The problem of track control is studied for a class of strict-feedback stochastic nonlinear systems in which unknown virtual control gain function is the main feature.First,the so-called stochastic LaSalle theory is e...The problem of track control is studied for a class of strict-feedback stochastic nonlinear systems in which unknown virtual control gain function is the main feature.First,the so-called stochastic LaSalle theory is extended to some extent,and accordingly,the results of global ultimate boundedness for stochastic nonlinear systems are developed.Next,a new design scheme of fuzzy adaptive control is proposed.The advantage of it is that it does not require priori knowledge of virtual control gain function sign,which is usually demanded in many designs.At the same time,the track performance of closed-loop systems is improved by adaptive modifying the estimated error upper bound.By theoretical analysis,the signals of closed-loop systems are globally ultimately bounded in probability and the track error converges to a small residual set around the origin in 4th-power expectation.展开更多
This paper investigates the fixed-time stability theorem and state-feedback controller design for stochastic nonlinear systems.We propose an improved fixed-time Lyapunov theorem with a more rigorous and reasonable pro...This paper investigates the fixed-time stability theorem and state-feedback controller design for stochastic nonlinear systems.We propose an improved fixed-time Lyapunov theorem with a more rigorous and reasonable proof procedure.In particular,an important corollary is obtained,which can give a less conservative upper-bound estimate of the settling time.Based on the backstepping technique and the addition of a power integrator method,a state-feedback controller is skillfully designed for a class of stochastic nonlinear systems.It is proved that the proposed controller can render the closed-loop system fixed-time stable in probability with the help of the proposed fixed-time stability criteria.Finally,the effectiveness of the proposed controller is demonstrated by simulation examples and comparisons.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
This paper is concerned with the global boundedness problem for a class of stochastic nonlinear systems with matched conditions. The uncertainties in the systems are due to parameter variations and external stochastic...This paper is concerned with the global boundedness problem for a class of stochastic nonlinear systems with matched conditions. The uncertainties in the systems are due to parameter variations and external stochastic disturbance. Only the matched conditions and the possible bound of the uncertainties are demanded. Based on the stochastic Lyapunov stability theory, an explicit controller is constructed in the gradient direction, which renders responses of the closed-loop systems be globally bounded in probability. When the systems degrade to linear systems, the controller becomes linear. Illustrative examples are given to show the effectiveness of the proposed method.展开更多
The problem of adaptive stabilization is addressed for a class of uncertain stochastic nonlinear strict-feedback systems with both unknown dead-zone and unknown gain functions.By using the backstepping method and neur...The problem of adaptive stabilization is addressed for a class of uncertain stochastic nonlinear strict-feedback systems with both unknown dead-zone and unknown gain functions.By using the backstepping method and neural network（NN） parameterization,a novel adaptive neural control scheme which contains fewer learning parameters is developed to solve the stabilization problem of such systems.Meanwhile,stability analysis is presented to guarantee that all the error variables are semi-globally uniformly ultimately bounded with desired probability in a compact set.The effectiveness of the proposed design is illustrated by simulation results.展开更多
In this paper, for a class of high-order stochastic nonlinear systems with zero dynamics which are neither necessarily feedback linearizable nor affine in the control input, the problem of state feedback stabilization...In this paper, for a class of high-order stochastic nonlinear systems with zero dynamics which are neither necessarily feedback linearizable nor affine in the control input, the problem of state feedback stabilization is investigated for the first time. Under some weaker assumptions, a smooth state feedback controller is designed, which ensures that the closed-loop system has an almost surely unique solution on [0,∞）, the equilibrium at the origin of the closed-loop system is globally asymptotically stable in probability, and all the states can be regulated to the origin almost surely. A simulation example demonstrates the control scheme.展开更多
This paper considers a concrete stochastic nonlinear system with stochastic unmeasurable inverse dynamics. Motivated by the concept of integral input-to-state stability （iISS） in deterministic systems and stochastic...This paper considers a concrete stochastic nonlinear system with stochastic unmeasurable inverse dynamics. Motivated by the concept of integral input-to-state stability （iISS） in deterministic systems and stochastic input-to-state stability （SISS） in stochastic systems, a concept of stochastic integral input-to-state stability （SiISS） using Lyapunov functions is first introduced. A constructive strategy is proposed to design a dynamic output feedback control law, which drives the state to the origin almost surely while keeping all other closed-loop signals almost surely bounded. At last, a simulation is given to verify the effectiveness of the control law.展开更多
This paper considers the output tracking problem for more general classes of stochastic nonlinear systems with unknown control coefficients and driven by noise of unknown covariance. By utilizing the radial basis func...This paper considers the output tracking problem for more general classes of stochastic nonlinear systems with unknown control coefficients and driven by noise of unknown covariance. By utilizing the radial basis function neural network approximation method and backstepping technique, we successfully construct a controller to guarantee the solution process to be bounded in probability.The tracking error signal is 4th-moment semi-globally uniformly ultimately bounded（SGUUB） and can be regulated into a small neighborhood of the origin in probability. A simulation example is given to demonstrate the effectiveness of the control scheme.展开更多
In this paper,we studied the approximate sampleddata observer design for a class of stochastic nonlinear systems.Euler-Maruyama approximation was investigated in this paper because it is the basis of other higher prec...In this paper,we studied the approximate sampleddata observer design for a class of stochastic nonlinear systems.Euler-Maruyama approximation was investigated in this paper because it is the basis of other higher precision numerical methods,and it preserves important structures of the nonlinear systems.Also,the form of Euler-Maruyama model is simple and easy to be calculated.The results provide a reference for sampled-data observer design method for such stochastic nonlinear systems,and may be useful to many practical control applications,such as tracking control in mechanical systems.And the effectiveness of the approach is demonstrated by a simulation example.展开更多
This paper investigates a multiplayer Pareto game for affine nonlinear stochastic systems disturbed by both external and the internal multiplicative noises.The Pareto cooperative optimal strategies with the H_(∞) con...This paper investigates a multiplayer Pareto game for affine nonlinear stochastic systems disturbed by both external and the internal multiplicative noises.The Pareto cooperative optimal strategies with the H_(∞) constraint are resolved by integrating H_(2)/H_(∞) theory with Pareto game theory.First,a nonlinear stochastic bounded real lemma(SBRL)is derived,explicitly accounting for non-zero initial conditions.Through the analysis of four cross-coupled Hamilton-Jacobi equations(HJEs),we establish necessary and sufficient conditions for the existence of Pareto optimal strategies with the H_(∞) constraint.Secondly,to address the complexity of solving these nonlinear partial differential HJEs,we propose a neural network(NN)framework with synchronous tuning rules for the actor,critic,and disturbance components,based on a reinforcement learning(RL)approach.The designed tuning rules ensure convergence of the actor-critic-disturbance components to the desired values,enabling the realization of robust Pareto control strategies.The convergence of the proposed algorithm is rigorously analyzed using a constructed Lyapunov function for the NN weight errors.Finally,a numerical simulation example is provided to demonstrate the effectiveness of the proposed methods and main results.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
In this paper, the property of practical input-to-state stability and its application to stability of cascaded nonlinear systems are investigated in the stochastic framework. Firstly, the notion of （practical） stoch...In this paper, the property of practical input-to-state stability and its application to stability of cascaded nonlinear systems are investigated in the stochastic framework. Firstly, the notion of （practical） stochastic input-to-state stability with respect to a stochastic input is introduced, and then by the method of changing supply functions, （a） an （practical） SISS-Lyapunov function for the overall system is obtained from the corresponding Lyapunov functions for cascaded （practical） SISS subsystems.展开更多
This paper presents new results on the robust global stabilization and the gain assignment problems for stochastic nonlinear systems. Three stochastic nonlinear control design schemes are developed. Furthermore, a new...This paper presents new results on the robust global stabilization and the gain assignment problems for stochastic nonlinear systems. Three stochastic nonlinear control design schemes are developed. Furthermore, a new stochastic gain assignment method is developed for a class of uncertain interconnected stochastic nonlinear systems. This method can be combined with the nonlinear small-gain theorem to design partial-state feedback controllers for stochastic nonlinear systems. Two numerical examples are given to illustrate the effectiveness of the proposed methodology.展开更多
In this paper,a state feedback adaptive stabilization for a class of large-scale stochastic nonlinear systems is designed with Lyapunov and Backstepping method.In the systems there are uncertain terms,whose bounds are...In this paper,a state feedback adaptive stabilization for a class of large-scale stochastic nonlinear systems is designed with Lyapunov and Backstepping method.In the systems there are uncertain terms,whose bounds are governed by a set of unknown parameters.The designed controllers would make the close-loop systems asymptotically stable and adaptive for the unknown parameters.As an application,a second order example is delivered to illustrate the approach.展开更多
In this study,an adaptive asymptotic tracking control problem is considered for stochastic nonlinear systems with unknown backlash-like hysteresis.By utilizing backstepping technology and bound estimation approach,an ...In this study,an adaptive asymptotic tracking control problem is considered for stochastic nonlinear systems with unknown backlash-like hysteresis.By utilizing backstepping technology and bound estimation approach,an adaptive asymptotic tracking control scheme is designed,where fuzzy systems are applied to approximate unknown function terms,the effect of hysteresis and stochastic disturbances is compensated appropriately.The proposed scheme ensures that the tracking error can asymptotically converge to zero in probability and all signals of the closed-loop system are bounded almost surely.Finally,the effectiveness of the control scheme is verified by giving a simulation example.展开更多
This paper tackles the maximum correntropy Kalman filtering problem for discrete time-varying non-Gaussian systems subject to state saturations and stochastic nonlinearities.The stochastic nonlinearities,which take th...This paper tackles the maximum correntropy Kalman filtering problem for discrete time-varying non-Gaussian systems subject to state saturations and stochastic nonlinearities.The stochastic nonlinearities,which take the form of statemultiplicative noises,are introduced in systems to describe the phenomenon of nonlinear disturbances.To resist non-Gaussian noises,we consider a new performance index called maximum correntropy criterion(MCC)which describes the similarity between two stochastic variables.To enhance the“robustness”of the kernel parameter selection on the resultant filtering performance,the Cauchy kernel function is adopted to calculate the corresponding correntropy.The goal of this paper is to design a Kalman-type filter for the underlying systems via maximizing the correntropy between the system state and its estimate.By taking advantage of an upper bound on the one-step prediction error covariance,a modified MCC-based performance index is constructed.Subsequently,with the assistance of a fixed-point theorem,the filter gain is obtained by maximizing the proposed cost function.In addition,a sufficient condition is deduced to ensure the uniqueness of the fixed point.Finally,the validity of the filtering method is tested by simulating a numerical example.展开更多
A new prescribed-time state-feedback design is presented for stochastic nonlinear strictfeedback systems.Different from the existing stochastic prescribed-time design where scaling-free quartic Lyapunov functions or s...A new prescribed-time state-feedback design is presented for stochastic nonlinear strictfeedback systems.Different from the existing stochastic prescribed-time design where scaling-free quartic Lyapunov functions or scaled quadratic Lyapunov functions are used,the design is based on new scaled quartic Lyapunov functions.The designed controller can ensure that the plant has an almost surely unique strong solution and the equilibrium at the origin of the plant is prescribed-time mean-square stable.After that,the authors redesign the controller to solve the prescribed-time inverse optimal mean-square stabilization problem.The merit of the design is that the order of the scaling function in the controller is reduced dramatically,which effectively reduces the control effort.Two simulation examples are given to illustrate the designs.展开更多
The shape control of probability density function(PDF) of the system state is an important topic in stochastic systems. In this paper, we propose a control technique for PDF shape of the state variable in nonlinear st...The shape control of probability density function(PDF) of the system state is an important topic in stochastic systems. In this paper, we propose a control technique for PDF shape of the state variable in nonlinear stochastic systems. Firstly, we derive and prove the form of the controller by investigating the Fokker-PlanckKolmogorov(FPK) equation arising from the stochastic system. Secondly, an approach for getting approximate solution of the FPK equation is provided. A special function including some parameters is taken as the approximate stationary solution of the FPK equation. We use nonlinear least square method to solve the parameters in the function, and capture the approximate solution of the FPK equation. Substituting the approximate solution into the form of the controller, we can acquire the PDF shape controller. Lastly, some example simulations are conducted to verify the algorithm.展开更多
In this work,a novel shape control approach of the probability density function(PDF)for nonlinear stochastic systems is presented.First,we provide the formula for the PDF shape controller without devising the control ...In this work,a novel shape control approach of the probability density function(PDF)for nonlinear stochastic systems is presented.First,we provide the formula for the PDF shape controller without devising the control law of the controller.Then,based on the exact analytical solution of the Fokker-PlanckKolmogorov(FPK)equation,the product function of the polynomial and the exponential polynomial is regarded as the stationary PDF of the state response.To validate the performance of the proposed control approach,we compared it with the exponential polynomial method and the multi-Gaussian closure method by implementing comparative simulation experiments.The results show that the novel PDF shape control approach is effective and feasible.Using an equal number of parameters,our method can achieve a similar or better control effect as the exponential polynomial method.By comparison with the multiGaussian closure method,our method has clear advantages in PDF shape control performance.For all cases,the integral of squared error and the errors of first four moments of our proposed method were very small,indicating superior performance and promising good overall control effects of our method.The approach presented in this study provides an alternative for PDF shape control in nonlinear stochastic systems.展开更多
Using graph theory, matrix theory, adaptive control, fuzzy logic systems and other tools, this paper studies the leader-follower global consensus of two kinds of stochastic uncertain nonlinear multi-agent systems(MAS)...Using graph theory, matrix theory, adaptive control, fuzzy logic systems and other tools, this paper studies the leader-follower global consensus of two kinds of stochastic uncertain nonlinear multi-agent systems(MAS). Firstly, the fuzzy logic systems replaces the feedback compensator as the feedforward compensator to describe the uncertain nonlinear dynamics. Secondly, based on the network topology, all followers are divided into two categories: One is the followers who can obtain the leader signal, and the other is the follower who cannot obtain the leader signal. Thirdly, based on the adaptive control method, distributed control protocols are designed for the two types of followers. Fourthly, based on matrix theory and stochastic Lyapunov stability theory, the stability of the closed-loop systems is analyzed. Finally, three simulation examples are given to verify the effectiveness of the proposed control algorithms.展开更多
基金Supported by National Natural Science Foundation of P.R.China(60572070,60325311,60534010)Natural Science Foundation of Liaoning Province(20022030)
文摘The problem of track control is studied for a class of strict-feedback stochastic nonlinear systems in which unknown virtual control gain function is the main feature.First,the so-called stochastic LaSalle theory is extended to some extent,and accordingly,the results of global ultimate boundedness for stochastic nonlinear systems are developed.Next,a new design scheme of fuzzy adaptive control is proposed.The advantage of it is that it does not require priori knowledge of virtual control gain function sign,which is usually demanded in many designs.At the same time,the track performance of closed-loop systems is improved by adaptive modifying the estimated error upper bound.By theoretical analysis,the signals of closed-loop systems are globally ultimately bounded in probability and the track error converges to a small residual set around the origin in 4th-power expectation.
基金supported in part by the National Natural Science Foundation of China(62073166,61673215)the Key Laboratory of Jiangsu Province。
文摘This paper investigates the fixed-time stability theorem and state-feedback controller design for stochastic nonlinear systems.We propose an improved fixed-time Lyapunov theorem with a more rigorous and reasonable proof procedure.In particular,an important corollary is obtained,which can give a less conservative upper-bound estimate of the settling time.Based on the backstepping technique and the addition of a power integrator method,a state-feedback controller is skillfully designed for a class of stochastic nonlinear systems.It is proved that the proposed controller can render the closed-loop system fixed-time stable in probability with the help of the proposed fixed-time stability criteria.Finally,the effectiveness of the proposed controller is demonstrated by simulation examples and comparisons.
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 National Natural Science Foundation of China(61304020)
文摘This paper is concerned with the global boundedness problem for a class of stochastic nonlinear systems with matched conditions. The uncertainties in the systems are due to parameter variations and external stochastic disturbance. Only the matched conditions and the possible bound of the uncertainties are demanded. Based on the stochastic Lyapunov stability theory, an explicit controller is constructed in the gradient direction, which renders responses of the closed-loop systems be globally bounded in probability. When the systems degrade to linear systems, the controller becomes linear. Illustrative examples are given to show the effectiveness of the proposed method.
基金supported by the National Natural Science Foundation of China (60704013)the Special Foundation of East China University of Science and Technology for Youth Teacher (YH0157134)
文摘The problem of adaptive stabilization is addressed for a class of uncertain stochastic nonlinear strict-feedback systems with both unknown dead-zone and unknown gain functions.By using the backstepping method and neural network（NN） parameterization,a novel adaptive neural control scheme which contains fewer learning parameters is developed to solve the stabilization problem of such systems.Meanwhile,stability analysis is presented to guarantee that all the error variables are semi-globally uniformly ultimately bounded with desired probability in a compact set.The effectiveness of the proposed design is illustrated by simulation results.
基金Program for New Century Excellent Talents in University of China (NCET-05-0607)National Natural Science Fou-ndation of China (No.60774010)Project for Fundamental Research of Natural Sciences in Universities of Jingsu Province (No.07KJB510114)
文摘In this paper, for a class of high-order stochastic nonlinear systems with zero dynamics which are neither necessarily feedback linearizable nor affine in the control input, the problem of state feedback stabilization is investigated for the first time. Under some weaker assumptions, a smooth state feedback controller is designed, which ensures that the closed-loop system has an almost surely unique solution on [0,∞）, the equilibrium at the origin of the closed-loop system is globally asymptotically stable in probability, and all the states can be regulated to the origin almost surely. A simulation example demonstrates the control scheme.
基金supported by National Natural Science Foundation of China (No. 60774010, 10971256, and 60974028)Jiangsu"Six Top Talents" (No. 07-A-020)+2 种基金Natural Science Foundation of Jiangsu Province (No. BK2009083)Program for Fundamental Research of Natural Sciences in Universities of Jiangsu Province(No.07KJB510114)Natural Science Foundation of Xuzhou Normal University (No. 08XLB20)
文摘This paper considers a concrete stochastic nonlinear system with stochastic unmeasurable inverse dynamics. Motivated by the concept of integral input-to-state stability （iISS） in deterministic systems and stochastic input-to-state stability （SISS） in stochastic systems, a concept of stochastic integral input-to-state stability （SiISS） using Lyapunov functions is first introduced. A constructive strategy is proposed to design a dynamic output feedback control law, which drives the state to the origin almost surely while keeping all other closed-loop signals almost surely bounded. At last, a simulation is given to verify the effectiveness of the control law.
基金supported by National Natural Science Foundation of China(Nos.61573172,61305149 and 61403174)333 High-level Talents Training Program in Jiangsu Province(No.BRA2015352)Program for Fundamental Research of Natural Sciences in Universities of Jiangsu Province(No.15KJB510011)
文摘This paper considers the output tracking problem for more general classes of stochastic nonlinear systems with unknown control coefficients and driven by noise of unknown covariance. By utilizing the radial basis function neural network approximation method and backstepping technique, we successfully construct a controller to guarantee the solution process to be bounded in probability.The tracking error signal is 4th-moment semi-globally uniformly ultimately bounded（SGUUB） and can be regulated into a small neighborhood of the origin in probability. A simulation example is given to demonstrate the effectiveness of the control scheme.
基金supported by the National High Technology Research and Development Program of China(863 Program)(2014AA06A503)the National Natural Science Foundation of China(61422307,61673361)+3 种基金the Scientific Research Starting Foundation for the Returned Overseas Chinese Scholars and Ministry of Education of Chinasupports from the Youth Top-notch Talent Support Programthe 1000-talent Youth Programthe Youth Yangtze River Scholarship
文摘In this paper,we studied the approximate sampleddata observer design for a class of stochastic nonlinear systems.Euler-Maruyama approximation was investigated in this paper because it is the basis of other higher precision numerical methods,and it preserves important structures of the nonlinear systems.Also,the form of Euler-Maruyama model is simple and easy to be calculated.The results provide a reference for sampled-data observer design method for such stochastic nonlinear systems,and may be useful to many practical control applications,such as tracking control in mechanical systems.And the effectiveness of the approach is demonstrated by a simulation example.
基金supported by the National Natural Science Foundation of China(12426609,62203220,62373229)the Taishan Scholar Project Foundation of Shandong Province(tsqnz20230619,tsqn202408110)+2 种基金the Fundamental Research Foundation of the Central Universities(23Cx06024A)the Natural Science Foundation of Shandong Province(ZR2024QF096)the Outstanding Youth Innovation Team in Shandong Higher Education Institutions(2023KJ061).
文摘This paper investigates a multiplayer Pareto game for affine nonlinear stochastic systems disturbed by both external and the internal multiplicative noises.The Pareto cooperative optimal strategies with the H_(∞) constraint are resolved by integrating H_(2)/H_(∞) theory with Pareto game theory.First,a nonlinear stochastic bounded real lemma(SBRL)is derived,explicitly accounting for non-zero initial conditions.Through the analysis of four cross-coupled Hamilton-Jacobi equations(HJEs),we establish necessary and sufficient conditions for the existence of Pareto optimal strategies with the H_(∞) constraint.Secondly,to address the complexity of solving these nonlinear partial differential HJEs,we propose a neural network(NN)framework with synchronous tuning rules for the actor,critic,and disturbance components,based on a reinforcement learning(RL)approach.The designed tuning rules ensure convergence of the actor-critic-disturbance components to the desired values,enabling the realization of robust Pareto control strategies.The convergence of the proposed algorithm is rigorously analyzed using a constructed Lyapunov function for the NN weight errors.Finally,a numerical simulation example is provided to demonstrate the effectiveness of the proposed methods and main results.
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the National Natural Science Foundation of China (No.60221301, No.60428304).
文摘In this paper, the property of practical input-to-state stability and its application to stability of cascaded nonlinear systems are investigated in the stochastic framework. Firstly, the notion of （practical） stochastic input-to-state stability with respect to a stochastic input is introduced, and then by the method of changing supply functions, （a） an （practical） SISS-Lyapunov function for the overall system is obtained from the corresponding Lyapunov functions for cascaded （practical） SISS subsystems.
基金This work was partially supported by the National Science Foundation （Nos. ECCS-1230040, ECCS-1501044）.
文摘This paper presents new results on the robust global stabilization and the gain assignment problems for stochastic nonlinear systems. Three stochastic nonlinear control design schemes are developed. Furthermore, a new stochastic gain assignment method is developed for a class of uncertain interconnected stochastic nonlinear systems. This method can be combined with the nonlinear small-gain theorem to design partial-state feedback controllers for stochastic nonlinear systems. Two numerical examples are given to illustrate the effectiveness of the proposed methodology.
基金The research is supported by the National Science Foundation of Henan Educational Committee of China(No.2003110002).
文摘In this paper,a state feedback adaptive stabilization for a class of large-scale stochastic nonlinear systems is designed with Lyapunov and Backstepping method.In the systems there are uncertain terms,whose bounds are governed by a set of unknown parameters.The designed controllers would make the close-loop systems asymptotically stable and adaptive for the unknown parameters.As an application,a second order example is delivered to illustrate the approach.
基金supported in part by the Natural Science Foundation of Shandong Province for Key Projects under Grant No.ZR2020KA010in part by the National Natural Science Foundation of China under Grant No.62073187+1 种基金in part by the Major Scientific and Technological Innovation Project in Shandong Province under Grant No.2019JZZY011111“Guangyue Young Scholar Innovation Team”of Liaocheng University under Grant No.LCUGYTD2022-01。
文摘In this study,an adaptive asymptotic tracking control problem is considered for stochastic nonlinear systems with unknown backlash-like hysteresis.By utilizing backstepping technology and bound estimation approach,an adaptive asymptotic tracking control scheme is designed,where fuzzy systems are applied to approximate unknown function terms,the effect of hysteresis and stochastic disturbances is compensated appropriately.The proposed scheme ensures that the tracking error can asymptotically converge to zero in probability and all signals of the closed-loop system are bounded almost surely.Finally,the effectiveness of the control scheme is verified by giving a simulation example.
基金supported in part by the National Natural Science Foundation of China(62273088,62273087)the Shanghai Pujiang Program of China(22PJ1400400)the Program of Shanghai Academic/Technology Research Leader(20XD1420100)。
文摘This paper tackles the maximum correntropy Kalman filtering problem for discrete time-varying non-Gaussian systems subject to state saturations and stochastic nonlinearities.The stochastic nonlinearities,which take the form of statemultiplicative noises,are introduced in systems to describe the phenomenon of nonlinear disturbances.To resist non-Gaussian noises,we consider a new performance index called maximum correntropy criterion(MCC)which describes the similarity between two stochastic variables.To enhance the“robustness”of the kernel parameter selection on the resultant filtering performance,the Cauchy kernel function is adopted to calculate the corresponding correntropy.The goal of this paper is to design a Kalman-type filter for the underlying systems via maximizing the correntropy between the system state and its estimate.By taking advantage of an upper bound on the one-step prediction error covariance,a modified MCC-based performance index is constructed.Subsequently,with the assistance of a fixed-point theorem,the filter gain is obtained by maximizing the proposed cost function.In addition,a sufficient condition is deduced to ensure the uniqueness of the fixed point.Finally,the validity of the filtering method is tested by simulating a numerical example.
基金the National Natural Science Foundation of China under Grant No.61973150the Young Taishan Scholars Program of Shandong Province of China under Grant No.tsqn20161043+1 种基金Shandong Provincial Natural Science Foundation for Distinguished Young Scholars under Grant No.ZR2019JQ22Shandong Province Higher Educational Excellent Youth Innovation team under Grant No.2019KJN017。
文摘A new prescribed-time state-feedback design is presented for stochastic nonlinear strictfeedback systems.Different from the existing stochastic prescribed-time design where scaling-free quartic Lyapunov functions or scaled quadratic Lyapunov functions are used,the design is based on new scaled quartic Lyapunov functions.The designed controller can ensure that the plant has an almost surely unique strong solution and the equilibrium at the origin of the plant is prescribed-time mean-square stable.After that,the authors redesign the controller to solve the prescribed-time inverse optimal mean-square stabilization problem.The merit of the design is that the order of the scaling function in the controller is reduced dramatically,which effectively reduces the control effort.Two simulation examples are given to illustrate the designs.
基金the National Natural Science Foundation of China(No.61273127)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20116118110008)the Scientific Research Plan Projects of Shaanxi Education Department(No.12JK0524)
文摘The shape control of probability density function(PDF) of the system state is an important topic in stochastic systems. In this paper, we propose a control technique for PDF shape of the state variable in nonlinear stochastic systems. Firstly, we derive and prove the form of the controller by investigating the Fokker-PlanckKolmogorov(FPK) equation arising from the stochastic system. Secondly, an approach for getting approximate solution of the FPK equation is provided. A special function including some parameters is taken as the approximate stationary solution of the FPK equation. We use nonlinear least square method to solve the parameters in the function, and capture the approximate solution of the FPK equation. Substituting the approximate solution into the form of the controller, we can acquire the PDF shape controller. Lastly, some example simulations are conducted to verify the algorithm.
基金supported in part by the National Natural Science Foundation of China(61903298,62073259,61773016)。
文摘In this work,a novel shape control approach of the probability density function(PDF)for nonlinear stochastic systems is presented.First,we provide the formula for the PDF shape controller without devising the control law of the controller.Then,based on the exact analytical solution of the Fokker-PlanckKolmogorov(FPK)equation,the product function of the polynomial and the exponential polynomial is regarded as the stationary PDF of the state response.To validate the performance of the proposed control approach,we compared it with the exponential polynomial method and the multi-Gaussian closure method by implementing comparative simulation experiments.The results show that the novel PDF shape control approach is effective and feasible.Using an equal number of parameters,our method can achieve a similar or better control effect as the exponential polynomial method.By comparison with the multiGaussian closure method,our method has clear advantages in PDF shape control performance.For all cases,the integral of squared error and the errors of first four moments of our proposed method were very small,indicating superior performance and promising good overall control effects of our method.The approach presented in this study provides an alternative for PDF shape control in nonlinear stochastic systems.
基金supported by Natural Science Foundation of China(No.61573013)。
文摘Using graph theory, matrix theory, adaptive control, fuzzy logic systems and other tools, this paper studies the leader-follower global consensus of two kinds of stochastic uncertain nonlinear multi-agent systems(MAS). Firstly, the fuzzy logic systems replaces the feedback compensator as the feedforward compensator to describe the uncertain nonlinear dynamics. Secondly, based on the network topology, all followers are divided into two categories: One is the followers who can obtain the leader signal, and the other is the follower who cannot obtain the leader signal. Thirdly, based on the adaptive control method, distributed control protocols are designed for the two types of followers. Fourthly, based on matrix theory and stochastic Lyapunov stability theory, the stability of the closed-loop systems is analyzed. Finally, three simulation examples are given to verify the effectiveness of the proposed control algorithms.
