Adaptive neural control of state-constrained MIMO nonlinear systems with unmodeled dynamics

In this paper, a robust adaptive neural control scheme is proposed for a class of multi-input multi-output nonlinear systems in pure-feedback form with unmodeled dynamics and full state constraints. Radial basis function neural networks are employed to approximate and compensate for the unknown nonlinear continuous functions. By introducing nonlinear symmetric mapping, the full state-constrained tracking control problem of the multi-input multi-output pure-feedback system is transformed into a novel equivalent unconstrained one. For the transformed systems, a dynamic surface control method is applied to remove the difficulties for the multiple explosion of complexity problem. The use of Nussbaum-type function removes the need for any assumption on the function of control gain. By combining variable separation technique and the function's monotonously increasing property, the restrictive assumption of the dynamic disturbances caused by unmodeled dynamics is relaxed. One advantage is that only one adjustable parameter is used in the controller design. It is proved that all the closed-loop signals remain semi-globally uniformly ultimately bounded with good tracking performance, while the system states never violate the constraints.