A discrete-time multivariable neuro-adaptive control for nonlinear unknowndynamic systems

First, we assume that the controlled systems contain a nonlinear matrix gai n before a linear discrete-time multivarable dynamic system. Then, a forwar d control based on a nominal system is employed to cancel the system nonlin ear 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 Omega. The linearly parameterized connection weight for the function approximation error of th e proposed network is also derived, An e-modification updating law with pro jection 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 Omega) stability of the overall system is then verified by t he Lyapunov stability theory, Finally, simulations are given to demonstrate the usefulness of the proposed controller.