Robust adaptive sliding control of linearizable systems

A switching adaptive control algorithm based on a sliding mode method is proposed for a class of SISO nonlinear systems with unknown dynamics. The plant is assumed to be linear-in-the-control input but otherwise be completely unknown. The unknown dynamics are assumed to include smooth nonlinear functions. A single layer neural network model is used to approximate the unknown plant dynamics. A robust adaptive law is used to generate online estimates of the neural network weights. The adaptive algorithm combines four types of control actions to steer the output to track a desired trajectory: a switching law, a PD controller, adaptive estimators, and two σ-modified time-varying sliding controllers. The control law guarantees closed loop stability and forces the tracking error to converge to a small residual set. The control law overcomes the problem of loss of controllability generally encountered in adaptive control of feedback realizable systems without imposing any restrictive assumptions