Neural Network-Based Adaptive Control of Uncertain Multivariable Systems: Theory and Experiments

This paper is concerned with design of an adaptive neural network (NN)-based controller for a class of multi-input multi-output (MIMO) nonlinear systems. Unlike most of the previous methods, the MIMO system under study is assumed to be in nonaffine form with unknown nonlinear functions in which the nonlinearities are completely coupled with system states and inputs. The system dynamics are first transformed into an affine form via mean value theorem. Then, a direct adaptive control strategy is developed by utilizing NNs universal approximation theory. In the proposed control scheme, the common assumption on fixing the NN hidden weights is removed. Hence, the suggested controller uses full approximation capabilities of NNs and is applicable to systems with higher degrees of nonlinearity. The tracking error and NN weights errors are ensured to be bounded via Lyapunov's direct method. Finally, experimental results are performed on a 6 degree of freedom (DoF) robotic system to illustrate performance of the proposed control scheme when applied to a completely unknown nonlinear system.