Fuzzy Adaptive Finite-Time Control Design for Nontriangular Stochastic Nonlinear Systems

• Published in: IEEE transactions on fuzzy systems Vol. 27; no. 1; pp. 172 - 184
• Main Authors: Sui, Shuai, Chen, C. L. Philip, Tong, Shaocheng
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.01.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive control; Adaptive systems; Computer simulation; Control design; Differential equations; Fuzzy control; Fuzzy logic; Fuzzy systems; MIMO (control systems); MIMO communication; Multiple-input and multiple-output (MIMO) stochastic nonlinear systems; Nonlinear systems; nontriangular form; state filter; Stochastic processes; Stochastic systems; stochastically finite-time control
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2018.2882167

This paper solves the stochastically finite-time control problem for uncertain stochastic nonlinear systems in nontriangular form. The considered controlled plants are different from the previous results of finite-time control systems, which are the multiple-input and multiple-output (MIMO) stochastic systems with the unknown functions consisting of all states, stochastic disturbance, and immeasurable states. Fuzzy logic systems and a state filter are used to model the uncertain systems and estimate the immeasurable states, respectively. Based on the finite-time theory and It<inline-formula><tex-math notation="LaTeX">\hat{o}</tex-math></inline-formula> differential equation, a novel stochastically finite-time stability theorem is first raised. By combining the novel criterion and backstepping technique, an adaptive fuzzy stochastically finite-time control method is proposed. It is testified that all signals in the closed-loop signals are semiglobal finite-time stable in probability, and the tracking performances are well. Simulation example results further show the effectiveness of the proposed approach.