An RBF Neural Network-based Adaptive Control for SISO Linearisable Nonlinear Systems

An RBF neural network-based adaptive control is proposed for Single-Input and Single-Output (SISO) linearisable nonlinear systems in this paper. It is shown that a SISO nonlinear system is first linearised by using the differential geometric approach in the state space, and the linearised nonlinear system is then treated as a partially known system. The known dynamics are used to design a nominal feedback controller to stabilise the nominal system, and an adaptive RBF neural network-based compensator is then designed to compensate for the effects of uncertain dynamics. The main function of the RBF neural network in this work is to adaptively learn the upper bound of the system uncertainty, and the output of the neural network is then used to adaptively adjust the gain of the compensator so that the strong robustness with respect to unknown dynamics can be obtained, and the tracking error between the plant output and the desired reference signal can asymptotically converge to zero. A simulation example is performed in support of the proposed scheme.