Adaptive variable structure control of MIMO nonlinear systems with time-varying delays and unknown dead-zones

In this paper, adaptive variable structure neural control is presented for a class of uncertain multi-input multi-output (MIMO) nonlinear systems with state time-varying delays and unknown nonlincar dead-zones. The unknown time-varying delay uncertainties are compensated for using appropriate Lyapunov-Krasovskii functionals in the design. The approach removes the assumption of linear function outside the deadband without necessarily constructing a dead-zone inverse as an added contribution. By utilizing the integral-type Lyapunov function and introducing an adaptive compensation term for the uppcr bound of the residual and optimal approximation error as well as the dead-zone disturbance, the closed-loop control system is proved to be semi-globally uniformly ultimately bounded. In addition, a modified adaptive control algorithm is given in order to avoid the high-frequency chattering phenomenon. Simulation results demonstrate the effectiveness of the approach.