A discrete-time multivariable neuro-adaptive control for nonlinear unknown dynamic systems

First, we assume that the controlled systems contain a nonlinear matrix gain before a linear discrete-time multivariable dynamic system. Then, a forward control based on a nominal system is employed to cancel the system nonlinear matrix gain and track the desired trajectory. A novel recurrent-neural-network (RNN) with a compensation of upper bound of its residue is applied to model the remained uncertainties in a compact subset Ω. The linearly parameterized connection weight for the function approximation error of the proposed network is also derived. An e-modification updating law with projection for weight matrix is employed to guarantee its boundedness and the stability of network without the requirement of persistent excitation. Then a discrete-time multivariable neuro-adaptive variable structure control is designed to improve the system performances. The semi-global (i.e., for a compact subset Ω) stability of the overall system is then verified by the Lyapunov stability theory. Finally, simulations are given to demonstrate the usefulness of the proposed controller.