Abstract
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 study, an 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 control performance with a prescribed disturbance attenuation level. The system structure is of a strict-feedback form. Based on backstepping design technique and control theory, robust adaptive control law is constructed for MIMO nonlinear stochastic Poisson jump diffusion system to achieve performance with a prescribed attenuation level of external disturbance, fuzzy approximation error and the effect of continuous and discontinuous fluctuations. The proposed adaptive control law combines both merits of control and adaptive control scheme to sufficiently solve the robust adaptive tracking control problem for MIMO nonlinear stochastic system with continuous and discontinuous random fluctuations. In addition, the uniformly positive definite assumption of control coefficient matrix is relaxed for MIMO adaptive control as well. The simulation results are provided to show the effectiveness of the proposed robust adaptive control law.