Sliding mode mean-module filtering for linear stochastic systems

This paper addresses the mean-module filtering problem for a linear system with Gaussian white noises. The obtained solution contains a sliding mode term, signum of the innovations process. It is shown that the designed sliding mode filter generates the mean-module estimate, which yields a better value of the mean-module criterion in comparison to the mean-square Kalman-Bucy filter. To the best of our knowledge, this is the first designed sliding mode filter that is optimal with respect to the mean-module criterion. The theoretical result is complemented with an illustrative example verifying performance of the designed filter, which is compared to the conventional Kalman-Bucy filter. The simulation results confirm an advantage in favor of the designed sliding mode filter.

[1]  Przemyslaw Ignaciuk,et al.  Linear Quadratic Optimal Discrete-Time Sliding-Mode Controller for Connection-Oriented Communication Networks , 2008, IEEE Transactions on Industrial Electronics.

[2]  Xinghuo Yu,et al.  ZOH Discretization Effect on Higher-Order Sliding-Mode Control Systems , 2008, IEEE Transactions on Industrial Electronics.

[3]  Liu Hsu,et al.  Design of First-Order Approximation Filters for Sliding-Mode Control of Uncertain Systems , 2008, IEEE Transactions on Industrial Electronics.

[4]  Christopher Edwards,et al.  Adaptive Sliding-Mode-Observer-Based Fault Reconstruction for Nonlinear Systems With Parametric Uncertainties , 2008, IEEE Transactions on Industrial Electronics.

[5]  Engin Yaz,et al.  Sliding-Mode Adaptive Observer Approach to Chaotic Synchronization , 2000 .

[6]  Michael Basin,et al.  Optimal and robust integral sliding mode filter design for systems with continuous and delayed measurements , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[7]  Sarah K. Spurgeon,et al.  Sliding mode observers: a survey , 2008, Int. J. Syst. Sci..

[8]  K. Åström.  Introduction to Stochastic Control Theory , 1970 .

[9]  Vadim I. Utkin,et al.  Sliding mode control in electromechanical systems , 1999 .

[10]  Han Ho Choi.  Sliding-Mode Output Feedback Control Design , 2008, IEEE Transactions on Industrial Electronics.

[11]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[12]  Katsuhisa Furuta,et al.  VS-CONTROL WITH TIME-VARYING SLIDING SECTOR — DESIGN AND APPLICATION TO PENDULUM — , 2008 .

[13]  Vadim I. Utkin,et al.  Sliding Modes in Control and Optimization , 1992, Communications and Control Engineering Series.

[14]  Leonid M. Fridman,et al.  Analysis and design of integral sliding manifolds for systems with unmatched perturbations , 2006, IEEE Transactions on Automatic Control.

[15]  R. E. Kalman,et al.  New Results in Linear Filtering and Prediction Theory , 1961 .

[16]  Michael Basin,et al.  Integral sliding mode design for robust filtering and control of linear stochastic time‐delay systems , 2005 .

[17]  Yuri B. Shtessel,et al.  Higher order sliding modes , 2008 .

[18]  Antonella Ferrara,et al.  On second order sliding mode controllers , 1998 .

[19]  James Lam,et al.  Robust integral sliding mode control for uncertain stochastic systems with time-varying delay , 2005, Autom..

[20]  Yuanqing Xia,et al.  On designing of sliding-mode control for stochastic jump systems , 2006, IEEE Transactions on Automatic Control.

[21]  Leonid M. Fridman,et al.  Analysis of Chattering in Systems With Second-Order Sliding Modes , 2007, IEEE Transactions on Automatic Control.

[22]  V. Utkin,et al.  Integral sliding mode in systems operating under uncertainty conditions , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[23]  Yuanqing Xia,et al.  Robust sliding-mode control for uncertain time-delay systems: an LMI approach , 2003, IEEE Trans. Autom. Control..

[24]  Y. Shtessel,et al.  Output feedback tracking in causal nonminimum-phase nonlinear systems using HOSM techniques , 2008, 2008 International Workshop on Variable Structure Systems.

[25]  Jeang-Lin Chang.  Robust Discrete-Time Model Reference Sliding-Mode Controller Design With State and Disturbance Estimation , 2008, IEEE Transactions on Industrial Electronics.

[26]  V. Pugachev,et al.  Stochastic Systems: Theory and Applications , 2002 .

[27]  Antonella Ferrara,et al.  Sliding mode optimal regulator for a bolza-meyer criterion with non-quadratic state energy terms , 2009, 2009 American Control Conference.

[28]  Antonella Ferrara,et al.  Sliding mode regulator as solution to optimal control problem , 2008, 2008 47th IEEE Conference on Decision and Control.