Multivariable Adaptive Control of Nonlinear Unknown Dynamic Systems Using Recurrent Neural-Network

From the very beginning, an approximate nonlinear autoregressive moving average (NARMA) model is employed to represent an unknown and multivariable nonlinear dynamic system. A recurrent neural network with a compensation of upper bound of its residue is applied to model the unknown functions in a compact subset. The linearly parameterized weight for the function approximation error of the proposed network is also derived. An e-modification learning law with projection for weight matrix is employed to guarantee its boundedness and the stability of network without the requirement of persistent excitation. The proposed controller contains an equivalent control and a switching control. The equivalent control uses the learning functions by RNN, switching surface, and a bounded reference input. To compensate the residue of RNN, a simple network is applied to estimate its upper bound for the design of the switching control. Under some conditions, the semi-globally ultimately bounded tracking with the boundedness of estimated weight matrix is accomplished by Lyapunov stability theory.