Robust ${\cal H}_{\infty}$ Finite-Horizon Control for a Class of Stochastic Nonlinear Time-Varying Systems Subject to Sensor and Actuator Saturations

This technical note addresses the robust H∞ finite-horizon output feedback control problem for a class of uncertain discrete stochastic nonlinear time-varying systems with both sensor and actuator saturations. In the system under investigation, all the system parameters are allowed to be time-varying, the parameter uncertainties are assumed to be of the polytopic type, and the stochastic nonlinearities are described by statistical means which can cover several classes of well-studied nonlinearities. The purpose of the problem addressed is to design an output feedback controller, over a given finite-horizon, such that the H∞ disturbance attenuation level is guaranteed for the nonlinear stochastic polytopic system in the presence of saturated sensor and actuator outputs. Sufficient conditions are first established for the robust H∞ performance through intensive stochastic analysis, and then a recursive linear matrix inequality (RLMI) approach is employed to design the desired output feedback controller achieving the prescribed H∞ disturbance rejection level. Simulation results demonstrate the effectiveness of the developed controller design scheme.

[1]  Jian Chu,et al.  D-stability and D-stabilization of linear discrete time-delay systems with polytopic uncertainties , 2009, Autom..

[2]  Fernando Paganini,et al.  IEEE Transactions on Automatic Control , 2006 .

[3]  Guang-Ren Duan,et al.  H∞ filtering for multiple-time-delay measurements , 2006, IEEE Trans. Signal Process..

[4]  Jinzhi Wang,et al.  Output feedback H controller design for linear discrete-time systems with sensor nonlinearities , 2005 .

[5]  Fuwen Yang,et al.  Robust finite-horizon filtering for stochastic systems with missing measurements , 2005, IEEE Signal Processing Letters.

[6]  Shengyuan Xu,et al.  Robust control of descriptor discrete-time Markovian jump systems , 2007, Int. J. Control.

[7]  Ben M. Chen,et al.  An Output Feedback Controller Design for Linear Systems Subject to Sensor Nonlinearities , 2003 .

[8]  Lixian Zhang,et al.  H∞ estimation for discrete-time piecewise homogeneous Markov jump linear systems , 2009, Autom..

[9]  Zongli Lin,et al.  Output Feedback Stabilization of Linear Systems With Actuator Saturation , 2007, IEEE Transactions on Automatic Control.

[10]  Isaac Yaesh,et al.  H-Control and Estimation of State-multiplicative Linear Systems , 2005 .

[11]  Tingshu Hu,et al.  Control Systems with Actuator Saturation: Analysis and Design , 2001 .

[12]  Y. Huang,et al.  Stochastic H2/H8 control for discrete-time systems with state and disturbance dependent noise. , 2007 .

[13]  U. Shaked,et al.  H-infinity Control and Estimation of State-multiplicative Linear Systems , 2005 .

[14]  U. Shaked,et al.  Difference LMI'S for robust H∞ control and filtering , 2001, 2001 European Control Conference (ECC).

[15]  Yuanqing Xia,et al.  Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching , 2008, 2008 27th Chinese Control Conference.

[16]  Michael V. Basin,et al.  Central suboptimal H ∞ filter design for linear time-varying systems with state and measurement delays , 2010, Int. J. Syst. Sci..

[17]  Zongli Lin,et al.  Robust filtering for discrete-time systems with saturation and its application to transmultiplexers , 2004, IEEE Trans. Signal Process..

[18]  U. Shaked,et al.  H∞ Control for Discrete-Time Nonlinear Stochastic Systems , 2004 .

[19]  Daniel W. C. Ho,et al.  Robust H∞ control for a class of nonlinear discrete time-delay stochastic systems with missing measurements , 2009, Autom..

[20]  Peng Shi,et al.  Central Suboptimal H∞ Filter Design for Linear Time-Varying Systems with State or Measurement Delay , 2009, Circuits Syst. Signal Process..

[21]  Yulin Huang,et al.  Stochastic H2/Hinfinity control for discrete-time systems with state and disturbance dependent noise , 2007, Autom..

[22]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[23]  Fuwen Yang,et al.  Robust H∞ filtering with error variance constraints for discrete time-varying systems with uncertainty , 2003, Autom..

[24]  B Moshiri,et al.  Stochastic dynamic output feedback stabilization of uncertain stochastic state-delayed systems. , 2006, ISA transactions.

[25]  Edwin Engin Yaz,et al.  Recursive estimator for linear and nonlinear systems with uncertain observations , 1997, Signal Process..

[26]  Tingshu Hu,et al.  Control Systems with Actuator Saturation: Analysis and Design , 2001 .

[27]  Uri Shaked,et al.  H/sub /spl infin// control for discrete-time nonlinear stochastic systems , 2006, IEEE Transactions on Automatic Control.

[28]  Tingshu Hu,et al.  Analysis of linear systems in the presence of actuator saturation and I-disturbances , 2004, Autom..

[29]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[30]  Fuwen Yang,et al.  Set-membership filtering for systems with sensor saturation , 2009, Autom..

[31]  Zongli Lin,et al.  An output feedback /spl Hscr//sub /spl infin// controller design for linear systems subject to sensor nonlinearities , 2003 .

[32]  Lingjie Chen,et al.  Stability and Stabilization of a Class of Multimode Linear Discrete-Time Systems With Polytopic Uncertainties , 2009, IEEE Transactions on Industrial Electronics.

[33]  Sophie Tarbouriech,et al.  Dynamic output controller design for linear systems with actuator and sensor saturation , 2007, 2007 American Control Conference.

[34]  Liang Lu,et al.  Analysis and design of singular linear systems under actuator saturation and L2/linfintyA disturbances , 2008, Syst. Control. Lett..

[35]  Chung-Shi Tseng,et al.  Robust Fuzzy Filter Design for a Class of Nonlinear Stochastic Systems , 2007, IEEE Transactions on Fuzzy Systems.