The maximum principle for fully coupled forward-backward stochastic control system in the global form is proved, under the assumption that the forward diffusion coefficient does not contain the control variable, but t...The maximum principle for fully coupled forward-backward stochastic control system in the global form is proved, under the assumption that the forward diffusion coefficient does not contain the control variable, but the control domain is not necessarily convex.展开更多
The optimal control of the partially observable stochastic system at the risk-sensitive cost is considered in this paper. The system dynamics has a general correlation between system and measurement noise. And the ris...The optimal control of the partially observable stochastic system at the risk-sensitive cost is considered in this paper. The system dynamics has a general correlation between system and measurement noise. And the risk-sensitive cost contains a general quadratic term (with cross terms and extra linear terms). The explicit solution of such a problem is presented here using the output feedback control method. This clean and direct derivation enables one to convert such partial observable problems into the equivalent complete observable control problems and use the routine ways to solve them.展开更多
A new fault tolerant control（FTC） via a controller reconfiguration approach for general stochastic nonlinear systems is studied.Different from the formulation of classical FTC methods,it is supposed that the measure...A new fault tolerant control（FTC） via a controller reconfiguration approach for general stochastic nonlinear systems is studied.Different from the formulation of classical FTC methods,it is supposed that the measured information for the FTC is the probability density functions（PDFs） of the system output rather than its measured value.A radial basis functions（RBFs） neural network technique is proposed so that the output PDFs can be formulated in terms of the dynamic weighings of the RBFs neural network.As a result,the nonlinear FTC problem subject to dynamic relation between the input and the output PDFs can be transformed into a nonlinear FTC problem subject to dynamic relation between the control input and the weights of the RBFs neural network approximation to the output PDFs.The FTC design consists of two steps.The first step is fault detection and diagnosis（FDD）,which can produce an alarm when there is a fault in the system and also locate which component has a fault.The second step is to adapt the controller to the faulty case so that the system is able to achieve its target.A linear matrix inequality（LMI） based feasible FTC method is applied such that the fault can be detected and diagnosed.An illustrated example is included to demonstrate the efficiency of the proposed algorithm,and satisfactory results have been obtained.展开更多
The problem of robust H_∞ control for uncertain neutral stochastic systems with time-varying delay is discussed.The parameter uncertaintie is assumed to be time varying norm-bounded.First,the stochastic robust stabil...The problem of robust H_∞ control for uncertain neutral stochastic systems with time-varying delay is discussed.The parameter uncertaintie is assumed to be time varying norm-bounded.First,the stochastic robust stabilization of the stochastic system without disturbance input is investigated by nonlinear matrix inequality method.Then,a full-order stochastic dynamic output feedback controller is designed by solving a bilinear matrix inequality（BMI）,which ensures a prescribed stochastic robust H_∞ performance level for the resulting closed-loop system with nonzero disturbance input and for all admissible uncertainties.An illustrative example is provided to show the feasibility of the controller and the potential of the proposed technique.展开更多
To study the design problem of robust reliable guaranteed cost controller for nonlinear singular stochastic systems, the Takagi-Sugeno （T-S） fuzzy model is used to represent a nonlinear singular stochastic system wi...To study the design problem of robust reliable guaranteed cost controller for nonlinear singular stochastic systems, the Takagi-Sugeno （T-S） fuzzy model is used to represent a nonlinear singular stochastic system with norm-bounded parameter uncertainties and time delay. Based on the linear matrix inequality （LMI） techniques and stability theory of stochastic differential equations, a stochastic Lyapunov function method is adopted to design a state feedback fuzzy controller. The resulting closed-loop fuzzy system is robustly reliable stochastically stable, and the corresponding quadratic cost function is guaranteed to be no more than a certain upper bound for all admissible uncertainties, as well as different actuator fault cases. A sufficient condition of existence and design method of robust reliable guaranteed cost controller is presented. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed method.展开更多
A novel strategy of probability density function （PDF） shape control is proposed in stochastic systems. The control er is designed whose parameters are optimal y obtained through the improved particle swarm optimiza...A novel strategy of probability density function （PDF） shape control is proposed in stochastic systems. The control er is designed whose parameters are optimal y obtained through the improved particle swarm optimization algorithm. The parameters of the control er are viewed as the space position of a particle in particle swarm optimization algorithm and updated continual y until the control er makes the PDF of the state variable as close as possible to the expected PDF. The proposed PDF shape control technique is compared with the equivalent linearization technique through simulation experiments. The results show the superiority and the effectiveness of the proposed method. The control er is excellent in making the state PDF fol ow the expected PDF and has the very smal error between the state PDF and the expected PDF, solving the control problem of the PDF shape in stochastic systems effectively.展开更多
This paper develops the mean-square exponential input-to-state stability（exp-ISS） of the Euler-Maruyama（EM） method for stochastic delay control systems（SDCSs）.The definition of mean-square exp-ISS of numerical m...This paper develops the mean-square exponential input-to-state stability（exp-ISS） of the Euler-Maruyama（EM） method for stochastic delay control systems（SDCSs）.The definition of mean-square exp-ISS of numerical methods is established.The conditions of the exact and EM method for an SDCS with the property of mean-square exp-ISS are obtained without involving control Lyapunov functions or functional.Under the global Lipschitz coefficients and mean-square continuous measurable inputs,it is proved that the mean-square exp-ISS of an SDCS holds if and only if that of the EM method is preserved for a sufficiently small step size.The proposed results are evaluated by using numerical experiments to show their effectiveness.展开更多
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...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
A novel non-contact spacecraft architecture with the extended stochastic state observer for disturbance rejection control of the gravity satellite is proposed.First,the precise linear driving non-contact voice-coil ac...A novel non-contact spacecraft architecture with the extended stochastic state observer for disturbance rejection control of the gravity satellite is proposed.First,the precise linear driving non-contact voice-coil actuators are used to separate the whole spacecraft into the non-contact payload module and the service module,and to build an ideal loop with precise dynamics for disturbance rejection control of the payload module.Second,an extended stochastic state observer is enveloped to construct the overall nonlinear external terms and the internal coupled terms of the payload module,enabling the controller design of the payload module turned into the linear form with simple bandwidth-parameterization tuning in the frequency domain.As a result,the disturbance rejection control of the payload module can be explicitly achieved in a timely manner without complicated tuning in actual implementation.Finally,an extensive numerical simulation is conducted to validate the feasibility and effectiveness of the proposed approach.展开更多
This paper proposes a predictive compensation strategy to reduce the detrimental effect of stochastic time delays induced by communication networks on control performance. Values of a manipulated variable at the prese...This paper proposes a predictive compensation strategy to reduce the detrimental effect of stochastic time delays induced by communication networks on control performance. Values of a manipulated variable at the present sampling instant and future time instants can be determined by performing a receding horizon optimal procedure only once. When the present value of the manipulated variable does not arrive at a smart actuator, its predictive one is imposed to the corresponding process. Switching of a manipulated variable between its true present value and the predictive one usually results in unsmooth operation of a control system. This paper shows: 1) for a steady process,as long as its input is sufficiently smooth, the smoothness of its output can be guaranteed; 2) a manipulated variable can be switched smoothly by filtering the manipulated variable just using a simple low-pass filter. Thus the control performance can be improved. Finally, the effectiveness of the proposed method is demonstrated by simulation study.展开更多
A robust dissipative control problem for a class of It-type stochastic systems is discussed with Markovian jumping parameters and time-varying delay. A memoryless state feedback dissipative controller is developed bas...A robust dissipative control problem for a class of It-type stochastic systems is discussed with Markovian jumping parameters and time-varying delay. A memoryless state feedback dissipative controller is developed based on Lyapunov-Krasovskii functional approach such that the closed-loop system is robustly stochastically stable and weakly delay-dependent （RSSWDD） and strictly （Q, S, R）-dissipative. The sufficient condition on the existence of state feedback dissipative controller is presented by linear matrix inequality （LMI）. And the desired controller can be concluded as solving a set of LMI. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach.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, stochastic stabilization is investigated by max-plus algebra for a Markovian jump cloud control system with a reference signal. For the Markovian jump cloud control system, there exists framework adjust...In this paper, stochastic stabilization is investigated by max-plus algebra for a Markovian jump cloud control system with a reference signal. For the Markovian jump cloud control system, there exists framework adjustment whose evolution is satisfied with a Markov chain. Using max-plus algebra, a maxplus stochastic system is used to describe the Markovian jump cloud control system. A causal feedback matrix is obtained by exponential stability analysis for a causal feedback controller of the Markovian jump cloud control system. A sufficient condition is given to ensure existence on the causal feedback matrix of the causal feedback controller. Based on the causal feedback controller, stochastic stabilization in probability is analyzed for the Markovian jump cloud control system with a reference signal.Simulation results are given to show effectiveness of the causal feedback controller for the Markovian jump cloud control system.展开更多
The H∞-control problem of stochastic systems with time-delay is considered. The sufficient conditions are obtained, under which there are always state-feedback control and dynamic output-feedback control so that the ...The H∞-control problem of stochastic systems with time-delay is considered. The sufficient conditions are obtained, under which there are always state-feedback control and dynamic output-feedback control so that the resulting closed-loop system is internaly stable and L2 input-output stable in the sense of expectation. Furthermore, the explicit formulas of both kinds of controls are derived. An example is included to illustrate the correctness of theoretic results.展开更多
The paper presents an output feedback controller design method for high-order servo system with the constraints of multiple indices by using satisfactory control theory. The control strategy is to convert transfer-fun...The paper presents an output feedback controller design method for high-order servo system with the constraints of multiple indices by using satisfactory control theory. The control strategy is to convert transfer-function form of two-loop servo system into state-space form and assign the system poles in the specified region and H_∞ attenuation degree in the given range with the Riccati matrix inequality so that the closed-loop system has good dynamics and robust quality. A numeric example is given to show the effectiveness of the proposed approach.展开更多
This paper summarizes recent progress by the authors in developing two solution frameworks for dual control. The first solution framework considers a class of dual control problems where there exists a parameter uncer...This paper summarizes recent progress by the authors in developing two solution frameworks for dual control. The first solution framework considers a class of dual control problems where there exists a parameter uncertainty in the observation equation of the LQG problem. An analytical active dual control law is derived by a variance minimization approach. The issue of how to determine an optimal degree of active learning is then addressed, thus achieving an optimality for this class of dual control problems. The second solution framework considers a general class of discrete-time LQG problems with unknown parameters in both state and observation equations. The best possible (partial) closed-loop feedback control law is derived by exploring the future nominal posterior probabilities, thus taking into account the effect of future learning when constructing the optimal nominal dual control.展开更多
基金Supported by National Natural Science Foundation of P.R.China (10371067) the Youth Teacher Foundation of Fok Ying Tung Education Foundation (91064)New Century Excellent Young Teachers Foundation of P. R. China (NCEF-04-0633)
文摘The maximum principle for fully coupled forward-backward stochastic control system in the global form is proved, under the assumption that the forward diffusion coefficient does not contain the control variable, but the control domain is not necessarily convex.
基金Supported by National Natural Science Foundation of China(10571036)the Key Discipline Development Program of Beijing Municipal Commission (XK100080537)
基金This project was supported by the National Natural Science Foundation of China(60004005)the Excellent Young Teacher Program of MOE.
文摘The optimal control of the partially observable stochastic system at the risk-sensitive cost is considered in this paper. The system dynamics has a general correlation between system and measurement noise. And the risk-sensitive cost contains a general quadratic term (with cross terms and extra linear terms). The explicit solution of such a problem is presented here using the output feedback control method. This clean and direct derivation enables one to convert such partial observable problems into the equivalent complete observable control problems and use the routine ways to solve them.
基金supported by the UK Leverhulme Trust (F/00 120/BC)the National Natural Science Foundation of China (6082800760974029)
文摘A new fault tolerant control（FTC） via a controller reconfiguration approach for general stochastic nonlinear systems is studied.Different from the formulation of classical FTC methods,it is supposed that the measured information for the FTC is the probability density functions（PDFs） of the system output rather than its measured value.A radial basis functions（RBFs） neural network technique is proposed so that the output PDFs can be formulated in terms of the dynamic weighings of the RBFs neural network.As a result,the nonlinear FTC problem subject to dynamic relation between the input and the output PDFs can be transformed into a nonlinear FTC problem subject to dynamic relation between the control input and the weights of the RBFs neural network approximation to the output PDFs.The FTC design consists of two steps.The first step is fault detection and diagnosis（FDD）,which can produce an alarm when there is a fault in the system and also locate which component has a fault.The second step is to adapt the controller to the faulty case so that the system is able to achieve its target.A linear matrix inequality（LMI） based feasible FTC method is applied such that the fault can be detected and diagnosed.An illustrated example is included to demonstrate the efficiency of the proposed algorithm,and satisfactory results have been obtained.
基金supported by the National Natural Science Foundation of China(607404306646087403160904060)
文摘The problem of robust H_∞ control for uncertain neutral stochastic systems with time-varying delay is discussed.The parameter uncertaintie is assumed to be time varying norm-bounded.First,the stochastic robust stabilization of the stochastic system without disturbance input is investigated by nonlinear matrix inequality method.Then,a full-order stochastic dynamic output feedback controller is designed by solving a bilinear matrix inequality（BMI）,which ensures a prescribed stochastic robust H_∞ performance level for the resulting closed-loop system with nonzero disturbance input and for all admissible uncertainties.An illustrative example is provided to show the feasibility of the controller and the potential of the proposed technique.
基金the National Natural Science Foundation of China (60574088,60274014).
文摘To study the design problem of robust reliable guaranteed cost controller for nonlinear singular stochastic systems, the Takagi-Sugeno （T-S） fuzzy model is used to represent a nonlinear singular stochastic system with norm-bounded parameter uncertainties and time delay. Based on the linear matrix inequality （LMI） techniques and stability theory of stochastic differential equations, a stochastic Lyapunov function method is adopted to design a state feedback fuzzy controller. The resulting closed-loop fuzzy system is robustly reliable stochastically stable, and the corresponding quadratic cost function is guaranteed to be no more than a certain upper bound for all admissible uncertainties, as well as different actuator fault cases. A sufficient condition of existence and design method of robust reliable guaranteed cost controller is presented. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed method.
基金supported by the National Natural Science Fundation of China(61273127)the Specialized Research Fund of the Doctoral Program in Higher Education(20106118110009+2 种基金20116118110008)the Scientific Research Plan Projects of Shaanxi Education Department(12JK0524)the Young Teachers Scientific Research Fund of Xi’an University of Posts and Telecommunications(1100434)
文摘A novel strategy of probability density function （PDF） shape control is proposed in stochastic systems. The control er is designed whose parameters are optimal y obtained through the improved particle swarm optimization algorithm. The parameters of the control er are viewed as the space position of a particle in particle swarm optimization algorithm and updated continual y until the control er makes the PDF of the state variable as close as possible to the expected PDF. The proposed PDF shape control technique is compared with the equivalent linearization technique through simulation experiments. The results show the superiority and the effectiveness of the proposed method. The control er is excellent in making the state PDF fol ow the expected PDF and has the very smal error between the state PDF and the expected PDF, solving the control problem of the PDF shape in stochastic systems effectively.
基金supported by the National Natural Science Foundation of China(6127312660904032)the Natural Science Foundation of Guangdong Province(10251064101000008)
文摘This paper develops the mean-square exponential input-to-state stability（exp-ISS） of the Euler-Maruyama（EM） method for stochastic delay control systems（SDCSs）.The definition of mean-square exp-ISS of numerical methods is established.The conditions of the exact and EM method for an SDCS with the property of mean-square exp-ISS are obtained without involving control Lyapunov functions or functional.Under the global Lipschitz coefficients and mean-square continuous measurable inputs,it is proved that the mean-square exp-ISS of an SDCS holds if and only if that of the EM method is preserved for a sufficiently small step size.The proposed results are evaluated by using numerical experiments to show their effectiveness.
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 by the National Natural Science Foundation of China(5170532751805329)+1 种基金Fundamental Research Funds for the Central Universities of China(NS2020065)the Natural Science Foundation of Shanghai(19ZR1453300).
文摘A novel non-contact spacecraft architecture with the extended stochastic state observer for disturbance rejection control of the gravity satellite is proposed.First,the precise linear driving non-contact voice-coil actuators are used to separate the whole spacecraft into the non-contact payload module and the service module,and to build an ideal loop with precise dynamics for disturbance rejection control of the payload module.Second,an extended stochastic state observer is enveloped to construct the overall nonlinear external terms and the internal coupled terms of the payload module,enabling the controller design of the payload module turned into the linear form with simple bandwidth-parameterization tuning in the frequency domain.As a result,the disturbance rejection control of the payload module can be explicitly achieved in a timely manner without complicated tuning in actual implementation.Finally,an extensive numerical simulation is conducted to validate the feasibility and effectiveness of the proposed approach.
基金Supported by National High Technology Research and Development Program of P. R. China (2002AA412510)National Natural Science Foundation of P. R. China (60274034)
文摘This paper proposes a predictive compensation strategy to reduce the detrimental effect of stochastic time delays induced by communication networks on control performance. Values of a manipulated variable at the present sampling instant and future time instants can be determined by performing a receding horizon optimal procedure only once. When the present value of the manipulated variable does not arrive at a smart actuator, its predictive one is imposed to the corresponding process. Switching of a manipulated variable between its true present value and the predictive one usually results in unsmooth operation of a control system. This paper shows: 1) for a steady process,as long as its input is sufficiently smooth, the smoothness of its output can be guaranteed; 2) a manipulated variable can be switched smoothly by filtering the manipulated variable just using a simple low-pass filter. Thus the control performance can be improved. Finally, the effectiveness of the proposed method is demonstrated by simulation study.
基金Supported by National Basic Research Program of China （973 Program） （2007CB814904）, National Natural Science Foundation of China （10671112, 10701050）, and Natural Science Foundation of Shandong Province （Z2006A01）
基金supported in part by the National Natural Science Foundation of China (60874045 60904030)+1 种基金the Foundation of the Education Bureau of Jiangsu Province (09KJB510019)the Natural Science Foundation of Jiangsu Province (BK2009184)
文摘A robust dissipative control problem for a class of It-type stochastic systems is discussed with Markovian jumping parameters and time-varying delay. A memoryless state feedback dissipative controller is developed based on Lyapunov-Krasovskii functional approach such that the closed-loop system is robustly stochastically stable and weakly delay-dependent （RSSWDD） and strictly （Q, S, R）-dissipative. The sufficient condition on the existence of state feedback dissipative controller is presented by linear matrix inequality （LMI）. And the desired controller can be concluded as solving a set of LMI. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach.
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supported by the National Natural Science Foundation of China (61973230)Tianjin Research Innovation Project for Postgraduate Students (2021YJSO2S03)。
文摘In this paper, stochastic stabilization is investigated by max-plus algebra for a Markovian jump cloud control system with a reference signal. For the Markovian jump cloud control system, there exists framework adjustment whose evolution is satisfied with a Markov chain. Using max-plus algebra, a maxplus stochastic system is used to describe the Markovian jump cloud control system. A causal feedback matrix is obtained by exponential stability analysis for a causal feedback controller of the Markovian jump cloud control system. A sufficient condition is given to ensure existence on the causal feedback matrix of the causal feedback controller. Based on the causal feedback controller, stochastic stabilization in probability is analyzed for the Markovian jump cloud control system with a reference signal.Simulation results are given to show effectiveness of the causal feedback controller for the Markovian jump cloud control system.
基金Supported by National Natural Science Foundation of China （10671112）, National Basic Research Program of China （973 Program） （2007CB814904）, the Natural Science Foundation of Shandong Province （Z2006A01）, and the Chinese New Century Young Teachers Program The authors would like to thank the referees for a careful reading of this paper and helpful suggestions which made the revised version more readable.
文摘The H∞-control problem of stochastic systems with time-delay is considered. The sufficient conditions are obtained, under which there are always state-feedback control and dynamic output-feedback control so that the resulting closed-loop system is internaly stable and L2 input-output stable in the sense of expectation. Furthermore, the explicit formulas of both kinds of controls are derived. An example is included to illustrate the correctness of theoretic results.
文摘The paper presents an output feedback controller design method for high-order servo system with the constraints of multiple indices by using satisfactory control theory. The control strategy is to convert transfer-function form of two-loop servo system into state-space form and assign the system poles in the specified region and H_∞ attenuation degree in the given range with the Riccati matrix inequality so that the closed-loop system has good dynamics and robust quality. A numeric example is given to show the effectiveness of the proposed approach.
基金the Research Grants Council of Hong Kong, P.R.China under Grant CUHK 4180/03E
文摘This paper summarizes recent progress by the authors in developing two solution frameworks for dual control. The first solution framework considers a class of dual control problems where there exists a parameter uncertainty in the observation equation of the LQG problem. An analytical active dual control law is derived by a variance minimization approach. The issue of how to determine an optimal degree of active learning is then addressed, thus achieving an optimality for this class of dual control problems. The second solution framework considers a general class of discrete-time LQG problems with unknown parameters in both state and observation equations. The best possible (partial) closed-loop feedback control law is derived by exploring the future nominal posterior probabilities, thus taking into account the effect of future learning when constructing the optimal nominal dual control.
