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

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

“…To show that GBFSA has a lower computational burden than HMODEA, we compared the time complexity of GBFSA with NSGA-II based HMODEA (denoted as HMODEA/NSGA-II) [22,24].…”

“…In this study, we propose a grid‐based front‐squeezing searching algorithm (GBFSA) and use it to solve the observer‐based MOCP with nonlinear stochastic jump‐diffusion system (NSJDS) constraints. Most studies of MOCPs with NSJDS constraints assume all the state vectors are available [22–24, 31, 33, 35, 36], which can hardly be true in real world application. Few studies have discussed observer‐based MO controller design, especially for NSJDS constraints, the topic is worth further investigation.…”

“…The first step to applying HMODEAs is to replace the dynamical system constraints by a set of MIs. The T-S fuzzy model has been commonly applied to approximate deterministic and stochastic dynamic systems [22][23][24][25][26][27]. Through a fitting selection of fuzzy operation points, we can approximate the dynamical system and obtain the fuzzy Hamilton-Jacobi inequalities (HJIs).…”

“…Every objective vector is regarded as a candidate chromosome of MOEAs. One important characteristic of HMODEAs is that every candidate chromosome needs to undergo a feasibility assessment procedure [19,[22][23][24][30][31][32][33][34][35], which is used to ensure the obtained Pareto optimal controller can simultaneously stabilize the system and satisfy with the performance indices. The feasibility assessment procedure involves in solving LMI problems, usually coupling with high computational complexity.…”

“…Few studies have discussed observer-based MO controller design, especially for NSJDS constraints, the topic is worth further investigation. By using a T-S fuzzy model and properly selecting fuzzy operating points, the NSJDS can be perfectly approximated by a T-S fuzzy stochastic jump-diffusion system (SJDS) [22,24,37]. Once the T-S fuzzy SJDS is obtained, we can derive the fuzzy Hamilton-Jacobi inequalities and convert them into a set of MIs.…”