ABSTRACT
Unlike the conventional mixed H2 /H∞ control design method, this chapter provides a multi-objective fuzzy control design method for nonlinear stochastic Poisson jump-diffusion systems to simultaneously achieve optimal H2 stabilization and H∞ robustness performance in the Pareto optimal sense via the proposed evolutionary algorithm. For a nonlinear stochastic Poisson jump-diffusion system, the Poisson jumps cause its system behavior to change intensely and discontinuously. To design an efficient controller for a nonlinear stochastic jump-diffusion system is much more difficult. On the other hand, the H2 and H∞ control performance indices generally conflict with each other and can be regarded as a multi-objective optimization problem. It is not easy to directly solve this MOP, because the Pareto front of the MOP is difficult to obtain through direct calculation, and the MOP is a Hamilton-Jacobi inequality–constrained MOP. Further, we use the Takagi-Sugeno interpolation scheme to transform the HJI-constrained MOP into a linear matrix inequality–constrained MOP. Then, we employ the proposed reverse-order LMI-constrained multi-objective optimization evolutionary algorithm to efficiently search for the Pareto optimal solution, from which the designer can select a design according to their own preference. Finally, a design example is given to illustrate the design procedure and to verify our results.
