Multiobjective control for nonlinear stochastic Poisson jump-diffusion systems via T-S fuzzy interpolation and Pareto optimal scheme

Unlike the conventional mixed H-2/H-infinity control design method, this study provides a multiobjective fuzzy control design method for nonlinear stochastic Poisson jump-diffusion systems to simultaneously achieve optimal cost and 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 behaviors 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 H-2 and H-infinity performance indices generally conflict with each other and can be regarded as a multiobjective optimization problem (MOP). It is not easy to directly solve this MOP, owing to(i) the Pareto front of the MOP is difficult to obtain through direct calculation;(ii) the MOP is a Hamilton-Jacobi-Inequalities (HJIs)-constrained MOP. To address these issues, we use Takagi-Sugeno (T-S) interpolation scheme to transform the HJIs-constrained MOP into a linear matrix inequality (LMI)-constrained MOP. Then, we employ the proposed LMI-constrained multiobjective optimization evolutionary algorithm (LMI-constrained MOEA) to efficiently search for the Pareto optimal solution, from which the designer can select one kind of design according to their preference. Finally, a design example is given to illustrate the design procedure and to verify our results. (C) 2019 Elsevier B.V. All rights reserved.