Adaptive control of non-linear continuous-time systems using neural networks—general relative degree and MIMO cases

Multilayer neural networks are used in a non-linear adaptive control problem. The plant is an unknown feedback linearizable continuous-time system with relative degree ⩾1. The single-input:/single-output system is studied first and then the methodology is extended to control square multi-input/multi-output systems. The control objective is for the plant to track a reference trajectory, and the control law is defined in terms of the outputs of the neural networks. The parameters of the networks are updated on-line according to an augmented tracking error and the network derivatives. A local convergence theorem is given on the convergence of the tracking error. This control algorithm is applied to control a two-input/two-output relative-degree-two system.