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Applying Sliding Mode Technique to Filter and Controller Design for Nonlinear Polynomial Stochastic Systems

  • Michael Basin
  • Pablo Rodriguez-Ramirez
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 440)

Abstract

This chapter addresses the mean-square and mean-module filtering problems for stochastic polynomial systems 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 mean-square filter generates the mean-square estimate, which has the same minimum estimation error variance as the best estimate given by the conventional mean-square polynomial 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 to the conventional polynomial mean-square filter. The theoretical results are complemented with illustrative examples verifying performance of the designed filters. It is demonstrated that the estimates produced by the designed sliding mode mean-square filter and the conventional polynomial mean-square filter yield the same estimation error variance, and there is an advantage in favor of the designed sliding mode mean-module filter. The chapter then presents the solution to the optimal controller problems for a polynomial system over linear observations with respect to a Bolza-Meyer criterion, where the integral control and state energy terms are quadratic and the non-integral term is of the first degree. The simulation results confirm an advantage in favor of the designed sliding mode controller.

Keywords

Slide Mode Control Sliding Mode Polynomial System Slide Mode Controller Estimation Error Variance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Physical and Mathematical SciencesAutonomous University of Nuevo LeonNuevo LeonMexico

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