous disturbance caused by the road surface.The optimal control law expresses the desired dynamic characteristics of the suspension system.Next,the adaptive component is designed with the purpose of compensating for the effects caused by uncertain parameters and exogenous disturbance caused by the road surface;the adaptive component has adaptive parameter rules to estimate uncertain parameters and exogenous disturbance.When exogenous disturbances are eliminated,the system responds with an optimal controller designed.By separating theoretically the dynamic of a semi-active suspension system,this solution allows the design of two separate controllers easily and has reduced the computational burden and the use of too many tools,thus allowing for more convenient hardware implementation.The simulation results also show the effectiveness of damping oscillations of the proposed solution in this article.展开更多
Malaria is a significant global health challenge.This devastating disease continues to affect millions,especially in tropical regions.It is caused by Plasmodium parasites transmitted by female Anopheles mosquitoes.Thi...Malaria is a significant global health challenge.This devastating disease continues to affect millions,especially in tropical regions.It is caused by Plasmodium parasites transmitted by female Anopheles mosquitoes.This study introduces a nonlinear mathematical model for examining the transmission dynamics of malaria,incorporating both human and mosquito populations.We aim to identify the key factors driving the endemic spread of malaria,determine feasible solutions,and provide insights that lead to the development of effective prevention and management strategies.We derive the basic reproductive number employing the next-generation matrix approach and identify the disease-free and endemic equilibrium points.Stability analyses indicate that the disease-free equilibrium is locally and globally stable when the reproductive number is below one,whereas an endemic equilibrium persists when this threshold is exceeded.Sensitivity analysis identifies the most influential mosquito-related parameters,particularly the bite rate and mosquito mortality,in controlling the spread of malaria.Furthermore,we extend our model to include a treatment compartment and three disease-preventive control variables such as antimalaria drug treatments,use of larvicides,and the use of insecticide-treated mosquito nets for optimal control analysis.The results show that optimal use of mosquito nets,use of larvicides for mosquito population control,and treatment can lower the basic reproduction number and control malaria transmission with minimal intervention costs.The analysis of disease control strategies and findings offers valuable information for policymakers in designing cost-effective strategies to combat malaria.展开更多
This paper studies motor joint control of a 4-degree-of-freedom(DoF)robotic manipulator using learning-based Adaptive Dynamic Programming(ADP)approach.The manipulator’s dynamics are modelled as an open-loop 4-link se...This paper studies motor joint control of a 4-degree-of-freedom(DoF)robotic manipulator using learning-based Adaptive Dynamic Programming(ADP)approach.The manipulator’s dynamics are modelled as an open-loop 4-link serial kinematic chain with 4 Degrees of Freedom(DoF).Decentralised optimal controllers are designed for each link using ADP approach based on a set of cost matrices and data collected from exploration trajectories.The proposed control strategy employs an off-line,off-policy iterative approach to derive four optimal control policies,one for each joint,under exploration strategies.The objective of the controller is to control the position of each joint.Simulation and experimental results show that four independent optimal controllers are found,each under similar exploration strategies,and the proposed ADP approach successfully yields optimal linear control policies despite the presence of these complexities.The experimental results conducted on the Quanser Qarm robotic platform demonstrate the effectiveness of the proposed ADP controllers in handling significant dynamic nonlinearities,such as actuation limitations,output saturation,and filter delays.展开更多
A mixed adaptive dynamic programming(ADP)scheme based on zero-sum game theory is developed to address optimal control problems of autonomous underwater vehicle(AUV)systems subject to disturbances and safe constraints....A mixed adaptive dynamic programming(ADP)scheme based on zero-sum game theory is developed to address optimal control problems of autonomous underwater vehicle(AUV)systems subject to disturbances and safe constraints.By combining prior dynamic knowledge and actual sampled data,the proposed approach effectively mitigates the defect caused by the inaccurate dynamic model and significantly improves the training speed of the ADP algorithm.Initially,the dataset is enriched with sufficient reference data collected based on a nominal model without considering modelling bias.Also,the control object interacts with the real environment and continuously gathers adequate sampled data in the dataset.To comprehensively leverage the advantages of model-based and model-free methods during training,an adaptive tuning factor is introduced based on the dataset that possesses model-referenced information and conforms to the distribution of the real-world environment,which balances the influence of model-based control law and data-driven policy gradient on the direction of policy improvement.As a result,the proposed approach accelerates the learning speed compared to data-driven methods,concurrently also enhancing the tracking performance in comparison to model-based control methods.Moreover,the optimal control problem under disturbances is formulated as a zero-sum game,and the actor-critic-disturbance framework is introduced to approximate the optimal control input,cost function,and disturbance policy,respectively.Furthermore,the convergence property of the proposed algorithm based on the value iteration method is analysed.Finally,an example of AUV path following based on the improved line-of-sight guidance is presented to demonstrate the effectiveness of the proposed method.展开更多
In this paper,based on the SVIQR model we develop a stochastic epidemic model with multiple vaccinations and time delay.Firstly,we prove the existence and uniqueness of the global positive solution of the model,and co...In this paper,based on the SVIQR model we develop a stochastic epidemic model with multiple vaccinations and time delay.Firstly,we prove the existence and uniqueness of the global positive solution of the model,and construct suitable functions to obtain sufficient conditions for disease extinction.Secondly,in order to effectively control the spread of the disease,appropriate control strategies are formulated by using optimal control theory.Finally,the results are verified by numerical simulation.展开更多
To better complete various missions, it is necessary to plan an optimal trajectory or provide the optimal control law for the multirole missile according to the actual situation, including launch conditions and target...To better complete various missions, it is necessary to plan an optimal trajectory or provide the optimal control law for the multirole missile according to the actual situation, including launch conditions and target location. Since trajectory optimization struggles to meet real-time requirements, the emergence of data-based generation methods has become a significant focus in contemporary research. However, due to the large differences in the characteristics of the optimal control laws caused by the diversity of tasks, it is difficult to achieve good prediction results by modeling all data with one single model.Therefore, the modeling idea of the mixture of experts(MoE) is adopted. Firstly, the K-means clustering algorithm is used to partition the sample data set, and the corresponding neural network classification model is established as the gate switch of MoE. Then, the expert models, i.e., the mappings from the generation conditions to the optimal control law represented by the results of principal component analysis(PCA), are represented by Kriging models. Finally, multiple rounds of accuracy evaluation, sample supplementation, and model updating are conducted to improve the generation accuracy. The Monte Carlo simulation shows that the accuracy of the proposed model reaches 96% and the generation efficiency meets the real-time requirement.展开更多
This paper investigates a new SEIQR(susceptible–exposed–infected–quarantined–recovered) epidemic model with quarantine mechanism on heterogeneous complex networks. Firstly, the nonlinear SEIQR epidemic spreading d...This paper investigates a new SEIQR(susceptible–exposed–infected–quarantined–recovered) epidemic model with quarantine mechanism on heterogeneous complex networks. Firstly, the nonlinear SEIQR epidemic spreading dynamic differential coupling model is proposed. Then, by using mean-field theory and the next-generation matrix method, the equilibriums and basic reproduction number are derived. Theoretical results indicate that the basic reproduction number significantly relies on model parameters and topology of the underlying networks. In addition, the globally asymptotic stability of equilibrium and the permanence of the disease are proved in detail by the Routh–Hurwitz criterion, Lyapunov method and La Salle's invariance principle. Furthermore, we find that the quarantine mechanism, that is the quarantine rate(γ1, γ2), has a significant effect on epidemic spreading through sensitivity analysis of basic reproduction number and model parameters. Meanwhile, the optimal control model of quarantined rate and analysis method are proposed, which can optimize the government control strategies and reduce the number of infected individual. Finally, numerical simulations are given to verify the correctness of theoretical results and a practice application is proposed to predict and control the spreading of COVID-19.展开更多
This paper proposes an optimal midcourse guidance method for dual pulse air-to-air missiles,which is based on the framework of the linear Gauss pseudospectral model predictive control method.Firstly,a multistage optim...This paper proposes an optimal midcourse guidance method for dual pulse air-to-air missiles,which is based on the framework of the linear Gauss pseudospectral model predictive control method.Firstly,a multistage optimal control problem with unspecified terminal time is formulated.Secondly,the control and terminal time update formulas are derived analytically.In contrast to previous work,the derivation process fully considers the Hamiltonian function corresponding to the unspecified terminal time,which is coupled with control,state,and costate.On the assumption of small perturbation,a special algebraic equation is provided to represent the equivalent optimal condition for the terminal time.Also,using Gauss pseudospectral collocation,error propagation dynamical equations involving the first-order correction term of the terminal time are transformed into a set of algebraic equations.Furthermore,analytical modification formulas can be derived by associating those equations and optimal conditions to eliminate terminal error and approach nonlinear optimal control.Even with their mathematical complexity,these formulas produce more accurate control and terminal time corrections and remove reliance on task-related parameters.Finally,several numerical simulations,comparisons with typical methods,and Monte Carlo simulations have been done to verify its optimality,high convergence rate,great stability and robustness.展开更多
Spillover of trypanosomiasis parasites from wildlife to domestic livestock and humans remains a major challenge world over.With the disease targeted for elimination by 2030,assessing the impact of control strategies i...Spillover of trypanosomiasis parasites from wildlife to domestic livestock and humans remains a major challenge world over.With the disease targeted for elimination by 2030,assessing the impact of control strategies in communities where there are human-cattle-wildlife interactions is therefore essential.A compartmental framework incorporating tsetse flies,humans,cattle,wildlife and various disease control strategies is developed and analyzed.The reproduction is derived and its sensitivity to different model parameters is investigated.Meanwhile,the optimal control theory is used to identify a combination of control strategies capable of minimizing the infected human and cattle population over time at minimal costs of implementation.The results indicates that tsetse fly mortality rate is strongly and negatively correlated to the reproduction number.It is also established that tsetse fly feeding rate in strongly and positively correlated to the reproduction number.Simulation results indicates that time dependent control strategies can significantly reduce the infections.Overall,the study shows that screening and treatment of humans may not lead to disease elimination.Combining this strategy with other strategies such as screening and treatment of cattle and vector control strategies will result in maximum reduction of tsetse fly population and disease elimination.展开更多
This paper aims to study the optimal control and algorithm implementation of a generalized epidemic model governed by reaction-diffusion equations.Considering individual mobility,this paper first proposes a reaction-d...This paper aims to study the optimal control and algorithm implementation of a generalized epidemic model governed by reaction-diffusion equations.Considering individual mobility,this paper first proposes a reaction-diffusion epidemic model with two strains.Furthermore,applying vaccines as a control strategy in the model,an optimal control problem is proposed to increase the number of healthy individuals while reducing control costs.By applying the truncation function technique and the operator semigroup methods,we prove the existence and uniqueness of a globally positive strong solution for the control model.The existence of the optimal control strategy is proven by using functional analysis theory and minimum sequence methods.The first-order necessary condition satisfied by the optimal control is established by employing the dual techniques.Finally,a specific example and its algorithm are provided.展开更多
Inverse reinforcement learning optimal control is under the framework of learner-expert.The learner system can imitate the expert system's demonstrated behaviors and does not require the predefined cost function,s...Inverse reinforcement learning optimal control is under the framework of learner-expert.The learner system can imitate the expert system's demonstrated behaviors and does not require the predefined cost function,so it can handle optimal control problems effectively.This paper proposes an inverse reinforcement learning optimal control method for Takagi-Sugeno(T-S)fuzzy systems.Based on learner systems,an expert system is constructed,where the learner system only knows the expert system's optimal control policy.To reconstruct the unknown cost function,we firstly develop a model-based inverse reinforcement learning algorithm for the case that systems dynamics are known.The developed model-based learning algorithm is consists of two learning stages:an inner reinforcement learning loop and an outer inverse optimal control loop.The inner loop desires to obtain optimal control policy via learner's cost function and the outer loop aims to update learner's state-penalty matrices via only using expert's optimal control policy.Then,to eliminate the requirement that the system dynamics must be known,a data-driven integral learning algorithm is presented.It is proved that the presented two algorithms are convergent and the developed inverse reinforcement learning optimal control scheme can ensure the controlled fuzzy learner systems to be asymptotically stable.Finally,we apply the proposed fuzzy optimal control to the truck-trailer system,and the computer simulation results verify the effectiveness of the presented approach.展开更多
文摘Continued increases in the emission of greenhouse gases by passenger ve<span style="font-family:Verdana;">hicles ha</span><span style="font-family:Verdana;">ve</span><span style="font-family:;" "=""><span style="font-family:Verdana;"> accelerated the production of hybrid electric vehicles. With this increase in production, there has been a parallel demand for continuously improving strategies of hybrid electric vehicle control. The goal of an ideal control strategy is to maximize fuel economy while minimizing emissions. Methods exist by which the globally optimal control strategy may be found. However, these methods are not applicable in real-world driving applications since these methods require </span><i><span style="font-family:Verdana;">a</span></i> <i><span style="font-family:Verdana;">priori</span></i><span style="font-family:Verdana;"> knowledge of the upcoming drive cycle. Real-time control strategies use the global optimal as a benchmark against which performance can be evaluated. The goal of this work is to use a previously defined strategy that has been shown to closely approximate the global optimal and implement a radial basis function (RBF) artificial neural network (ANN) that dynamically adapts the strategy based on past driving conditions. The strate</span><span style="font-family:Verdana;">gy used is the Equivalent Consumption Minimization Strategy (ECMS),</span><span style="font-family:Verdana;"> which uses an equivalence factor to define the control strategy and the power train </span><span style="font-family:Verdana;">component torque split. An equivalence factor that is optimal for a single</span><span style="font-family:Verdana;"> drive cycle can be found offline</span></span><span style="font-family:;" "=""> </span><span style="font-family:;" "=""><span style="font-family:Verdana;">with </span><i><span style="font-family:Verdana;">a</span></i> <i><span style="font-family:Verdana;">priori</span></i><span style="font-family:Verdana;"> knowledge of the drive cycle. The RBF-ANN is used to dynamically update the equivalence factor by examining a past time window of driving characteristics. A total of 30 sets of training data (drive cycles) are used to train the RBF-ANN. For the majority of drive cycles examined, the RBF-ANN implementation is shown to produce fuel economy values that are within ±2.5% of the fuel economy obtained with the optimal equivalence factor. The advantage of the RBF-ANN is that it does not require </span><i><span style="font-family:Verdana;">a</span></i> <i><span style="font-family:Verdana;">priori</span></i><span style="font-family:Verdana;"> drive cycle knowledge and is able to be implemented in real-time while meeting or exceeding the performance of the optimal ECMS. Recommendations are made on how the RBF-ANN could be improved to produce better results across a greater array of driving conditions.</span></span>
基金supported in part by the National Key Research and Development Program of China(No.2021YFB2400900)the Integration Projects of National Natural Science Foundation of China-State Grid Joint Fund for Smart Grid(No.U2166602)+1 种基金the National Natural Science Foundation of China(No.52207200)the Science and Technology Innovation Program of Hunan Province(No.2024RC3113).
文摘The introduction of fully controlled devices to build hybrid line commutated converter(H-LCC)has become a new idea to solve the commutation failure.However,existing H-LCC has not considered the implementation of a targeted firing angle control strategy during AC faults,with the objective of enhancing their power transmission and fault response performance.For this reason,this paper proposes an optimized control method for firing angle of H-LCC,designated as flexible virtual firing(FVF).This method first analyzes the influence of alterations in firing angle on reactive power,commutation process and associated action paths.By combining prediction and dynamic search,it optimizes the natural commutation process through the utilization of dynamic boundary and minimum commutation area difference.This can mitigate the impact of AC faults on H-LCC and DC system,thereby improving power transmission and defense to commutation failure,which is beneficial for improving the stability of AC/DC power grids.Finally,the simulation results in PSCAD/EMTDC verify the effectiveness of the proposed method.
基金supported by China Postdoctoral Science Foundation(Project ID:2024M762602)the National Natural Science Foundation of China under Grant No.62306232Natural Science Basic Research Program of Shaanxi Province under Grant No.2023-JC-QN-0662.
文摘This paper presents an optimized shared control algorithm for human–AI interaction, implemented through a digital twin framework where the physical system and human operator act as the real agent while an AI-driven digital system functions as the virtual agent. In this digital twin architecture, the real agent acquires an optimal control strategy through observed actions, while the AI virtual agent mirrors the real agent to establish a digital replica system and corresponding control policy. Both the real and virtual optimal controllers are approximated using reinforcement learning(RL) techniques. Specifically, critic neural networks(NNs) are employed to learn the virtual and real optimal value functions, while actor NNs are trained to derive their respective optimal controllers. A novel shared mechanism is introduced to integrate both virtual and real value functions into a unified learning framework, yielding an optimal shared controller. This controller adaptively adjusts the confidence ratio between virtual and real agents, enhancing the system's efficiency and flexibility in handling complex control tasks. The stability of the closed-loop system is rigorously analyzed using the Lyapunov method. The effectiveness of the proposed AI–human interactive system is validated through two numerical examples: a representative nonlinear system and an unmanned aerial vehicle(UAV) control system.
基金supported in part by the National Natural Science Foundation of China(62173255,62188101)Shenzhen Key Laboratory of Control Theory and Intelligent Systems(ZDSYS20220330161800001)
文摘Dear Editor,In this letter,a constrained networked predictive control strategy is proposed for the optimal control problem of complex nonlinear highorder fully actuated(HOFA)systems with noises.The method can effectively deal with nonlinearities,constraints,and noises in the system,optimize the performance metric,and present an upper bound on the stable output of the system.
基金supported by the National Natural Science Foundation of China(Nos.42005086,91844301,and 41805100)the National Key Research and Development Programof China(No.2022YFC3703500)+2 种基金China Postdoctoral Science Foundation(No.2023M733028)the Key Research and Development Program of Zhejiang Province(Nos.2021C03165 and 2022C03084)the Ecological and Environmental Scientific Research and Achievement Promotion Project of Zhejiang Province(No.2020HT0048).
文摘Assessing the impact of anthropogenic volatile organic compounds(VOCs)on ozone(O_(3))formation is vital for themanagement of emission reduction and pollution control.Continuousmeasurement of O_(3)and the major precursorswas conducted in a typical light industrial city in the YRD region from 1 May to 25 July in 2021.Alkanes were the most abundant VOC group,contributing to 55.0%of TVOCs concentration(56.43±21.10 ppb).OVOCs,aromatics,halides,alkenes,and alkynes contributed 18.7%,9.6%,9.3%,5.2%and 1.9%,respectively.The observational site shifted from a typical VOC control regime to a mixed regime from May to July,which can be explained by the significant increase of RO_(x)production,resulting in the transition of environment from NOx saturation to radical saturation with respect to O_(3)production.The optimal O_(3)control strategy should be dynamically changed depending on the transition of control regime.Under NOx saturation condition,minimizing the proportion of NOx in reduction could lead to better achievement of O_(3)alleviation.Under mixed control regime,the cut percentage gets the top priority for the effectiveness of O_(3)control.Five VOCs sources were identified:temperature dependent source(28.1%),vehicular exhausts(19.9%),petrochemical industries(7.2%),solvent&gasoline usage(32.3%)and manufacturing industries(12.6%).The increase of temperature and radiation would enhance the evaporation related VOC emissions,resulting in the increase of VOC concentration and the change of RO_(x)circulation.Our results highlight determination of the optimal control strategies for O_(3)pollution in a typical YRD industrial city.
基金supported by the National Natural Science Foundation of China(Grant Nos.12441502,12122506,12204230,and 12404554)the National Science and Technology Major Project of the Ministry of Science and Technology of China(2024ZD0300404)+6 种基金Guangdong Basic and Applied Basic Research Foundation(Grant No.2021B1515020070)Shenzhen Science and Technology Program(Grant No.RCYX20200714114522109)China Postdoctoral Science Foundation(CPSF)(2024M762114)Postdoctoral Fellowship Program of CPSF(GZC20231727)supported by the National Natural Science Foundation of China(Grant Nos.92165206 and 11974330)Innovation Program for Quantum Science and Technology(Grant No.2021ZD0301603)the Fundamental Research Funds for the Central Universities。
文摘We present a robust quantum optimal control framework for implementing fast entangling gates on ion-trap quantum processors.The framework leverages tailored laser pulses to drive the multiple vibrational sidebands of the ions to create phonon-mediated entangling gates and,unlike the state of the art,requires neither weakcoupling Lamb-Dicke approximation nor perturbation treatment.With the application of gradient-based optimal control,it enables finding amplitude-and phase-modulated laser control protocols that work without the Lamb-Dicke approximation,promising gate speeds on the order of microseconds comparable to the characteristic trap frequencies.Also,robustness requirements on the temperature of the ions and initial optical phase can be conveniently included to pursue high-quality fast gates against experimental imperfections.Our approach represents a step in speeding up quantum gates to achieve larger quantum circuits for quantum computation and simulation,and thus can find applications in near-future experiments.
基金co-supported by the National Natural Science Foundation of China(No.62003019)the Young Talents Support Program of Beihang University,China(No.YWF21-BJ-J-1180)。
文摘This paper addresses the Singular Optimal Control Problem(SOCP)for a surface-to-air missile with limited control,fully considering aerodynamic effects with a parabolic drag polar.This problem is an extension of the typical Goddard problem.First,the classical Legendre-Clebsch condition is applied to derive optimal conditions for the singular angle of attack,revealing that the missile turns by gravity along the singular arc.Second,the higher-order differentiation of the switching function provides the necessary conditions to determine the optimal thrust,expressed as linear functions of the costate variables.The vanishing coefficient determinant is then employed to decouple the control and costate variables,yielding the singular thrust solely dependent on state variables and identifying the singular surface.Moreover,the analytical singular control can be regarded as path constraints subject to the typical Optimal Control Problem(OCP),enabling the GPOPS-Ⅱ,a direct method framework that does not involve the singular condition,to solve the SOCP.Finally,three cases with different structures are presented to evaluate the performance of the proposed method.The results show that it takes a few steps to obtain the numerical optimal solution,which is consistent with the analytical solution derived from the calculus of variations,highlighting its great computational accuracy and effectiveness.
文摘The electromagnetic levitation system(EMLS)serves as the most important part of any magnetic levitation system.However,its characteristics are defined by its highly nonlinear dynamics and instability.Furthermore,the uncertainties in the dynamics of an electromagnetic levitation system make the controller design more difficult.Therefore,it is necessary to design a robust control law that will ensure the system’s stability in the presence of these uncertainties.In this framework,the dynamics of an electromagnetic levitation system are addressed in terms of matched and unmatched uncertainties.The robust control problem is translated into the optimal control problem,where the uncertainties of the electromagnetic levitation system are directly reflected in the cost function.The optimal control method is used to solve the robust control problem.The solution to the optimal control problem for the electromagnetic levitation system is indeed a solution to the robust control problem of the electromagnetic levitation system under matched and unmatched uncertainties.The simulation and experimental results demonstrate the performance of the designed control scheme.The performance indices such as integral absolute error(IAE),integral square error(ISE),integral time absolute error(ITAE),and integral time square error(ITSE)are compared for both uncertainties to showcase the robustness of the designed control scheme.
基金supported by NASA Oklahoma Established Program to Stimulate Competitive Research(EPSCoR)Infrastructure Development,“Machine Learning Ocean World Biosignature Detection from Mass Spec”(PI:BrettMcKinney),Grant No.80NSSC24M0109Tandy School of Computer Science,University of Tulsa.
文摘The co-infection of corona and influenza viruses has emerged as a significant threat to global public health due to their shared modes of transmission and overlapping clinical symptoms.This article presents a novel mathematical model that addresses the dynamics of this co-infection by extending the SEIR(Susceptible-Exposed-Infectious-Recovered)framework to incorporate treatment and hospitalization compartments.The population is divided into eight compartments,with infectious individuals further categorized into influenza infectious,corona infectious,and co-infection cases.The proposed mathematical model is constrained to adhere to fundamental epidemiological properties,such as non-negativity and boundedness within a feasible region.Additionally,the model is demonstrated to be well-posed with a unique solution.Equilibrium points,including the disease-free and endemic equilibria,are identified,and various properties related to these equilibrium points,such as the basic reproduction number,are determined.Local and global sensitivity analyses are performed to identify the parameters that highly influence disease dynamics and the reproduction number.Knowing the most influential parameters is crucial for understanding their impact on the co-infection’s spread and severity.Furthermore,an optimal control problem is defined to minimize disease transmission and to control strategy costs.The purpose of our study is to identify the most effective(optimal)control strategies for mitigating the spread of the co-infection with minimum cost of the controls.The results illustrate the effectiveness of the implemented control strategies in managing the co-infection’s impact on the population’s health.This mathematical modeling and control strategy framework provides valuable tools for understanding and combating the dual threat of corona and influenza co-infection,helping public health authorities and policymakers make informed decisions in the face of these intertwined epidemics.
基金supported in part by the Thai Nguyen University of Technology,Vietnam.
文摘This article presents an adaptive optimal control method for a semi-active suspension system.The model of the suspension system is built,in which the components of uncertain parameters and exogenous disturbance are described.The adaptive optimal control law consists of the sum of the optimal control component and the adaptive control component.First,the optimal control law is designed for the model of the suspension system after ignoring the components of uncertain parameters and exogenous disturbance caused by the road surface.The optimal control law expresses the desired dynamic characteristics of the suspension system.Next,the adaptive component is designed with the purpose of compensating for the effects caused by uncertain parameters and exogenous disturbance caused by the road surface;the adaptive component has adaptive parameter rules to estimate uncertain parameters and exogenous disturbance.When exogenous disturbances are eliminated,the system responds with an optimal controller designed.By separating theoretically the dynamic of a semi-active suspension system,this solution allows the design of two separate controllers easily and has reduced the computational burden and the use of too many tools,thus allowing for more convenient hardware implementation.The simulation results also show the effectiveness of damping oscillations of the proposed solution in this article.
基金supported by the Deanship of Scientific Research,Vice Presidency for Graduate Studies and Scientific Research,King Faisal University,Saudi Arabia[Grant No.KFU252959].
文摘Malaria is a significant global health challenge.This devastating disease continues to affect millions,especially in tropical regions.It is caused by Plasmodium parasites transmitted by female Anopheles mosquitoes.This study introduces a nonlinear mathematical model for examining the transmission dynamics of malaria,incorporating both human and mosquito populations.We aim to identify the key factors driving the endemic spread of malaria,determine feasible solutions,and provide insights that lead to the development of effective prevention and management strategies.We derive the basic reproductive number employing the next-generation matrix approach and identify the disease-free and endemic equilibrium points.Stability analyses indicate that the disease-free equilibrium is locally and globally stable when the reproductive number is below one,whereas an endemic equilibrium persists when this threshold is exceeded.Sensitivity analysis identifies the most influential mosquito-related parameters,particularly the bite rate and mosquito mortality,in controlling the spread of malaria.Furthermore,we extend our model to include a treatment compartment and three disease-preventive control variables such as antimalaria drug treatments,use of larvicides,and the use of insecticide-treated mosquito nets for optimal control analysis.The results show that optimal use of mosquito nets,use of larvicides for mosquito population control,and treatment can lower the basic reproduction number and control malaria transmission with minimal intervention costs.The analysis of disease control strategies and findings offers valuable information for policymakers in designing cost-effective strategies to combat malaria.
基金supported by the DEEPCOBOT project under Grant 306640/O70 funded by the Research Council of Norway.
文摘This paper studies motor joint control of a 4-degree-of-freedom(DoF)robotic manipulator using learning-based Adaptive Dynamic Programming(ADP)approach.The manipulator’s dynamics are modelled as an open-loop 4-link serial kinematic chain with 4 Degrees of Freedom(DoF).Decentralised optimal controllers are designed for each link using ADP approach based on a set of cost matrices and data collected from exploration trajectories.The proposed control strategy employs an off-line,off-policy iterative approach to derive four optimal control policies,one for each joint,under exploration strategies.The objective of the controller is to control the position of each joint.Simulation and experimental results show that four independent optimal controllers are found,each under similar exploration strategies,and the proposed ADP approach successfully yields optimal linear control policies despite the presence of these complexities.The experimental results conducted on the Quanser Qarm robotic platform demonstrate the effectiveness of the proposed ADP controllers in handling significant dynamic nonlinearities,such as actuation limitations,output saturation,and filter delays.
基金National Key Research and Development Program of China,Grant/Award Number:2021YFC2801700Defense Industrial Technology Development Program,Grant/Award Numbers:JCKY2021110B024,JCKY2022110C072+6 种基金Science and Technology Innovation 2030-“New Generation Artificial Intelligence”Major Project,Grant/Award Number:2022ZD0116305Natural Science Foundation of Hefei,China,Grant/Award Number:202321National Natural Science Foundation of China,Grant/Award Numbers:U2013601,U20A20225Yangtze River Delta S&T Innovation Community Joint Research Project,Grant/Award Number:2022CSJGG0900Anhui Province Natural Science Funds for Distinguished Young Scholar,Grant/Award Number:2308085J02State Key Laboratory of Intelligent Green Vehicle and Mobility,Grant/Award Number:KFY2417State Key Laboratory of Advanced Design and Manufacturing Technology for Vehicle,Grant/Award Number:32215010。
文摘A mixed adaptive dynamic programming(ADP)scheme based on zero-sum game theory is developed to address optimal control problems of autonomous underwater vehicle(AUV)systems subject to disturbances and safe constraints.By combining prior dynamic knowledge and actual sampled data,the proposed approach effectively mitigates the defect caused by the inaccurate dynamic model and significantly improves the training speed of the ADP algorithm.Initially,the dataset is enriched with sufficient reference data collected based on a nominal model without considering modelling bias.Also,the control object interacts with the real environment and continuously gathers adequate sampled data in the dataset.To comprehensively leverage the advantages of model-based and model-free methods during training,an adaptive tuning factor is introduced based on the dataset that possesses model-referenced information and conforms to the distribution of the real-world environment,which balances the influence of model-based control law and data-driven policy gradient on the direction of policy improvement.As a result,the proposed approach accelerates the learning speed compared to data-driven methods,concurrently also enhancing the tracking performance in comparison to model-based control methods.Moreover,the optimal control problem under disturbances is formulated as a zero-sum game,and the actor-critic-disturbance framework is introduced to approximate the optimal control input,cost function,and disturbance policy,respectively.Furthermore,the convergence property of the proposed algorithm based on the value iteration method is analysed.Finally,an example of AUV path following based on the improved line-of-sight guidance is presented to demonstrate the effectiveness of the proposed method.
基金supported by the Fundamental Research Funds for the Central Universities(No.3122025090)。
文摘In this paper,based on the SVIQR model we develop a stochastic epidemic model with multiple vaccinations and time delay.Firstly,we prove the existence and uniqueness of the global positive solution of the model,and construct suitable functions to obtain sufficient conditions for disease extinction.Secondly,in order to effectively control the spread of the disease,appropriate control strategies are formulated by using optimal control theory.Finally,the results are verified by numerical simulation.
基金Defense Industrial Technology Development Program (JCKY2020204B016)National Natural Science Foundation of China (92471206)。
文摘To better complete various missions, it is necessary to plan an optimal trajectory or provide the optimal control law for the multirole missile according to the actual situation, including launch conditions and target location. Since trajectory optimization struggles to meet real-time requirements, the emergence of data-based generation methods has become a significant focus in contemporary research. However, due to the large differences in the characteristics of the optimal control laws caused by the diversity of tasks, it is difficult to achieve good prediction results by modeling all data with one single model.Therefore, the modeling idea of the mixture of experts(MoE) is adopted. Firstly, the K-means clustering algorithm is used to partition the sample data set, and the corresponding neural network classification model is established as the gate switch of MoE. Then, the expert models, i.e., the mappings from the generation conditions to the optimal control law represented by the results of principal component analysis(PCA), are represented by Kriging models. Finally, multiple rounds of accuracy evaluation, sample supplementation, and model updating are conducted to improve the generation accuracy. The Monte Carlo simulation shows that the accuracy of the proposed model reaches 96% and the generation efficiency meets the real-time requirement.
基金Project supported the Natural Science Foundation of Zhejiang Province, China (Grant No. LQN25F030011)the Fundamental Research Project of Hangzhou Dianzi University (Grant No. KYS065624391)+1 种基金the National Natural Science Foundation of China (Grant No. 61573148)the Science and Technology Planning Project of Guangdong Province, China (Grant No. 2019A050520001)。
文摘This paper investigates a new SEIQR(susceptible–exposed–infected–quarantined–recovered) epidemic model with quarantine mechanism on heterogeneous complex networks. Firstly, the nonlinear SEIQR epidemic spreading dynamic differential coupling model is proposed. Then, by using mean-field theory and the next-generation matrix method, the equilibriums and basic reproduction number are derived. Theoretical results indicate that the basic reproduction number significantly relies on model parameters and topology of the underlying networks. In addition, the globally asymptotic stability of equilibrium and the permanence of the disease are proved in detail by the Routh–Hurwitz criterion, Lyapunov method and La Salle's invariance principle. Furthermore, we find that the quarantine mechanism, that is the quarantine rate(γ1, γ2), has a significant effect on epidemic spreading through sensitivity analysis of basic reproduction number and model parameters. Meanwhile, the optimal control model of quarantined rate and analysis method are proposed, which can optimize the government control strategies and reduce the number of infected individual. Finally, numerical simulations are given to verify the correctness of theoretical results and a practice application is proposed to predict and control the spreading of COVID-19.
基金supported by the National Natural Science Foundation of China(No.62003019)the Young Talents Support Program of Beihang University,China(No.YWF-21-BJ-J-1180).
文摘This paper proposes an optimal midcourse guidance method for dual pulse air-to-air missiles,which is based on the framework of the linear Gauss pseudospectral model predictive control method.Firstly,a multistage optimal control problem with unspecified terminal time is formulated.Secondly,the control and terminal time update formulas are derived analytically.In contrast to previous work,the derivation process fully considers the Hamiltonian function corresponding to the unspecified terminal time,which is coupled with control,state,and costate.On the assumption of small perturbation,a special algebraic equation is provided to represent the equivalent optimal condition for the terminal time.Also,using Gauss pseudospectral collocation,error propagation dynamical equations involving the first-order correction term of the terminal time are transformed into a set of algebraic equations.Furthermore,analytical modification formulas can be derived by associating those equations and optimal conditions to eliminate terminal error and approach nonlinear optimal control.Even with their mathematical complexity,these formulas produce more accurate control and terminal time corrections and remove reliance on task-related parameters.Finally,several numerical simulations,comparisons with typical methods,and Monte Carlo simulations have been done to verify its optimality,high convergence rate,great stability and robustness.
文摘Spillover of trypanosomiasis parasites from wildlife to domestic livestock and humans remains a major challenge world over.With the disease targeted for elimination by 2030,assessing the impact of control strategies in communities where there are human-cattle-wildlife interactions is therefore essential.A compartmental framework incorporating tsetse flies,humans,cattle,wildlife and various disease control strategies is developed and analyzed.The reproduction is derived and its sensitivity to different model parameters is investigated.Meanwhile,the optimal control theory is used to identify a combination of control strategies capable of minimizing the infected human and cattle population over time at minimal costs of implementation.The results indicates that tsetse fly mortality rate is strongly and negatively correlated to the reproduction number.It is also established that tsetse fly feeding rate in strongly and positively correlated to the reproduction number.Simulation results indicates that time dependent control strategies can significantly reduce the infections.Overall,the study shows that screening and treatment of humans may not lead to disease elimination.Combining this strategy with other strategies such as screening and treatment of cattle and vector control strategies will result in maximum reduction of tsetse fly population and disease elimination.
基金Supported by the National Natural Science Foundation of China(Grant Nos.125610811246108612271147)。
文摘This paper aims to study the optimal control and algorithm implementation of a generalized epidemic model governed by reaction-diffusion equations.Considering individual mobility,this paper first proposes a reaction-diffusion epidemic model with two strains.Furthermore,applying vaccines as a control strategy in the model,an optimal control problem is proposed to increase the number of healthy individuals while reducing control costs.By applying the truncation function technique and the operator semigroup methods,we prove the existence and uniqueness of a globally positive strong solution for the control model.The existence of the optimal control strategy is proven by using functional analysis theory and minimum sequence methods.The first-order necessary condition satisfied by the optimal control is established by employing the dual techniques.Finally,a specific example and its algorithm are provided.
基金The National Natural Science Foundation of China(62173172).
文摘Inverse reinforcement learning optimal control is under the framework of learner-expert.The learner system can imitate the expert system's demonstrated behaviors and does not require the predefined cost function,so it can handle optimal control problems effectively.This paper proposes an inverse reinforcement learning optimal control method for Takagi-Sugeno(T-S)fuzzy systems.Based on learner systems,an expert system is constructed,where the learner system only knows the expert system's optimal control policy.To reconstruct the unknown cost function,we firstly develop a model-based inverse reinforcement learning algorithm for the case that systems dynamics are known.The developed model-based learning algorithm is consists of two learning stages:an inner reinforcement learning loop and an outer inverse optimal control loop.The inner loop desires to obtain optimal control policy via learner's cost function and the outer loop aims to update learner's state-penalty matrices via only using expert's optimal control policy.Then,to eliminate the requirement that the system dynamics must be known,a data-driven integral learning algorithm is presented.It is proved that the presented two algorithms are convergent and the developed inverse reinforcement learning optimal control scheme can ensure the controlled fuzzy learner systems to be asymptotically stable.Finally,we apply the proposed fuzzy optimal control to the truck-trailer system,and the computer simulation results verify the effectiveness of the presented approach.
