Robust H Adaptive Fuzzy Tracking Control for MIMO Nonlinear Stochastic Poisson Jump Diffusion Systems

• Published in: IEEE transactions on cybernetics Vol. 49; no. 8; pp. 3116 - 3130
• Main Authors: Lin, Xue-Lin, Wu, Chien-Feng, Chen, Bor-Sen
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.08.2019
• Subjects: <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">H ∞ adaptive tracking control; Adaptation models; Adaptive control; Backstepping control design; Control systems; fuzzy logic function; Itô – Lévy formula; MIMO communication; multi-input multi-output (MIMO) nonlinear Poisson jump diffusion systems; Robustness; Stochastic processes
• ISSN: 2168-2267; 2168-2275
• DOI: 10.1109/TCYB.2018.2839364

Recently, stochastic Poisson jump diffusion system has attracted much attention in stochastic control. Poisson jump process has been used to model the random discontinuous jump behavior of the intrinsic discontinuous perturbation in stochastic system. Wiener process also called diffusion process represents the continuous random fluctuation to the system. In this paper, a robust adaptive control is introduced for multi-input multi-output (MIMO) nonlinear stochastic Poisson jump diffusion system with continuous and discontinuous random fluctuations to achieve the <inline-formula> <tex-math notation="LaTeX">{{ {H}}}_{{\infty }} </tex-math></inline-formula> tracking performance with a prescribed disturbance attenuation level. The system structure is of a strict-feedback form. Based on the backstepping design technique and <inline-formula> <tex-math notation="LaTeX">{{{H}}}_{{\infty }} </tex-math></inline-formula> control theory, a robust adaptive control law is constructed for MIMO nonlinear stochastic Poisson jump diffusion system to achieve the <inline-formula> <tex-math notation="LaTeX">{{{H}}}_{{\infty }} </tex-math></inline-formula> tracking performance with a prescribed attenuation level of external disturbance, despite of fuzzy approximation error and the effect of continuous and discontinuous random fluctuations. The proposed <inline-formula> <tex-math notation="LaTeX">{{ {H}}}_{{\infty }} </tex-math></inline-formula> adaptive control law combines both merits of <inline-formula> <tex-math notation="LaTeX">{{ {H}}}_{{\infty }} </tex-math></inline-formula> tracking control and adaptive control scheme to sufficiently solve the robust <inline-formula> <tex-math notation="LaTeX">{{ {H}}}_{{\infty }} </tex-math></inline-formula> adaptive tracking control problem for MIMO stochastic nonlinear systems with continuous and discontinuous random fluctuations. In addition, the uniformly positive definite assumption of control coefficient matrix is relaxed for the proposed MIMO adaptive control as well. A stochastic quadrotor trajectory tracking control simulation is provided to show the effectiveness of the proposed <inline-formula> <tex-math notation="LaTeX">{{ {H}}}_{{\infty }} </tex-math></inline-formula> robust adaptive control law.