Sliding-Mode Filter Design for Linear Systems With Unmeasured States

This paper addresses the mean-square and mean-module filtering problems for a linear system with Gaussian white noises. The obtained solutions contain a sliding-mode term, signum of the innovation process. It is shown that the designed sliding-mode mean-square filter generates the mean-square estimate, which has the same minimum estimation-error variance as the best estimate given by the classical Kalman-Bucy filter, although the gain matrices of both filters are different. The designed sliding-mode mean-module filter generates the mean-module estimate, which yields a better value of the mean-module criterion in comparison with the mean-square Kalman-Bucy filter. The theoretical result is complemented with an illustrative example verifying the performance of the designed filters. It is demonstrated that the estimates produced by the designed sliding-mode mean-square filter and the Kalman-Bucy filter yield the same estimation-error variance, and there is an advantage in favor of the designed sliding-mode mean-module filter.

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

[2]  Yuanqing Xia,et al.  Robust Sliding-Mode Control for Uncertain Time-Delay Systems Based on Delta Operator , 2009, IEEE Transactions on Industrial Electronics.

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

[4]  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..

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

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

[7]  Alexander G. Loukianov,et al.  Multimachine Power-System Control: Integral-SM Approach , 2009, IEEE Transactions on Industrial Electronics.

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

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

[10]  Saeid Habibi,et al.  Parameter Identification for a High-Performance Hydrostatic Actuation System Using the Variable Structure Filter Concept , 2007 .

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

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

[13]  Okyay Kaynak,et al.  A Grey System Modeling Approach for Sliding-Mode Control of Antilock Braking System , 2009, IEEE Transactions on Industrial Electronics.

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

[15]  S. Habibi,et al.  The Variable Structure Filter , 2003 .

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

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

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

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

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

[21]  Tianyou Chai,et al.  Neural-Network-Based Terminal Sliding-Mode Control of Robotic Manipulators Including Actuator Dynamics , 2009, IEEE Transactions on Industrial Electronics.

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

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

[24]  Christopher Edwards,et al.  Sliding mode control : theory and applications , 1998 .

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

[26]  Mohamed S. Zaky,et al.  Wide-Speed-Range Estimation With Online Parameter Identification Schemes of Sensorless Induction Motor Drives , 2009, IEEE Transactions on Industrial Electronics.

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

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

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

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

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

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

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

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

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

[36]  Yuanqing Xia,et al.  Robust delay-dependent sliding mode control for uncertain time-delay systems , 2008 .

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

[38]  Michael Basin,et al.  Sliding mode mean-module filtering for linear stochastic systems , 2010, 2010 IEEE International Conference on Industrial Technology.

[39]  Vadim I. Utkin,et al.  Simultaneous State and Parameter Estimation in Induction Motors Using First- and Second-Order Sliding Modes , 2009, IEEE Transactions on Industrial Electronics.

[40]  Kouhei Ohnishi,et al.  Infinite-Mode Networks for Motion Control , 2009, IEEE Transactions on Industrial Electronics.