Neural-network-based simple adaptive control of uncertain multi-input multi-output non-linear systems

An adaptive control scheme based on radial basis function (RBF) neural networks (NNs) has been developed in this study for a class of uncertain multi-input multi-output (MIMO) non-linear systems in block-triangular forms via dynamic surface approach and `minimal learning parameters (MLP)` algorithm. In the algorithm, the RBF NNs are only used to deal with those unstructured system functions, whereas the unknown virtual control gain functions do not need to be estimated. Consequently, the potential controller singularity problem can be overcome. Two key advantages of our scheme are that (i) only one parameter needs to be updated online for each subsystem, and (ii) both problems of `dimension curse` and `explosion of complexity` are avoided. The computational burden has thus been greatly reduced. It is proved via Lyapunov stability theory that all signals in the interconnected closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking errors converge to a small neighbourhood around zero. Finally, the simulation results are presented to demonstrate the effectiveness of the proposed scheme.