Abstract
Because the nonlinear dynamic systems may suffer from both continuous Wiener noise and discontinuous Poisson noise, the robust optimal scheduling filter design problem of nonlinear stochastic Poisson diffusion system with external disturbance is studied in this paper. The robust optimal filter deign is considered to estimate state variable from noise measurement for nonlinear stochastic system so that we have to solve two second-order nonlinear Hamilton-Jocobi inequality (HJI)-constrained optimization problems. However, it is very difficult to directly solve the second-order HJI-constrained problems. Therefore, we develop the Polytopic Linear Model (PLM) scheduling scheme to obtain linear matrix inequalities (LMI)-constrained optimization problems for simplification of and filter design procedure. Afterwards, the LMI-constrained optimization problems can be solved efficiently via LMI toolbox of MATLAB. Furthermore, a multiobjective (MO) filter design problem for nonlinear stochastic Poisson diffusion system is proposed for attenuating both and performance simultaneously. Since it is difficult to solve the MO filtering problem directly, we propose an indirect method to minimize the upper bounds of and filtering performance and transform the MO filtering problem into an LMI-constrained multiobjective problem (MOP). Additionally, we provide an LMI-constrained multiobjective evolution algorithm (MOEA) to efficiently find the Pareto optimal solutions for the MOP of scheduling filter deign for nonlinear stochastic Poisson diffusion system. Finally, a simulation example is provided to illustrate the design procedure of robust optimal filter deign.