Adaptive control of Markov jump distributed parameter systems via model reference

• Published in: Fuzzy sets and systems Vol. 392; pp. 115 - 135
• Main Authors: Ji, Huihui, Cui, Baotong, Liu, Xinzhi
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.08.2020
• Subjects: Adaptive control; Markov jump; Most surely exponential stability; Parabolic partial differential equation; Reference-model-based; T-S fuzzy model; Parabolic partial differential equation; Most surely exponential stability; Markov jump; T-S fuzzy model; Adaptive control; Reference-model-based
• ISSN: 0165-0114; 1872-6801
• DOI: 10.1016/j.fss.2019.06.016

This paper studies adaptive control of Markov jump distributed parameter systems via model reference, where a finite dimensional adaptive control approach is used for the distributed parameter systems. In order to obtain the stability criteria, the Galerkin's technique is initially applied to the distributed parameter systems to get a slow system of finite dimensional Markov jump system governed by nonlinear ordinary differential functions. Subsequently, a T-S fuzzy model is employed to represent exactly the nonlinear Markov jump slow system. Then, an adaptive controller subject to reference model is proposed to control the Markov jump distributed parameter systems. By employing the Gronwall inequality and strong law of large numbers technics, criterion on most surely exponential stability of the closed-loop system is established. Finally, two examples and numerical simulations are given to illustrate the effectiveness of the obtained results.