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 /spl Omega/. 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 /spl Omega/) 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.
IEEE Transactions on Systems, Man and Cybern, Part B- Cybernetics 30(6), pp.865-877