A grid‐based searching algorithm for observer‐based multiobjective control of T–S fuzzy stochastic jump‐diffusion systems

Abstract

AbstractMost studies on a multiobjective optimal control problem (MOCP) with nonlinear stochastic jump‐diffusion system (NSJDS) constraints assume the state vector is available, but in practice, this is not necessarily the case. The observer‐based MOCP is worthy of further research. Furthermore, the hybrid multiobjective differential evolution algorithm (HMODEA) is usually employed to help solve MOCPs with dynamical system constraints, and such problems often have a higher computational burden. To address these two issues, a grid‐based front‐squeezing searching algorithm (GBFSA) is proposed to solve the observer‐based MOCP with NSJDS. Takagi‐Sugeno (T‐S) fuzzy model is used to approximate the NSJDS and convert the problem into an MOCP with linear matrix inequality (LMI) constraints. Then, the GBFSA efficiently searches for the Pareto front by merging the LMIs and the squeezing theorem. To automatically select a preferred Pareto controller, the minimum Manhattan distance (MMD) approch is applied. Mathematical proofs are given to show that the obtained Pareto optimal controller can concurrently stabilize the associated NSJDS and achieve the desired performance indices. In addition, computational complexity and convergence analysis are also provided.