Relaxing the Control-gain Assumptions of DSC Design for Nonlinear MIMO Systems

This work focuses on adaptive neural dynamic surface control (DSC) for an extended class of nonlinear MIMO strict-feedback systems whose control gain functions are continuous and possibly unbounded. The method is based on introducing a compact set which is eventually proved to be an invariant set: thanks to this set, the restrictive assumption that the upper and lower bounds of control gain functions must be bounded is removed. This method substantially enlarges the class of systems for which DSC can be applied. By utilizing Lyapunov theorem and invariant set theory, it is rigorously proved that all signals in the closed-loop systems are semi-globally uniformly ultimately bounded (SGUUB) and the output tracking errors converge to an arbitrarily small residual set. A simulation example is provided to demonstrate the effectiveness of the proposed approach.