Abstract
This paper is concerned with the multiobjective H2/H∞ filtering design problem in nonlinear signal processing which can be approximated by a Takagi-Sugerno (T-S) fuzzy signal system. We propose a multi-objective filter design to estimate state variables from noisy measurements for nonlinear signal systems, and we focus our effort on achieving optimal concurrent performance for H2 and H∞ filtering. In general, it is difficult to solve the multiobjective (MO) H2/H∞ fuzzy filter problem directly, and we therefore propose an indirect approach to minimize the upper bounds and transform the MO H2/H∞ filtering problem to a linear matrix inequality (LMI)-constrained multiobjective problem (MOP). In addition, we propose an LMI-based multiobjective evolution algorithm (MOEA) to find Pareto optimal solutions for the MOP of fuzzy filter design for nonlinear stochastic signal processing. Furthermore, for comparison, we also suggest the MO H2/H∞ 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, two simulation examples are provided that illustrate the design procedure of the Pareto MO optimal filter.