Control for a Class of Stochastic Mechanical Systems Based on the Discrete-Time Approximate Observer
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摘要
This paper investigates the observer-based control problem of a class of stochastic mechanical systems. The system is modelled as a continuous-time It o stochastic differential equation with a discrete-time output. Euler-Maruyama approximation is used to design the discrete-time approximate observer, and an observer-based feedback controller is derived such that the closed-loop nonlinear system is exponentially stable in the mean-square sense. Also, the authors analyze the convergence of observer error when the discrete-time approximate observer servers as a state observer for the exact system. Finally, a simulation example is used to demonstrate the effectiveness of the proposed method.
This paper investigates the observer-based control problem of a class of stochastic mechanical systems. The system is modelled as a continuous-time It o stochastic differential equation with a discrete-time output. Euler-Maruyama approximation is used to design the discrete-time approximate observer, and an observer-based feedback controller is derived such that the closed-loop nonlinear system is exponentially stable in the mean-square sense. Also, the authors analyze the convergence of observer error when the discrete-time approximate observer servers as a state observer for the exact system. Finally, a simulation example is used to demonstrate the effectiveness of the proposed method.
This paper investigates the observer-based control problem of a class of stochastic mechanical systems. The system is modelled as a continuous-time It o stochastic differential equation with a discrete-time output. Euler-Maruyama approximation is used to design the discrete-time approximate observer, and an observer-based feedback controller is derived such that the closed-loop nonlinear system is exponentially stable in the mean-square sense. Also, the authors analyze the convergence of observer error when the discrete-time approximate observer servers as a state observer for the exact system. Finally, a simulation example is used to demonstrate the effectiveness of the proposed method.
引文
[1]Li J G,Yuan J Q,and Lu J G,Observer-based H∞control for networked nonlinear systems with random packet losses,ISA transactions,2010,49(1):39-46.
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[8]Wu Z J,Yang J,and Shi P,Adaptive tracking for stochastic nonlinear systems with markovian switching,IEEE Transactions on Automatic Control,2010,55(9):2135-2141.
[9]Xian B,Queiroz M S,Dawson D M,et al.,A discontinuous output feedback controller and velocity observer for nonlinear mechanical systems,Automatica,2004,40(4):695-700.
[10]Driessen B J,Observer/controller with global practical stability for tracking in robots without velocity measurement,Asian Journal of Control,2015,17(5):1898-1913.
[11]Wang Z,Yang F,Ho D W,et al.,Robust H∞control for networked systems with random packet losses,IEEE Transactions on Systems,Man,and Cybernetics,Part B(Cybernetics),2007,37(4):916-924.
[12]Arcak M and NeˇsI′c D,A framework for nonlinear sampled-data observer design via approximate discrete-time models and emulation,Automatica,2004,40(11):1931-1938.
[13]Jin H,Yin B,Ling Q,et al.,Sampled-data observer design for nonlinear autonomous systems,Control and Decision Conference,2009,CCDC 09,Chinese,2009,1516-1520.
[14]Katayama H and Aoki H,Straight-line trajectory tracking control for sampled-data underactuated ships,IEEE Transactions on Control Systems Technology,2014,22(4):1638-1645.
[15]Beikzadeh H and Marquez H J,Multirate observers for nonlinear sampled-data systems using input-to-state stability and discrete-time approximation,IEEE Transactions on Automatic Control,2014,59(9):2469-2474.
[16]Yang S M and Ke S J,Performance evaluation of a velocity observer for accurate velocity estimation of servo motor drives,IEEE Transactions on Industry Applications,2000,36(1):98-104.
[17]Fossen T I,Marine Control Systems:Guidance,Navigation and Control of Ships,Rigs and Underwater Vehicles,Marine Cybernetics,Norway,2002.
[18]Oksendal B,Stochastic Differential Equations:An Introduction with Applications,Springer Science&Business Media,New York,2013.
[19]Xie L and Khargonekar P P,Lyapunov-based adaptive state estimation for a class of nonlinear stochastic systems,Automatica,2012,48(7):1423-1431.
[20]Miao X and Li L,Adaptive observer-based control for a class of nonlinear stochastic systems,International Journal of Computer Mathematics,2015,92(11):2251-2260.
[21]Cheng Y and Xie D,Distributed observer design for bounded tracking control of leader-follower multi-agent systems in a sampled-data setting,International Journal of Control,2014,87(1):41-51.
[22]Katayama H and Aoki H,Straight-line trajectory tracking control for sampled-data underactuated ships,IEEE Transactions on Control Systems Technology,2014,22(4):1638-1645.
[23]Beikzadeh H and Marquez H J,Multirate observers for nonlinear sampled-data systems using input-to-state stability and discrete-time approximation,IEEE Transactions on Automatic Control,2014,59(9):2469-2474.
[24]Dani A P,Chung S J,and Hutchinson S,Observer design for stochastic nonlinear systems via contraction-based incremental stability,IEEE Transactions on Automatic Control,2015,60(3):700-714.
[2]Gao Z and Shi X,Observer-based controller design for stochastic descriptor systems with brownian motions,Automatica,2013,49(7):2229-2235.
[3]Chen W and Li X,Observer-based consensus of second-order multi-agent system with fixed and stochastically switching topology via sampled data,International Journal of Robust and Nonlinear Control,2014,24(3):567-584.
[4]Ibrir S,Circle-criterion approach to discrete-time nonlinear observer design,Automatica,2007,43(8):1432-1441.
[5]Zemouche A and Boutayeb M,On LMI conditions to design observers for Lipschitz nonlinear systems,Automatica,2013,49(2):585-591.
[6]Barbata A,Zasadzinski M,Ali H S,et al.,Exponential observer for a class of one-sided lipschitz stochastic nonlinear systems,IEEE Transactions on Automatic Control,2015,60(1):259-264.
[7]Benallouch M,Boutayeb M,and Zasadzinski M,Observer design for one-sided lipschitz discretetime systems,Systems&Control Letters,2012,61(9):879-886.
[8]Wu Z J,Yang J,and Shi P,Adaptive tracking for stochastic nonlinear systems with markovian switching,IEEE Transactions on Automatic Control,2010,55(9):2135-2141.
[9]Xian B,Queiroz M S,Dawson D M,et al.,A discontinuous output feedback controller and velocity observer for nonlinear mechanical systems,Automatica,2004,40(4):695-700.
[10]Driessen B J,Observer/controller with global practical stability for tracking in robots without velocity measurement,Asian Journal of Control,2015,17(5):1898-1913.
[11]Wang Z,Yang F,Ho D W,et al.,Robust H∞control for networked systems with random packet losses,IEEE Transactions on Systems,Man,and Cybernetics,Part B(Cybernetics),2007,37(4):916-924.
[12]Arcak M and NeˇsI′c D,A framework for nonlinear sampled-data observer design via approximate discrete-time models and emulation,Automatica,2004,40(11):1931-1938.
[13]Jin H,Yin B,Ling Q,et al.,Sampled-data observer design for nonlinear autonomous systems,Control and Decision Conference,2009,CCDC 09,Chinese,2009,1516-1520.
[14]Katayama H and Aoki H,Straight-line trajectory tracking control for sampled-data underactuated ships,IEEE Transactions on Control Systems Technology,2014,22(4):1638-1645.
[15]Beikzadeh H and Marquez H J,Multirate observers for nonlinear sampled-data systems using input-to-state stability and discrete-time approximation,IEEE Transactions on Automatic Control,2014,59(9):2469-2474.
[16]Yang S M and Ke S J,Performance evaluation of a velocity observer for accurate velocity estimation of servo motor drives,IEEE Transactions on Industry Applications,2000,36(1):98-104.
[17]Fossen T I,Marine Control Systems:Guidance,Navigation and Control of Ships,Rigs and Underwater Vehicles,Marine Cybernetics,Norway,2002.
[18]Oksendal B,Stochastic Differential Equations:An Introduction with Applications,Springer Science&Business Media,New York,2013.
[19]Xie L and Khargonekar P P,Lyapunov-based adaptive state estimation for a class of nonlinear stochastic systems,Automatica,2012,48(7):1423-1431.
[20]Miao X and Li L,Adaptive observer-based control for a class of nonlinear stochastic systems,International Journal of Computer Mathematics,2015,92(11):2251-2260.
[21]Cheng Y and Xie D,Distributed observer design for bounded tracking control of leader-follower multi-agent systems in a sampled-data setting,International Journal of Control,2014,87(1):41-51.
[22]Katayama H and Aoki H,Straight-line trajectory tracking control for sampled-data underactuated ships,IEEE Transactions on Control Systems Technology,2014,22(4):1638-1645.
[23]Beikzadeh H and Marquez H J,Multirate observers for nonlinear sampled-data systems using input-to-state stability and discrete-time approximation,IEEE Transactions on Automatic Control,2014,59(9):2469-2474.
[24]Dani A P,Chung S J,and Hutchinson S,Observer design for stochastic nonlinear systems via contraction-based incremental stability,IEEE Transactions on Automatic Control,2015,60(3):700-714.