ABSTRACT
This chapter is concerned with the multi-objective H2 /H∞ filtering design problem in nonlinear signal processing systems, which can be approximated by a Takagi-Sugeno fuzzy signal system. We propose a multi-objective filter design to estimate state variables from noisy measurements for nonlinear signal processing systems, and we focus our effort on achieving the optimal concurrent performance for H2 and H∞ filtering simultaneously. In general, it is difficult to solve the multi-objective 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 into a linear matrix inequality–constrained multi-objective problem. In addition, we propose a reverse-order LMI-based multi-objective evolution algorithm to efficiently find Pareto optimal solutions for the MOP of the multi-objective H2 /H∞ fuzzy filter design for nonlinear stochastic signal processing. Furthermore, for comparison, we also suggest a MO H2 /H∞ filter design problem based on the weighted sum method. The proposed indirect method can be widely employed to practically address the MO filter design problem in nonlinear signal processing. Finally, a trajectory estimation of a reentry vehicle by radar is provided to illustrate the design procedure of the Pareto MO optimal filter.
