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 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
Piecewise linear systems are prevalent in engineering practice,and can be categorized into symmetric and asymmetric piecewise linear systems.Considering that symmetry is a special case of asymmetry,it is essential to ...Piecewise linear systems are prevalent in engineering practice,and can be categorized into symmetric and asymmetric piecewise linear systems.Considering that symmetry is a special case of asymmetry,it is essential to investigate the broader model,namely the asymmetric piecewise linear system.The traditional averaging method is frequently used for studying nonlinear systems,particularly symmetric piecewise linear systems,with the harmonic response of the oscillator serving as a key prerequisite for calculating steady-state solutions.However,asymmetric systems inherently exhibit nonharmonic,asymmetric responses,rendering the traditional averaging method inapplicable.To overcome this limitation,this paper introduces an improved averaging method tailored for an oscillator characterized by asymmetric gaps and springs.Unlike the traditional method,which assumes a purely harmonic response,the improved averaging method redefines the system response as a superposition of a direct current(DC)term and a first harmonic component.Herein,the DC term can be regarded as the offset induced by model asymmetry.Furthermore,the DC term is treated as a slow variable function of time,with its time derivative assumed to be zero when calculating the steady-state solution,akin to the amplitude and phase in the traditional averaging method.Numerical validation demonstrates that the responses computed in both time and frequency domains with the improved averaging method exhibit greater accuracy compared with those derived from the traditional method.Leveraging these improved results,the study also examines the parameter effect,stability,and bifurcation phenomena within the amplitude-frequency responses.展开更多
Optical synapses have an ability to perceive and remember visual information,making them expected to provide more intelligent and efficient visual solutions for humans.As a new type of artificial visual sensory device...Optical synapses have an ability to perceive and remember visual information,making them expected to provide more intelligent and efficient visual solutions for humans.As a new type of artificial visual sensory devices,photoelectric memristors can fully simulate synaptic performance and have great prospects in the development of biological vision.However,due to the urgent problems of nonlinear conductance and high-energy consumption,its further application in high-precision control scenarios and integration is hindered.In this work,we report an optoelectronic memristor with a structure of TiN/CeO_(2)/ZnO/ITO/Mica,which can achieve minimal energy consumption(187 pJ)at a single pulse(0.5 V,5 ms).Under the stimulation of continuous pulses,linearity can be achieved up to 99.6%.In addition,the device has a variety of synaptic functions under the combined action of photoelectric,which can be used for advanced vision.By utilizing its typical long-term memory characteristics,we achieved image recognition and long-term memory in a 3×3 synaptic array and further achieved female facial feature extraction behavior with an activation rate of over 92%.Moreover,we also use the linear response characteristic of the device to design and implement the night meeting behavior of autonomous vehicles based on the hardware platform.This work highlights the potential of photoelectric memristors for advancing neuromorphic vision systems,offering a new direction for bionic eyes and visual automation technology.展开更多
In the realm of nonlinear integrable systems,the presence of decompositions facilitates the establishment of linear superposition solutions and the derivation of novel coupled systems exhibiting nonlinear integrabilit...In the realm of nonlinear integrable systems,the presence of decompositions facilitates the establishment of linear superposition solutions and the derivation of novel coupled systems exhibiting nonlinear integrability.By focusing on single-component decompositions within the potential BKP hierarchy,it has been observed that specific linear superpositions of decomposition solutions remain consistent with the underlying equations.Moreover,through the implementation of multi-component decompositions within the potential BKP hierarchy,successful endeavors have been undertaken to formulate linear superposition solutions and novel coupled Kd V-type systems that resist decoupling via alterations in dependent variables.展开更多
This article investigates the time-varying output group formation tracking control(GFTC)problem for heterogeneous multi-agent systems(HMASs)under switching topologies.The objective is to design a distributed control s...This article investigates the time-varying output group formation tracking control(GFTC)problem for heterogeneous multi-agent systems(HMASs)under switching topologies.The objective is to design a distributed control strategy that enables the outputs of the followers to form the desired sub-formations and track the outputs of the leader in each subgroup.Firstly,novel distributed observers are developed to estimate the states of the leaders under switching topologies.Then,GFTC protocols are designed based on the proposed observers.It is shown that with the distributed protocol,the GFTC problem for HMASs under switching topologies is solved if the average dwell time associated with the switching topologies is larger than a fixed threshold.Finally,an example is provided to illustrate the effectiveness of the proposed control strategy.展开更多
For multidimensional first order semilinear hyperbolic systems of diagonal form without self-interaction,we show the global nonlinear stability of traveling wave solutions.
In this paper,the efficient preconditioned modified Hermitian and skew-Hermitian splitting(PMHSS)iteration method is further explored and it is extended to solve more general block two-by-two linear systems with diffe...In this paper,the efficient preconditioned modified Hermitian and skew-Hermitian splitting(PMHSS)iteration method is further explored and it is extended to solve more general block two-by-two linear systems with different and nonsymmetric off-diagonal blocks.With the aid of the singular value decomposition technique,the detailed analysis of the algebraic and convergence properties of the PMHSS iteration method demonstrates that it is still convergent unconditionally as when it is used to solve the well-studied case of block two-by-two linear systems with same and symmetric off-diagonal blocks.Moreover,the PMHSS preconditioned matrix is almost unitary diagonalizable with clustered eigenvalue distributions for this more general case.On account of the favorable spectral properties of the PMHSS preconditioned matrix,a parameter free Chebyshev accelerated PMHSS(CAPMHSS)method is established to further improve its convergence rate.Numerical experiments about Kroncker structured block two-by-two linear systems arising from a time-dependent PDE-constrained optimal control problem demonstrate quite satisfactory and competitive performance of the CAPMHSS method compared with some existing preconditioned Krylov subspace methods.展开更多
This paper investigates the prescribed-time tracking control problem for a class of multi-input multi-output(MIMO)nonlinear strict-feedback systems subject to non-vanishing uncertainties. The inherent unmatched and no...This paper investigates the prescribed-time tracking control problem for a class of multi-input multi-output(MIMO)nonlinear strict-feedback systems subject to non-vanishing uncertainties. The inherent unmatched and non-vanishing uncertainties make the prescribed-time control problem become much more nontrivial. The solution to address the challenges mentioned above involves incorporating a prescribed-time filter, as opposed to a finite-time filter, and formulating a prescribed-time Lyapunov stability lemma(Lemma 5). The prescribed-time Lyapunov stability lemma is based on time axis shifting time-varying yet bounded gain, which establishes a novel link between the fixed-time and prescribed-time control method. This allows the restriction condition that the time-varying gain function must satisfy as imposed in most exist prescribed-time control works to be removed. Under the proposed control method, the desire trajectory is ensured to closely track the output of the system in prescribed time. The effectiveness of the theoretical results are verified through numerical simulation.展开更多
With the development of science and technology,the design and optimization of control systems are widely applied.This paper focuses on the application of matrix equations in linear time-invariant systems.Taking the in...With the development of science and technology,the design and optimization of control systems are widely applied.This paper focuses on the application of matrix equations in linear time-invariant systems.Taking the inverted pendulum model as an example,the algebraic Riccati equation is used to solve the optimal control problem,and the system performance and stability are achieved by selecting the closed-loop pole and designing the gain matrix.Then,the numerical methods for solving the stochastic algebraic Riccati equations are applied to practical problems,with Newton’s iteration method as the outer iteration and the solution of the mixed-type Lyapunov equations as the inner iteration.Two methods for solving the Lyapunov equations are introduced,providing references for related research.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
This paper studies global stabilization via predictor-based sampled-data output feedback for a class of feedforward nonlinear time-delay systems.Note that the traditional sampled-data observer via zero-order holder ma...This paper studies global stabilization via predictor-based sampled-data output feedback for a class of feedforward nonlinear time-delay systems.Note that the traditional sampled-data observer via zero-order holder may result in the performance degradation of the observer.In this paper,an improved predictor-based observer is designed to compensate for the influence of the unmeasurable states,sampling errors and output delay.In addition,a sampled-data output-feedback controller is also constructed using the gain scaling technique.By the Lyapunov-Krasovskii functional method,the global exponential stability of the resulting closed-loop system can be guaranteed under some sufficient conditions.The simulation results are provided to demonstrate the main results.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
Switched systems play an imperative role in modeling many real industrial systems with abrupt changes.Due to possible exposure to unreliable and complex physical environments,switching dynamics may simultaneously face...Switched systems play an imperative role in modeling many real industrial systems with abrupt changes.Due to possible exposure to unreliable and complex physical environments,switching dynamics may simultaneously face multiple faults,including the unexpected controller disconnect,the temporary mismatch between subsystems and desired corresponding controllers,and the intermittent disordering of mode transitions.These commonly arising faults may result in severe and detrimental impacts on the reliability and convergence of the closed-loop solution,thereby bringing significant yet challenging issues to be tackled.This paper provides the first attempt to investigate the stabilization problem for a class of constrained switched linear systems with multiple faults under mode-dependent dwell time(MDT).From a set-theory perspective,we demonstrate a critical necessary and sufficient stability condition for switched systems without uncertainties.Moreover,the non-conservative stability criterion is further extended to the perturbed switched systems with rigorous proof.A switching communication network example verifies the validity of the theoretical result and demonstrates their advantages.展开更多
This paper discusses the design of event-triggered output-feedback controller for a class of nonlinear time-delay systems with multiple uncertainties. In sharp contrast to previous works, the considered systems posses...This paper discusses the design of event-triggered output-feedback controller for a class of nonlinear time-delay systems with multiple uncertainties. In sharp contrast to previous works, the considered systems possess two important characteristics: (i) The uncertain nonlinear terms meet the linearly unmeasurable-states dependent growth with the growth rate being an unknown function of the input and output. (ii) There exist input matching uncertainty and unknown measurement sensitivity. By introducing a single dynamic gain and employing a cleverly devised event-triggering mechanism (ETM), we design a new gain-based event-triggered output-feedback controller, which globally regulates all states of the considered systems and maintains global boundedness of the closed-loop system. Furthermore, the estimation of input matching uncertainty achieves convergence towards its actual value, and Zeno behavior does not happen. Two simulation examples including a practical one show that the proposed approach is effective.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 deals with the stabilization problem of nonlinear stochastic systems via self-triggered impulsive control(STIC), where the timing of impulsive control actions is not dependent on continuous sta...Dear Editor,This letter deals with the stabilization problem of nonlinear stochastic systems via self-triggered impulsive control(STIC), where the timing of impulsive control actions is not dependent on continuous state monitoring. In contrast to the existing self-triggered control method, novel self-triggered mechanism(STM) is proposed by incorporating a waiting time for stabilizing impulses. This allows for direct prediction of the next impulsive instant.展开更多
The coupled nonlocal nonlinear Schrödinger equations with variable coefficients are researched using the nonstandard Hirota bilinear method.The two-soliton and double-hump one-soliton solutions for the equations ...The coupled nonlocal nonlinear Schrödinger equations with variable coefficients are researched using the nonstandard Hirota bilinear method.The two-soliton and double-hump one-soliton solutions for the equations are first obtained.By assigning different functions to the variable coefficients,we obtain V-shaped,Y-shaped,wave-type,exponential solitons,and so on.Next,we reveal the influence of the real and imaginary parts of the wave numbers on the double-hump structure based on the soliton solutions.Finally,by setting different wave numbers,we can change the distance and transmission direction of the solitons to analyze their dynamic behavior during collisions.This study establishes a theoretical framework for controlling the dynamics of optical fiber in nonlocal nonlinear systems.展开更多
In this paper,fixed-time consensus tracking for mul-tiagent systems(MASs)with dynamics in the form of strict feed-back affine nonlinearity is addressed.A fixed-time antidistur-bance consensus tracking protocol is prop...In this paper,fixed-time consensus tracking for mul-tiagent systems(MASs)with dynamics in the form of strict feed-back affine nonlinearity is addressed.A fixed-time antidistur-bance consensus tracking protocol is proposed,which consists of a distributed fixed-time observer,a fixed-time disturbance observer,a nonsmooth antidisturbance backstepping controller,and the fixed-time stability analysis is conducted by using the Lyapunov theory correspondingly.This paper includes three main improvements.First,a distributed fixed-time observer is developed for each follower to obtain an estimate of the leader’s output by utilizing the topology of the communication network.Second,a fixed-time disturbance observer is given to estimate the lumped disturbances for feedforward compensation.Finally,a nonsmooth antidisturbance backstepping tracking controller with feedforward compensation for lumped disturbances is designed.In order to mitigate the“explosion of complexity”in the tradi-tional backstepping approach,we have implemented a modified nonsmooth command filter to enhance the performance of the closed-loop system.The simulation results show that the pro-posed method is effective.展开更多
This paper presents a risk-informed data-driven safe control design approach for a class of stochastic uncertain nonlinear discrete-time systems.The nonlinear system is modeled using linear parameter-varying(LPV)syste...This paper presents a risk-informed data-driven safe control design approach for a class of stochastic uncertain nonlinear discrete-time systems.The nonlinear system is modeled using linear parameter-varying(LPV)systems.A model-based probabilistic safe controller is first designed to guarantee probabilisticλ-contractivity(i.e.,stability and invariance)of the LPV system with respect to a given polyhedral safe set.To obviate the requirement of knowing the LPV system model and to bypass identifying its open-loop model,its closed-loop data-based representation is provided in terms of state and scheduling data as well as a decision variable.It is shown that the variance of the closedloop system,as well as the probability of safety satisfaction,depends on the decision variable and the noise covariance.A minimum-variance direct data-driven gain-scheduling safe control design approach is presented next by designing the decision variable such that all possible closed-loop system realizations satisfy safety with the highest confidence level.This minimum-variance approach is a control-oriented learning method since it minimizes the variance of the state of the closed-loop system with respect to the safe set,and thus minimizes the risk of safety violation.Unlike the certainty-equivalent approach that results in a risk-neutral control design,the minimum-variance method leads to a risk-averse control design.It is shown that the presented direct risk-averse learning approach requires weaker data richness conditions than existing indirect learning methods based on system identification and can lead to a lower risk of safety violation.Two simulation examples along with an experimental validation on an autonomous vehicle are provided to show the effectiveness of the presented approach.展开更多
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(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.
基金Project supported by the National Natural Science Foundation of China(Nos.12272242 and U1934201)。
文摘Piecewise linear systems are prevalent in engineering practice,and can be categorized into symmetric and asymmetric piecewise linear systems.Considering that symmetry is a special case of asymmetry,it is essential to investigate the broader model,namely the asymmetric piecewise linear system.The traditional averaging method is frequently used for studying nonlinear systems,particularly symmetric piecewise linear systems,with the harmonic response of the oscillator serving as a key prerequisite for calculating steady-state solutions.However,asymmetric systems inherently exhibit nonharmonic,asymmetric responses,rendering the traditional averaging method inapplicable.To overcome this limitation,this paper introduces an improved averaging method tailored for an oscillator characterized by asymmetric gaps and springs.Unlike the traditional method,which assumes a purely harmonic response,the improved averaging method redefines the system response as a superposition of a direct current(DC)term and a first harmonic component.Herein,the DC term can be regarded as the offset induced by model asymmetry.Furthermore,the DC term is treated as a slow variable function of time,with its time derivative assumed to be zero when calculating the steady-state solution,akin to the amplitude and phase in the traditional averaging method.Numerical validation demonstrates that the responses computed in both time and frequency domains with the improved averaging method exhibit greater accuracy compared with those derived from the traditional method.Leveraging these improved results,the study also examines the parameter effect,stability,and bifurcation phenomena within the amplitude-frequency responses.
基金supported by Science and Technology Project of Hebei Education Department(grant no.QN2023092)High-level Talent Research Startup Project of Hebei University(grant no.521100221071,521000981426,521100223225)+17 种基金National Key R&D Plan"Nano Frontier"Key Special Project(Grant Nos.2024YFA1208400,2021YFA1200502)National Key R&D Program Disruptive Technology Innovation Project(Grant No.2024YFF1504300)National Natural Science Foundation of China(Grant Nos.62004056,62104058,Grant No.61874158)National Major R&D Project Cultivation Projects(Grant No.92164109)Natural Science Foundation of Hebei Province(Grant Nos.F2021201045,F2021201022,F2022201054,F2023201044,F2022201002)Special Support Funds for National High-Level Talents(Grant No.041500120001)Hebei Province Yanzhao Young Scientist Project(Grant No.F2023201076)Support Program for the Top Young Talents of Hebei Province(Grant No.70280011807)Hebei Province High-Level Talent Funding Project(Grant No.B20231003)Strategic Leading Science and Technology Special Project of Chinese Academy of Sciences(Grant No.XDB44000000-7)Interdisciplinary Research Program of Natural Science of Hebei University(Grant No.DXK202101)Institute of Life Sciences and Green Development(Grant No.521100311)Outstanding Young Scientific Research and Innovation Team of Hebei University(Grant No.605020521001)Advanced Talents Incubation Program of Hebei University(Grant Nos.521000981426,521100221071,521100224232,521000981363)Science and Technology Project of Hebei Education Department(Grant Nos.QN2020178,QN2021026)Baoding Science and Technology Plan Project(Grant No.2172P011)Hebei Province Key R&D Plan Projects(Grant No.22311101D)Baoding Science and Technology Plan Project(Grant No.2272P014)Regional Innovation and Development Joint Fund Key Project(Grant No.U23A20365)Hebei Province Natural Science Foundation(Grant No.F2023201044).
文摘Optical synapses have an ability to perceive and remember visual information,making them expected to provide more intelligent and efficient visual solutions for humans.As a new type of artificial visual sensory devices,photoelectric memristors can fully simulate synaptic performance and have great prospects in the development of biological vision.However,due to the urgent problems of nonlinear conductance and high-energy consumption,its further application in high-precision control scenarios and integration is hindered.In this work,we report an optoelectronic memristor with a structure of TiN/CeO_(2)/ZnO/ITO/Mica,which can achieve minimal energy consumption(187 pJ)at a single pulse(0.5 V,5 ms).Under the stimulation of continuous pulses,linearity can be achieved up to 99.6%.In addition,the device has a variety of synaptic functions under the combined action of photoelectric,which can be used for advanced vision.By utilizing its typical long-term memory characteristics,we achieved image recognition and long-term memory in a 3×3 synaptic array and further achieved female facial feature extraction behavior with an activation rate of over 92%.Moreover,we also use the linear response characteristic of the device to design and implement the night meeting behavior of autonomous vehicles based on the hardware platform.This work highlights the potential of photoelectric memristors for advancing neuromorphic vision systems,offering a new direction for bionic eyes and visual automation technology.
基金sponsored by the National Natural Science Foundations of China under Grant Nos.12301315,12235007,11975131the Zhejiang Provincial Natural Science Foundation of China under Grant No.LQ20A010009。
文摘In the realm of nonlinear integrable systems,the presence of decompositions facilitates the establishment of linear superposition solutions and the derivation of novel coupled systems exhibiting nonlinear integrability.By focusing on single-component decompositions within the potential BKP hierarchy,it has been observed that specific linear superpositions of decomposition solutions remain consistent with the underlying equations.Moreover,through the implementation of multi-component decompositions within the potential BKP hierarchy,successful endeavors have been undertaken to formulate linear superposition solutions and novel coupled Kd V-type systems that resist decoupling via alterations in dependent variables.
文摘This article investigates the time-varying output group formation tracking control(GFTC)problem for heterogeneous multi-agent systems(HMASs)under switching topologies.The objective is to design a distributed control strategy that enables the outputs of the followers to form the desired sub-formations and track the outputs of the leader in each subgroup.Firstly,novel distributed observers are developed to estimate the states of the leaders under switching topologies.Then,GFTC protocols are designed based on the proposed observers.It is shown that with the distributed protocol,the GFTC problem for HMASs under switching topologies is solved if the average dwell time associated with the switching topologies is larger than a fixed threshold.Finally,an example is provided to illustrate the effectiveness of the proposed control strategy.
基金supported by the National Natural Science Foundation of China(12371217)the Fundamental Research Funds for the Central Universities(2232022D-27).
文摘For multidimensional first order semilinear hyperbolic systems of diagonal form without self-interaction,we show the global nonlinear stability of traveling wave solutions.
基金supported by the National Natural Science Foundation of China(Nos.11801242,11771193,and 11901267)the Fundamental Research Funds for the Central Universities(No.lzujbky-2022-05)the Natural Science Foundation of Gansu Province of China(Grant No.23JRRA1104).
文摘In this paper,the efficient preconditioned modified Hermitian and skew-Hermitian splitting(PMHSS)iteration method is further explored and it is extended to solve more general block two-by-two linear systems with different and nonsymmetric off-diagonal blocks.With the aid of the singular value decomposition technique,the detailed analysis of the algebraic and convergence properties of the PMHSS iteration method demonstrates that it is still convergent unconditionally as when it is used to solve the well-studied case of block two-by-two linear systems with same and symmetric off-diagonal blocks.Moreover,the PMHSS preconditioned matrix is almost unitary diagonalizable with clustered eigenvalue distributions for this more general case.On account of the favorable spectral properties of the PMHSS preconditioned matrix,a parameter free Chebyshev accelerated PMHSS(CAPMHSS)method is established to further improve its convergence rate.Numerical experiments about Kroncker structured block two-by-two linear systems arising from a time-dependent PDE-constrained optimal control problem demonstrate quite satisfactory and competitive performance of the CAPMHSS method compared with some existing preconditioned Krylov subspace methods.
基金supported in part by the National Key Research and Development Program of China(2023YFA1011803)the National Natural Science Foundation of China(62273064,61991400/61991403,61933012,62250710167,62203078)+2 种基金Natural Science Foundation of Chongqing(CSTB2023NSCQ-MSX0588)the Central University Project(2023CDJKYJH047)the Innovation Support Program for International Students Returning to China(cx2022016)
文摘This paper investigates the prescribed-time tracking control problem for a class of multi-input multi-output(MIMO)nonlinear strict-feedback systems subject to non-vanishing uncertainties. The inherent unmatched and non-vanishing uncertainties make the prescribed-time control problem become much more nontrivial. The solution to address the challenges mentioned above involves incorporating a prescribed-time filter, as opposed to a finite-time filter, and formulating a prescribed-time Lyapunov stability lemma(Lemma 5). The prescribed-time Lyapunov stability lemma is based on time axis shifting time-varying yet bounded gain, which establishes a novel link between the fixed-time and prescribed-time control method. This allows the restriction condition that the time-varying gain function must satisfy as imposed in most exist prescribed-time control works to be removed. Under the proposed control method, the desire trajectory is ensured to closely track the output of the system in prescribed time. The effectiveness of the theoretical results are verified through numerical simulation.
基金Supported by National Natural Science Foundation of China(Grant No.12571388)the Visiting Scholar Program of National Natural Science Foundation of China(Grant No.12426616)Natural Science Research Start-up Foundation of Recruiting Talents of Nanjing University of Posts and Telecommunications(Grant No.NY223127).
文摘With the development of science and technology,the design and optimization of control systems are widely applied.This paper focuses on the application of matrix equations in linear time-invariant systems.Taking the inverted pendulum model as an example,the algebraic Riccati equation is used to solve the optimal control problem,and the system performance and stability are achieved by selecting the closed-loop pole and designing the gain matrix.Then,the numerical methods for solving the stochastic algebraic Riccati equations are applied to practical problems,with Newton’s iteration method as the outer iteration and the solution of the mixed-type Lyapunov equations as the inner iteration.Two methods for solving the Lyapunov equations are introduced,providing references for related research.
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 by the Autonomous Innovation Team Foundation for“20 Items of the New University”of Jinan City(202228087)the National Natural Science Foundation of China(62073190).
文摘This paper studies global stabilization via predictor-based sampled-data output feedback for a class of feedforward nonlinear time-delay systems.Note that the traditional sampled-data observer via zero-order holder may result in the performance degradation of the observer.In this paper,an improved predictor-based observer is designed to compensate for the influence of the unmeasurable states,sampling errors and output delay.In addition,a sampled-data output-feedback controller is also constructed using the gain scaling technique.By the Lyapunov-Krasovskii functional method,the global exponential stability of the resulting closed-loop system can be guaranteed under some sufficient conditions.The simulation results are provided to demonstrate the main results.
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 Natural Sciences and Engineering Research Council of Canada(NSERC)supported by the National Natural Science Foundation of China under Grant 62303403Zhejiang Provincial Natural Science Foundation of China under Grants LR25F030004 and LQ24F030022。
文摘Switched systems play an imperative role in modeling many real industrial systems with abrupt changes.Due to possible exposure to unreliable and complex physical environments,switching dynamics may simultaneously face multiple faults,including the unexpected controller disconnect,the temporary mismatch between subsystems and desired corresponding controllers,and the intermittent disordering of mode transitions.These commonly arising faults may result in severe and detrimental impacts on the reliability and convergence of the closed-loop solution,thereby bringing significant yet challenging issues to be tackled.This paper provides the first attempt to investigate the stabilization problem for a class of constrained switched linear systems with multiple faults under mode-dependent dwell time(MDT).From a set-theory perspective,we demonstrate a critical necessary and sufficient stability condition for switched systems without uncertainties.Moreover,the non-conservative stability criterion is further extended to the perturbed switched systems with rigorous proof.A switching communication network example verifies the validity of the theoretical result and demonstrates their advantages.
基金supported by the fund of Beijing Municipal Commission of Education(KM202210017001 and 22019821001)the Natural Science Foundation of Henan Province(222300420253).
文摘This paper discusses the design of event-triggered output-feedback controller for a class of nonlinear time-delay systems with multiple uncertainties. In sharp contrast to previous works, the considered systems possess two important characteristics: (i) The uncertain nonlinear terms meet the linearly unmeasurable-states dependent growth with the growth rate being an unknown function of the input and output. (ii) There exist input matching uncertainty and unknown measurement sensitivity. By introducing a single dynamic gain and employing a cleverly devised event-triggering mechanism (ETM), we design a new gain-based event-triggered output-feedback controller, which globally regulates all states of the considered systems and maintains global boundedness of the closed-loop system. Furthermore, the estimation of input matching uncertainty achieves convergence towards its actual value, and Zeno behavior does not happen. Two simulation examples including a practical one show that the proposed approach is effective.
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(62403393,12202058,62103118)the China Postdoctoral Science Foundation(2021T140160,2023 T160051)the Natural Science Foundation of Chongqing(CSTB 2023NSCQ-MSX0152)
文摘Dear Editor,This letter deals with the stabilization problem of nonlinear stochastic systems via self-triggered impulsive control(STIC), where the timing of impulsive control actions is not dependent on continuous state monitoring. In contrast to the existing self-triggered control method, novel self-triggered mechanism(STM) is proposed by incorporating a waiting time for stabilizing impulses. This allows for direct prediction of the next impulsive instant.
基金supported by the National Key R&D Program of China(Grant No.2022YFA1604200)the National Natural Science Foundation of China(Grant No.12261131495)Institute of Systems Science,Beijing Wuzi University(Grant No.BWUISS21).
文摘The coupled nonlocal nonlinear Schrödinger equations with variable coefficients are researched using the nonstandard Hirota bilinear method.The two-soliton and double-hump one-soliton solutions for the equations are first obtained.By assigning different functions to the variable coefficients,we obtain V-shaped,Y-shaped,wave-type,exponential solitons,and so on.Next,we reveal the influence of the real and imaginary parts of the wave numbers on the double-hump structure based on the soliton solutions.Finally,by setting different wave numbers,we can change the distance and transmission direction of the solitons to analyze their dynamic behavior during collisions.This study establishes a theoretical framework for controlling the dynamics of optical fiber in nonlocal nonlinear systems.
基金supported by the National Defense Basic Scientific Research Project(JCKY2020130C025)the National Science and Technology Major Project(J2019-III-0020-0064,J2019-V-0014-0109)。
文摘In this paper,fixed-time consensus tracking for mul-tiagent systems(MASs)with dynamics in the form of strict feed-back affine nonlinearity is addressed.A fixed-time antidistur-bance consensus tracking protocol is proposed,which consists of a distributed fixed-time observer,a fixed-time disturbance observer,a nonsmooth antidisturbance backstepping controller,and the fixed-time stability analysis is conducted by using the Lyapunov theory correspondingly.This paper includes three main improvements.First,a distributed fixed-time observer is developed for each follower to obtain an estimate of the leader’s output by utilizing the topology of the communication network.Second,a fixed-time disturbance observer is given to estimate the lumped disturbances for feedforward compensation.Finally,a nonsmooth antidisturbance backstepping tracking controller with feedforward compensation for lumped disturbances is designed.In order to mitigate the“explosion of complexity”in the tradi-tional backstepping approach,we have implemented a modified nonsmooth command filter to enhance the performance of the closed-loop system.The simulation results show that the pro-posed method is effective.
基金supported in part by the Department of Navy award (N00014-22-1-2159)the National Science Foundation under award (ECCS-2227311)。
文摘This paper presents a risk-informed data-driven safe control design approach for a class of stochastic uncertain nonlinear discrete-time systems.The nonlinear system is modeled using linear parameter-varying(LPV)systems.A model-based probabilistic safe controller is first designed to guarantee probabilisticλ-contractivity(i.e.,stability and invariance)of the LPV system with respect to a given polyhedral safe set.To obviate the requirement of knowing the LPV system model and to bypass identifying its open-loop model,its closed-loop data-based representation is provided in terms of state and scheduling data as well as a decision variable.It is shown that the variance of the closedloop system,as well as the probability of safety satisfaction,depends on the decision variable and the noise covariance.A minimum-variance direct data-driven gain-scheduling safe control design approach is presented next by designing the decision variable such that all possible closed-loop system realizations satisfy safety with the highest confidence level.This minimum-variance approach is a control-oriented learning method since it minimizes the variance of the state of the closed-loop system with respect to the safe set,and thus minimizes the risk of safety violation.Unlike the certainty-equivalent approach that results in a risk-neutral control design,the minimum-variance method leads to a risk-averse control design.It is shown that the presented direct risk-averse learning approach requires weaker data richness conditions than existing indirect learning methods based on system identification and can lead to a lower risk of safety violation.Two simulation examples along with an experimental validation on an autonomous vehicle are provided to show the effectiveness of the presented approach.
