Pareto Optimal Filter Design for Nonlinear Stochastic Fuzzy Systems via Multiobjective <inline-formula> <tex-math>$H_{\bf 2} /H_{\bm \infty}$</tex-math></inline-formula> Optimization

Abstract

This paper is concerned with the multiobjective H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filtering design problem in nonlinear signal processing, which can be approximated by a Takagi-Sugerno (T-S) fuzzy signal system. We propose a multiobjective filter design to estimate state variables from noisy measurements for nonlinear signal systems, and we focus our effort on achieving optimal concurrent performance for H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filtering. In general, it is difficult to solve the multiobjective (MO) H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> fuzzy filter problem directly, and we therefore propose an indirect approach to minimize the upper bounds and transform the MO H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filtering problem in to a linear matrix inequality (LMI)-constrained multiobjective problem (MOP). In addition, we propose an LMI-based multiobjective evolution algorithm to efficiently find Pareto optimal solutions for the MOP of multiobjective fuzzy filter design for nonlinear stochastic signal processing. Furthermore, for comparison, we also suggest the MO H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filter design problem based on the weighted sum method. Our proposed indirect method can be widely employed to practically address the MO filter design problem in nonlinear signal processing. Finally, a trajectory estimation of reentry vehicle by radar is provided to illustrate the design procedure of the Pareto MO optimal filter.