ABSTRACT
In this chapter, multi-objective H2 /H∞ fuzzy control design is investigated for nonlinear mean-field stochastic jump diffusion (MFSJD) systems for concurrently minimizing both H2 and H∞ control performance. Since H2 and H∞ control performances usually conflict with one another, the optimization problem that concurrently minimizes H2 and H∞ control performance can be regarded as a Hamilton Jacobi inequality–constrained multi-objective optimization problem. Because HJIs of nonlinear MFSJD systems are difficult to derive, multi-objective H2 /H∞ control design problems of nonlinear MFSJD systems are difficult to solve directly. Based on the T-S fuzzy interpolation scheme, an indirect method is introduced to transform the HJI-constrained MOP into a linear matrix inequality–constrained MOP. Thus, one can accomplish the multi-objective H2 /H∞ fuzzy control design via reverse-order LMI-constrained multi-objective evolutionary algorithms. To efficiently solve the multi-objective H2 /H∞ stabilization control design problem, we propose a novel reverse-order LMI-constrained MOEA called a front-squeezing LMI-constrained MOEA to concurrently search Pareto fronts from both sides of feasible and infeasible regions and narrow the search region down to increase the search efficiency. Finally, we present a simulation example of the multi-objective regulation of a nonlinear MFSJD financial system to illustrate the design procedure and validate the control performance of the proposed schemes.
