Dear Editor,This letter embarks on an examination of fixed-time stability(FxTS)for random nonlinear systems(RNSs)governed by random differential equations.This endeavor encompasses a multifaceted analysis of FxTS,comm...Dear Editor,This letter embarks on an examination of fixed-time stability(FxTS)for random nonlinear systems(RNSs)governed by random differential equations.This endeavor encompasses a multifaceted analysis of FxTS,commencing with its rigorous definition and its integration with Lyapunov theory,along which a consequential corollary emerges.Particularly,the positive definiteness of the expectation of settling time is established,and a less conservative upper bound is derived.The effectiveness of the proposed fixed-time theorem is verified by an example.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
In this work,a self-healing predictive control method for discrete-time nonlinear systems is presented to ensure the system can be safely operated under abnormal states.First,a robust MPC controller for the normal cas...In this work,a self-healing predictive control method for discrete-time nonlinear systems is presented to ensure the system can be safely operated under abnormal states.First,a robust MPC controller for the normal case is constructed,which can drive the system to the equilibrium point when the closed-loop states are in the predetermined safe set.In this controller,the tubes are built based on the incremental Lyapunov function to tighten nominal constraints.To deal with the infeasible controller when abnormal states occur,a self-healing predictive control method is further proposed to realize self-healing by driving the system towards the safe set.This is achieved by an auxiliary softconstrained recovery mechanism that can solve the constraint violation caused by the abnormal states.By extending the discrete-time robust control barrier function theory,it is proven that the auxiliary problem provides a predictive control barrier bounded function to make the system asymptotically stable towards the safe set.The theoretical properties of robust recursive feasibility and bounded stability are further analyzed.The efficiency of the proposed controller is verified by a numerical simulation of a continuous stirred-tank reactor process.展开更多
The exact feedback linearization method implies an accurate knowledge of the model and its parameters.This assumption is an inherent limitation of the method,suffering from robustness issues.In general,the model struc...The exact feedback linearization method implies an accurate knowledge of the model and its parameters.This assumption is an inherent limitation of the method,suffering from robustness issues.In general,the model structure is only partially known and its parameters present uncertainties.The current paper extends the classical exact feedback linearization to the robust feedback linearization by adding an appropriatelydesigned robust control layer.This is then able to ensure robust stability and robust performance for the given uncertain system in a desired region of attraction.We consider the case of full relative degree input-affine nonlinear systems,which are of great practical importance in the literature.The inner loop contains the feedback linearization input for the nominal system and the resulting residual nonlinearities can always be characterized as inverse additive uncertainties.The constructive proofs provide exact representations of the uncertainty models in three considered scenarios:unmatched,fully-matched,and partially-matched uncertainties.The uncertainty model will be a descriptor system,which also represents one of the novelties of the paper.Our approach leads to a simplified control structure and a less conservative coverage of the uncertainty set compared to current alternatives.The end-to-end procedure is emphasized on an illustrative example,in two different hypotheses.展开更多
The paper develops a robust control approach for nonaffine nonlinear continuous systems with input constraints and unknown uncertainties. Firstly, this paper constructs an affine augmented system(AAS) within a pre-com...The paper develops a robust control approach for nonaffine nonlinear continuous systems with input constraints and unknown uncertainties. Firstly, this paper constructs an affine augmented system(AAS) within a pre-compensation technique for converting the original nonaffine dynamics into affine dynamics. Secondly, the paper derives a stability criterion linking the original nonaffine system and the auxiliary system, demonstrating that the obtained optimal policies from the auxiliary system can achieve the robust controller of the nonaffine system. Thirdly, an online adaptive dynamic programming(ADP) algorithm is designed for approximating the optimal solution of the Hamilton–Jacobi–Bellman(HJB) equation.Moreover, the gradient descent approach and projection approach are employed for updating the actor-critic neural network(NN) weights, with the algorithm's convergence being proven. Then, the uniformly ultimately bounded stability of state is guaranteed. Finally, in simulation, some examples are offered for validating the effectiveness of this presented approach.展开更多
This article presents an adaptive fault-tolerant tracking control strategy for unknown affine nonlinear systems subject to actuator faults and external disturbances.To address the hyperparameter initialization challen...This article presents an adaptive fault-tolerant tracking control strategy for unknown affine nonlinear systems subject to actuator faults and external disturbances.To address the hyperparameter initialization challenges inherent in conventional neural network training,an improved self-organizing radial basis function neural network(SRBFNN)with an input-dependent variable structure is developed.Furthermore,a novel selforganizing RBFNN-based observer is introduced to estimate system states across all dimensions.Leveraging the reconstructed states,the proposed adaptive controller effectively compensates for all uncertainties,including estimation errors in the observer,ensuring accurate state tracking with reduced control effort.The uniform ultimate boundedness of all closed-loop signals and tracking errors is rigorously established via Lyapunov stability analysis.Finally,simulations on two different nonlinear systems comprehensively validate the effectiveness and superiority of the proposed control approach.展开更多
This paper addresses the tracking control problem of a class of multiple-input–multiple-output nonlinear systems subject to actuator faults.Achieving a balance between input saturation and performance constraints,rat...This paper addresses the tracking control problem of a class of multiple-input–multiple-output nonlinear systems subject to actuator faults.Achieving a balance between input saturation and performance constraints,rather than conducting isolated analyses,especially in the presence of frequently encountered unknown actuator faults,becomes an interesting yet challenging problem.First,to enhance the tracking performance,Tunnel Prescribed Performance(TPP)is proposed to provide narrow tunnel-shape constraints instead of the common over-relaxed trumpet-shape performance constraints.A pair of non-negative signals produced by an auxiliary system is then integrated into TPP,resulting in Saturation-tolerant Prescribed Performance(SPP)with flexible performance boundaries that account for input saturation situations.Namely,SPP can appropriately relax TPP when needed and decrease the conservatism of control design.With the help of SPP,our developed Saturation-tolerant Prescribed Control(SPC)guarantees finite-time convergence while satisfying both input saturation and performance constraints,even under serious actuator faults.Simulations are conducted to illustrate the effectiveness of the proposed SPC.展开更多
This paper considers adaptive event-triggered stabilization for a class of uncertain time-varying nonlinear systems.Remarkably,the systems contain intrinsic time-varying unknown parameters which are allowed to be non-...This paper considers adaptive event-triggered stabilization for a class of uncertain time-varying nonlinear systems.Remarkably,the systems contain intrinsic time-varying unknown parameters which are allowed to be non-differentiable and in turn can be fast-varying.Moreover,the systems admit unknown control directions.To counteract the different uncertainties,more than one compensation mechanism has to be incorporated.However,in the context of event-triggered control,ensuring the effectiveness of these compensation mechanisms under reduced execution necessitates delicate design and analysis.This paper proposes a tight and powerful strategy for adaptive event-triggered control(ETC)by integrating the state-of-the-art adaptive techniques.In particular,the strategy substantially mitigates the conservatism caused by repetitive inequality-based treatments of uncertainties.Specifically,by leveraging the congelation-of-variables method and tuning functions,the conservatism in the treatment of the fast-varying parameters is significantly reduced.With multiple Nussbaum functions employed to handle unknown control directions,a set of dynamic compensations is designed to counteract unknown amplitudes of control coefficients without relying on inequality-based treatments.Moreover,a dedicated dynamic compensation is introduced to deal with the control coefficient coupled with the execution error,based on which a relativethreshold event-triggering mechanism(ETM)is rigorously validated.It turns out that the adaptive event-triggered controller achieves the closed-loop convergence while guaranteeing a uniform lower bound for inter-execution times.Simulation results verify the effectiveness and superiority of the proposed strategy.展开更多
This paper investigates the problem of dynamic event-triggered control for a class of large-scale nonlinear systems.In particular,both neutral delays and unknown backlash-like hysteresis are considered.This requires t...This paper investigates the problem of dynamic event-triggered control for a class of large-scale nonlinear systems.In particular,both neutral delays and unknown backlash-like hysteresis are considered.This requires to integrate a compensation mechanism into the event-triggered control architecture.To this end,dynamic gain and adaptive control techniques are introduced to address the effects of neutral delays,unknown hysteresis and parameter uncertainties simultaneously.By introducing a non-negative internal dynamic variable,a dynamic event-triggered controller is designed using the hyperbolic tangent function to reduce the communication burden.By means of the Lyapunov–Krasovskii method,it is demonstrated that all signals of the closed-loop system are globally bounded and eventually converge to a tunable bounded region.Moreover,the Zeno behavior is avoided.Finally,a simulation example is presented to verify the validity of the control scheme.展开更多
In this paper, a fault-tolerant-based online critic learning algorithm is developed to solve the optimal tracking control issue for nonaffine nonlinear systems with actuator faults.First, a novel augmented plant is co...In this paper, a fault-tolerant-based online critic learning algorithm is developed to solve the optimal tracking control issue for nonaffine nonlinear systems with actuator faults.First, a novel augmented plant is constructed by fusing the system state and the reference trajectory, which aims to transform the optimal fault-tolerant tracking control design with actuator faults into the optimal regulation problem of the conventional nonlinear error system. Subsequently, in order to ensure the normal execution of the online learning algorithm, a stability criterion condition is created to obtain an initial admissible tracking policy. Then, the constructed model neural network(NN) is pretrained to recognize the system dynamics and calculate trajectory control. The critic and action NNs are constructed to output the approximate cost function and approximate tracking control,respectively. The Hamilton-Jacobi-Bellman equation of the error system is solved online through the action-critic framework. In theoretical analysis, it is proved that all concerned signals are uniformly ultimately bounded according to the Lyapunov principle.The tracking control law can approach the optimal tracking control within a finite approximation error. Finally, two experimental examples are conducted to indicate the effectiveness and superiority of the developed fault-tolerant tracking control scheme.展开更多
Dear Editor,This letter investigates global stabilization of uncertain nonlinear systems via adaptive event-triggered output feedback.Uncertainties lie in both system nonlinearities and measurement sensitivity.To this...Dear Editor,This letter investigates global stabilization of uncertain nonlinear systems via adaptive event-triggered output feedback.Uncertainties lie in both system nonlinearities and measurement sensitivity.To this end,a dynamic high gain is introduced to cope with the influence of large uncertainties,the unknown measurement sensitivity and the execution error,while a time-varying threshold event-triggering mechanism is constructed to effectively exclude the Zeno phenomenon.As such,the adaptive event-triggered control ensures globally bounded and convergent of system states.The design method is demonstrated using a controlled pendulum example.展开更多
In this paper,a new technique is introduced to construct higher-order iterative methods for solving nonlinear systems.The order of convergence of some iterative methods can be improved by three at the cost of introduc...In this paper,a new technique is introduced to construct higher-order iterative methods for solving nonlinear systems.The order of convergence of some iterative methods can be improved by three at the cost of introducing only one additional evaluation of the function in each step.Furthermore,some new efficient methods with a higher-order of convergence are obtained by using only a single matrix inversion in each iteration.Analyses of convergence properties and computational efficiency of these new methods are made and testified by several numerical problems.By comparison,the new schemes are more efficient than the corresponding existing ones,particularly for large problem sizes.展开更多
In order to achieve higher accuracy in nonlinear/non-Gaussian state estimation, this paper proposes a new unscented Kalman filter (UKF). It uses a deterministic sampling approach. We choose the unscented transformatio...In order to achieve higher accuracy in nonlinear/non-Gaussian state estimation, this paper proposes a new unscented Kalman filter (UKF). It uses a deterministic sampling approach. We choose the unscented transformation (UT) scaling parameters α=0.85, β=2, l=0 to construct 2n + 1 sigma points. These sigma points completely capture the mean and covariance of the Gaussian random variables of the nonlinear system Yi=F(Xi). Simulation results show that the posterior mean and covariance of the sigma points can achieve the accuracy of the third-order Taylor series expansion after having propagated through the true nonlinear system Yi=F(Xi). Extended Kalman filter (EKF) only can achieve the first-order accuracy. The computational complexity of UKF is the same level as that of EKF. UKF can yield better performance and higher accuracy than EKF.展开更多
Driven by practical applications, the achievement of distributed observers for nonlinear systems has emerged as a crucial advancement in recent years. However, existing theoretical advancements face certain limitation...Driven by practical applications, the achievement of distributed observers for nonlinear systems has emerged as a crucial advancement in recent years. However, existing theoretical advancements face certain limitations: They either fail to address more complex nonlinear phenomena, rely on hard-to-verify assumptions, or encounter difficulties in solving system parameters.Consequently, this paper aims to address these challenges by investigating distributed observers for nonlinear systems through the full-measured canonical form(FMCF), which is inspired by full-measured system(FMS) theory. To begin with, this study addresses the fact that the FMCF can only be obtained through the observable canonical form(OCF) in existing FMS theories.The paper demonstrates that a class of nonlinear systems can directly obtain FMCF through state space equations, independent of OCF. Also, a general method for solving FMCF in such systems is provided. Furthermore, based on the FMCF, A distributed observer is developed for nonlinear systems under two scenarios: Lipschitz conditions and open-loop bounded conditions.The paper establishes their asymptotic omniscience and demonstrates that the designed distributed observer in this study has fewer design parameters and is more convenient to construct than existing approaches. Finally, the effectiveness of the proposed methods is validated through simulation results on Van der Pol oscillators and microgrid systems.展开更多
This paper is concerned with the problem of global output feedback stabilization in probability for a class of switched stochastic nonlinear systems under arbitrary switchings. The subsystems are assumed to be in outp...This paper is concerned with the problem of global output feedback stabilization in probability for a class of switched stochastic nonlinear systems under arbitrary switchings. The subsystems are assumed to be in output feedback form and driven by white noise. By introducing a common Lyapunov function, the common output feedback controller independent of switching signals is constructed based on the backstepping approach. It is proved that the zero solution of the closed-loop system is fourth-moment exponentially stable. An example is given to show the effectiveness of the proposed method.展开更多
In this paper, two types of mathematical models are developed to describe the dynamics of large-scale nonlinear systems, which are composed of several interconnected nonlinear subsystems. Each subsystem can be describ...In this paper, two types of mathematical models are developed to describe the dynamics of large-scale nonlinear systems, which are composed of several interconnected nonlinear subsystems. Each subsystem can be described by an input-output nonlinear discrete-time mathematical model, with unknown, but constant or slowly time-varying parameters. Then, two recursive estimation methods are used to solve the parametric estimation problem for the considered class of the interconnected nonlinear systems. These methods are based on the recursive least squares techniques and the prediction error method. Convergence analysis is provided using the hyper-stability and positivity method and the differential equation approach. A numerical simulation example of the parametric estimation of a stochastic interconnected nonlinear hydraulic system is treated.展开更多
A class of triangular non li near system with disturbances which has unknown multiplicative time varying par ametric uncertainties in each virtual control is treated by a backstepping techn ique. The controller desig...A class of triangular non li near system with disturbances which has unknown multiplicative time varying par ametric uncertainties in each virtual control is treated by a backstepping techn ique. The controller designed for all admissible uncertainties can guarantee tha t all states of its closed loop system are uniformly bounded. The robust contro ller design algorithm and a sufficient condition of the system stability are giv en. In addition, the closed loop system has an ISS property when the multiplica tive time varying parametric uncertainties are viewed as inputs to the system. Thus, this design provides a way to prevent a destabilizing effect of the multip licative time varying parametric uncertainties. Finally, simulational example i s given and simulational result shows that the controller exhibits effectiveness and excellent robustness.展开更多
A new type of nonlinear observer for nonlinear systems is presented. Instead of approximating thc cntire nonlinear system with the neural network （NN）, only the un-modeled part left over after the lincarization is a...A new type of nonlinear observer for nonlinear systems is presented. Instead of approximating thc cntire nonlinear system with the neural network （NN）, only the un-modeled part left over after the lincarization is approximated. Compared with the conventional linear observer, the observer provides more accurate estimation of the state. The state estimation error is proved to asymptotically approach zero with the Lyapunov method. The simulation result shows that the proposed observer scheme is effective and has a potential application ability in the fault detection and identification （FDI）, and the state estimation.展开更多
The variable selection of high dimensional nonparametric nonlinear systems aims to select the contributing variables or to eliminate the redundant variables.For a high dimensional nonparametric nonlinear system,howeve...The variable selection of high dimensional nonparametric nonlinear systems aims to select the contributing variables or to eliminate the redundant variables.For a high dimensional nonparametric nonlinear system,however,identifying whether a variable contributes or not is not easy.Therefore,based on the Fourier spectrum of densityweighted derivative,one novel variable selection approach is developed,which does not suffer from the dimensionality curse and improves the identification accuracy.Furthermore,a necessary and sufficient condition for testing a variable whether it contributes or not is provided.The proposed approach does not require strong assumptions on the distribution,such as elliptical distribution.The simulation study verifies the effectiveness of the novel variable selection algorithm.展开更多
An adaptive robust attitude tracking control law based on switched nonlinear systems is presented for a variable structure near space vehicle （VSNSV） in the presence of uncertainties and disturbances. The adaptive f...An adaptive robust attitude tracking control law based on switched nonlinear systems is presented for a variable structure near space vehicle （VSNSV） in the presence of uncertainties and disturbances. The adaptive fuzzy systems are employed for approximating unknown functions in the flight dynamic model and their parameters are updated online. To improve the flight robust performance, robust controllers with adaptive gains are designed to compensate for the approximation errors and thus they have less design conservation. Moreover, a systematic procedure is developed for the synthesis of adaptive fuzzy dynamic surface control （DSC） approach. According to the common Lyapunov function theory, it is proved that all signals of the closed-loop system are uniformly ultimately bounded by the continuous controller. The simulation results demonstrate the effectiveness and robustness of the proposed control scheme.展开更多
基金supported by the National Natural Science Foundation of China(62103203).
文摘Dear Editor,This letter embarks on an examination of fixed-time stability(FxTS)for random nonlinear systems(RNSs)governed by random differential equations.This endeavor encompasses a multifaceted analysis of FxTS,commencing with its rigorous definition and its integration with Lyapunov theory,along which a consequential corollary emerges.Particularly,the positive definiteness of the expectation of settling time is established,and a less conservative upper bound is derived.The effectiveness of the proposed fixed-time theorem is verified by an example.
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 in part the National Key Research and Development Program of China(2021YFC2902703)Open Foundation of State Key Laboratory of Process Automation in Mining&Metallurgy/Beijing Key Laboratory of Process Automation in Mining&Metallurgy(BGRIMM-KZSKL-2022-6)the National Natural Science Foundation of China(62173078,61873049).
文摘In this work,a self-healing predictive control method for discrete-time nonlinear systems is presented to ensure the system can be safely operated under abnormal states.First,a robust MPC controller for the normal case is constructed,which can drive the system to the equilibrium point when the closed-loop states are in the predetermined safe set.In this controller,the tubes are built based on the incremental Lyapunov function to tighten nominal constraints.To deal with the infeasible controller when abnormal states occur,a self-healing predictive control method is further proposed to realize self-healing by driving the system towards the safe set.This is achieved by an auxiliary softconstrained recovery mechanism that can solve the constraint violation caused by the abnormal states.By extending the discrete-time robust control barrier function theory,it is proven that the auxiliary problem provides a predictive control barrier bounded function to make the system asymptotically stable towards the safe set.The theoretical properties of robust recursive feasibility and bounded stability are further analyzed.The efficiency of the proposed controller is verified by a numerical simulation of a continuous stirred-tank reactor process.
基金funded by the project new smart and adaptive robotics solutions for personalized minimally invasive surgery in cancer treatment−ATHENA,European Union-NextGenerationEU and Romanian Government,under National Recovery and Resilience Plan for Romania(CF116/15.11.2022)through the Romanian Ministry of Research,Innovation and Digitalization(within Component 9,investment I8)。
文摘The exact feedback linearization method implies an accurate knowledge of the model and its parameters.This assumption is an inherent limitation of the method,suffering from robustness issues.In general,the model structure is only partially known and its parameters present uncertainties.The current paper extends the classical exact feedback linearization to the robust feedback linearization by adding an appropriatelydesigned robust control layer.This is then able to ensure robust stability and robust performance for the given uncertain system in a desired region of attraction.We consider the case of full relative degree input-affine nonlinear systems,which are of great practical importance in the literature.The inner loop contains the feedback linearization input for the nominal system and the resulting residual nonlinearities can always be characterized as inverse additive uncertainties.The constructive proofs provide exact representations of the uncertainty models in three considered scenarios:unmatched,fully-matched,and partially-matched uncertainties.The uncertainty model will be a descriptor system,which also represents one of the novelties of the paper.Our approach leads to a simplified control structure and a less conservative coverage of the uncertainty set compared to current alternatives.The end-to-end procedure is emphasized on an illustrative example,in two different hypotheses.
基金Project supported by the National Natural Science Foundation of China (Grant No. 62103408)Beijing Nova Program (Grant No. 20240484516)the Fundamental Research Funds for the Central Universities (Grant No. KG16314701)。
文摘The paper develops a robust control approach for nonaffine nonlinear continuous systems with input constraints and unknown uncertainties. Firstly, this paper constructs an affine augmented system(AAS) within a pre-compensation technique for converting the original nonaffine dynamics into affine dynamics. Secondly, the paper derives a stability criterion linking the original nonaffine system and the auxiliary system, demonstrating that the obtained optimal policies from the auxiliary system can achieve the robust controller of the nonaffine system. Thirdly, an online adaptive dynamic programming(ADP) algorithm is designed for approximating the optimal solution of the Hamilton–Jacobi–Bellman(HJB) equation.Moreover, the gradient descent approach and projection approach are employed for updating the actor-critic neural network(NN) weights, with the algorithm's convergence being proven. Then, the uniformly ultimately bounded stability of state is guaranteed. Finally, in simulation, some examples are offered for validating the effectiveness of this presented approach.
基金supported in part by the National Natural Science Foundation of China(62033008,62188101,62173343,62073339)the Natural Science Foundation of Shandong Province of China(ZR2024MF072,ZR2022ZD34)the Research Fund for the Taishan Scholar Project of Shandong Province of China.
文摘This article presents an adaptive fault-tolerant tracking control strategy for unknown affine nonlinear systems subject to actuator faults and external disturbances.To address the hyperparameter initialization challenges inherent in conventional neural network training,an improved self-organizing radial basis function neural network(SRBFNN)with an input-dependent variable structure is developed.Furthermore,a novel selforganizing RBFNN-based observer is introduced to estimate system states across all dimensions.Leveraging the reconstructed states,the proposed adaptive controller effectively compensates for all uncertainties,including estimation errors in the observer,ensuring accurate state tracking with reduced control effort.The uniform ultimate boundedness of all closed-loop signals and tracking errors is rigorously established via Lyapunov stability analysis.Finally,simulations on two different nonlinear systems comprehensively validate the effectiveness and superiority of the proposed control approach.
基金supported by the National Research Foundation Singapore under its AI Singapore Programme(Award Number:[AISG2-GC-2023-007]).
文摘This paper addresses the tracking control problem of a class of multiple-input–multiple-output nonlinear systems subject to actuator faults.Achieving a balance between input saturation and performance constraints,rather than conducting isolated analyses,especially in the presence of frequently encountered unknown actuator faults,becomes an interesting yet challenging problem.First,to enhance the tracking performance,Tunnel Prescribed Performance(TPP)is proposed to provide narrow tunnel-shape constraints instead of the common over-relaxed trumpet-shape performance constraints.A pair of non-negative signals produced by an auxiliary system is then integrated into TPP,resulting in Saturation-tolerant Prescribed Performance(SPP)with flexible performance boundaries that account for input saturation situations.Namely,SPP can appropriately relax TPP when needed and decrease the conservatism of control design.With the help of SPP,our developed Saturation-tolerant Prescribed Control(SPC)guarantees finite-time convergence while satisfying both input saturation and performance constraints,even under serious actuator faults.Simulations are conducted to illustrate the effectiveness of the proposed SPC.
基金supported in part by the National Natural Science Foundation of China(62033007)the Fundamental Research Program of Shandong Province(ZR2023ZD37).
文摘This paper considers adaptive event-triggered stabilization for a class of uncertain time-varying nonlinear systems.Remarkably,the systems contain intrinsic time-varying unknown parameters which are allowed to be non-differentiable and in turn can be fast-varying.Moreover,the systems admit unknown control directions.To counteract the different uncertainties,more than one compensation mechanism has to be incorporated.However,in the context of event-triggered control,ensuring the effectiveness of these compensation mechanisms under reduced execution necessitates delicate design and analysis.This paper proposes a tight and powerful strategy for adaptive event-triggered control(ETC)by integrating the state-of-the-art adaptive techniques.In particular,the strategy substantially mitigates the conservatism caused by repetitive inequality-based treatments of uncertainties.Specifically,by leveraging the congelation-of-variables method and tuning functions,the conservatism in the treatment of the fast-varying parameters is significantly reduced.With multiple Nussbaum functions employed to handle unknown control directions,a set of dynamic compensations is designed to counteract unknown amplitudes of control coefficients without relying on inequality-based treatments.Moreover,a dedicated dynamic compensation is introduced to deal with the control coefficient coupled with the execution error,based on which a relativethreshold event-triggering mechanism(ETM)is rigorously validated.It turns out that the adaptive event-triggered controller achieves the closed-loop convergence while guaranteeing a uniform lower bound for inter-execution times.Simulation results verify the effectiveness and superiority of the proposed strategy.
基金supported by the National Natural Science Foundation of China under Grant 62073190the Science Center Program of National Natural Science Foundation of China under Grant 62188101.
文摘This paper investigates the problem of dynamic event-triggered control for a class of large-scale nonlinear systems.In particular,both neutral delays and unknown backlash-like hysteresis are considered.This requires to integrate a compensation mechanism into the event-triggered control architecture.To this end,dynamic gain and adaptive control techniques are introduced to address the effects of neutral delays,unknown hysteresis and parameter uncertainties simultaneously.By introducing a non-negative internal dynamic variable,a dynamic event-triggered controller is designed using the hyperbolic tangent function to reduce the communication burden.By means of the Lyapunov–Krasovskii method,it is demonstrated that all signals of the closed-loop system are globally bounded and eventually converge to a tunable bounded region.Moreover,the Zeno behavior is avoided.Finally,a simulation example is presented to verify the validity of the control scheme.
基金supported in part by the National Natural Science Foundation of China(62222301,62373012,62473012,62021003)the National Science and Technology Major Project(2021ZD0112302,2021ZD0112301)the Beijing Natural Science Foundation(JQ19013)
文摘In this paper, a fault-tolerant-based online critic learning algorithm is developed to solve the optimal tracking control issue for nonaffine nonlinear systems with actuator faults.First, a novel augmented plant is constructed by fusing the system state and the reference trajectory, which aims to transform the optimal fault-tolerant tracking control design with actuator faults into the optimal regulation problem of the conventional nonlinear error system. Subsequently, in order to ensure the normal execution of the online learning algorithm, a stability criterion condition is created to obtain an initial admissible tracking policy. Then, the constructed model neural network(NN) is pretrained to recognize the system dynamics and calculate trajectory control. The critic and action NNs are constructed to output the approximate cost function and approximate tracking control,respectively. The Hamilton-Jacobi-Bellman equation of the error system is solved online through the action-critic framework. In theoretical analysis, it is proved that all concerned signals are uniformly ultimately bounded according to the Lyapunov principle.The tracking control law can approach the optimal tracking control within a finite approximation error. Finally, two experimental examples are conducted to indicate the effectiveness and superiority of the developed fault-tolerant tracking control scheme.
基金supported by the National Natural Science Foundation of China(62203283)Shandong Provincial Natural Science Foundation(ZR2022QF009,ZR2023QA063)the China Postdoctoral Science Foundation(2022M711981).
文摘Dear Editor,This letter investigates global stabilization of uncertain nonlinear systems via adaptive event-triggered output feedback.Uncertainties lie in both system nonlinearities and measurement sensitivity.To this end,a dynamic high gain is introduced to cope with the influence of large uncertainties,the unknown measurement sensitivity and the execution error,while a time-varying threshold event-triggering mechanism is constructed to effectively exclude the Zeno phenomenon.As such,the adaptive event-triggered control ensures globally bounded and convergent of system states.The design method is demonstrated using a controlled pendulum example.
基金Supported by the National Natural Science Foundation of China(12061048)NSF of Jiangxi Province(20232BAB201026,20232BAB201018)。
文摘In this paper,a new technique is introduced to construct higher-order iterative methods for solving nonlinear systems.The order of convergence of some iterative methods can be improved by three at the cost of introducing only one additional evaluation of the function in each step.Furthermore,some new efficient methods with a higher-order of convergence are obtained by using only a single matrix inversion in each iteration.Analyses of convergence properties and computational efficiency of these new methods are made and testified by several numerical problems.By comparison,the new schemes are more efficient than the corresponding existing ones,particularly for large problem sizes.
文摘In order to achieve higher accuracy in nonlinear/non-Gaussian state estimation, this paper proposes a new unscented Kalman filter (UKF). It uses a deterministic sampling approach. We choose the unscented transformation (UT) scaling parameters α=0.85, β=2, l=0 to construct 2n + 1 sigma points. These sigma points completely capture the mean and covariance of the Gaussian random variables of the nonlinear system Yi=F(Xi). Simulation results show that the posterior mean and covariance of the sigma points can achieve the accuracy of the third-order Taylor series expansion after having propagated through the true nonlinear system Yi=F(Xi). Extended Kalman filter (EKF) only can achieve the first-order accuracy. The computational complexity of UKF is the same level as that of EKF. UKF can yield better performance and higher accuracy than EKF.
基金supported by the National Natural Science Foundation of China(62133008,62303273,62188101,62373226,62473173)Young Taishan Scholars Program of Shandong Province of China(tsqn202408206)+2 种基金a Project of Shandong Province Higher Educational Youth and Innovation Talent Introduction and Education Programthe Natural Science Foundation of Shandong Province,China(ZR2023QF072)China Postdoctoral Science Foundation(2022M721932)
文摘Driven by practical applications, the achievement of distributed observers for nonlinear systems has emerged as a crucial advancement in recent years. However, existing theoretical advancements face certain limitations: They either fail to address more complex nonlinear phenomena, rely on hard-to-verify assumptions, or encounter difficulties in solving system parameters.Consequently, this paper aims to address these challenges by investigating distributed observers for nonlinear systems through the full-measured canonical form(FMCF), which is inspired by full-measured system(FMS) theory. To begin with, this study addresses the fact that the FMCF can only be obtained through the observable canonical form(OCF) in existing FMS theories.The paper demonstrates that a class of nonlinear systems can directly obtain FMCF through state space equations, independent of OCF. Also, a general method for solving FMCF in such systems is provided. Furthermore, based on the FMCF, A distributed observer is developed for nonlinear systems under two scenarios: Lipschitz conditions and open-loop bounded conditions.The paper establishes their asymptotic omniscience and demonstrates that the designed distributed observer in this study has fewer design parameters and is more convenient to construct than existing approaches. Finally, the effectiveness of the proposed methods is validated through simulation results on Van der Pol oscillators and microgrid systems.
基金supported by National Basic Research Program of China(973 Program)(No.2012CB821205)National Natural Science Foundation of China(Nos.61021002 and 61203125)Fundamental Research Funds for the Central Universities(No.HIT.NSRIF.2013039)
文摘This paper is concerned with the problem of global output feedback stabilization in probability for a class of switched stochastic nonlinear systems under arbitrary switchings. The subsystems are assumed to be in output feedback form and driven by white noise. By introducing a common Lyapunov function, the common output feedback controller independent of switching signals is constructed based on the backstepping approach. It is proved that the zero solution of the closed-loop system is fourth-moment exponentially stable. An example is given to show the effectiveness of the proposed method.
基金supported by the Ministry of Higher Education and Scientific Research of Tunisia
文摘In this paper, two types of mathematical models are developed to describe the dynamics of large-scale nonlinear systems, which are composed of several interconnected nonlinear subsystems. Each subsystem can be described by an input-output nonlinear discrete-time mathematical model, with unknown, but constant or slowly time-varying parameters. Then, two recursive estimation methods are used to solve the parametric estimation problem for the considered class of the interconnected nonlinear systems. These methods are based on the recursive least squares techniques and the prediction error method. Convergence analysis is provided using the hyper-stability and positivity method and the differential equation approach. A numerical simulation example of the parametric estimation of a stochastic interconnected nonlinear hydraulic system is treated.
文摘A class of triangular non li near system with disturbances which has unknown multiplicative time varying par ametric uncertainties in each virtual control is treated by a backstepping techn ique. The controller designed for all admissible uncertainties can guarantee tha t all states of its closed loop system are uniformly bounded. The robust contro ller design algorithm and a sufficient condition of the system stability are giv en. In addition, the closed loop system has an ISS property when the multiplica tive time varying parametric uncertainties are viewed as inputs to the system. Thus, this design provides a way to prevent a destabilizing effect of the multip licative time varying parametric uncertainties. Finally, simulational example i s given and simulational result shows that the controller exhibits effectiveness and excellent robustness.
文摘A new type of nonlinear observer for nonlinear systems is presented. Instead of approximating thc cntire nonlinear system with the neural network （NN）, only the un-modeled part left over after the lincarization is approximated. Compared with the conventional linear observer, the observer provides more accurate estimation of the state. The state estimation error is proved to asymptotically approach zero with the Lyapunov method. The simulation result shows that the proposed observer scheme is effective and has a potential application ability in the fault detection and identification （FDI）, and the state estimation.
基金Project supported by the National Key Research and Development Program of China(No.2021YFB3400700)the National Natural Science Foundation of China(Nos.12422201,12072188,12121002,and 12372017)。
文摘The variable selection of high dimensional nonparametric nonlinear systems aims to select the contributing variables or to eliminate the redundant variables.For a high dimensional nonparametric nonlinear system,however,identifying whether a variable contributes or not is not easy.Therefore,based on the Fourier spectrum of densityweighted derivative,one novel variable selection approach is developed,which does not suffer from the dimensionality curse and improves the identification accuracy.Furthermore,a necessary and sufficient condition for testing a variable whether it contributes or not is provided.The proposed approach does not require strong assumptions on the distribution,such as elliptical distribution.The simulation study verifies the effectiveness of the novel variable selection algorithm.
基金co-supported by National Natural Science Foundation of China (Nos. 91116017, 60974106 and 11102080)Funding for Outstanding Doctoral Dissertation in NUAA (No. BCXJ10-04)
文摘An adaptive robust attitude tracking control law based on switched nonlinear systems is presented for a variable structure near space vehicle （VSNSV） in the presence of uncertainties and disturbances. The adaptive fuzzy systems are employed for approximating unknown functions in the flight dynamic model and their parameters are updated online. To improve the flight robust performance, robust controllers with adaptive gains are designed to compensate for the approximation errors and thus they have less design conservation. Moreover, a systematic procedure is developed for the synthesis of adaptive fuzzy dynamic surface control （DSC） approach. According to the common Lyapunov function theory, it is proved that all signals of the closed-loop system are uniformly ultimately bounded by the continuous controller. The simulation results demonstrate the effectiveness and robustness of the proposed control scheme.
