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

The controlled system is assumed to be a nonlinear matrix gain before a linear discrete-time multivariable dynamic system. A forward control based on a nominal system is employed to cancel the system nonlinear matrix gain and to track the desired trajectory. Because the remaining uncertainties are dynamic, a recurrent neural network with a compensation of the upper bound of its residue is applied to model the remaining uncertainties in a compact subset Ω. The linearly parameterized connection weight for the function approximation error of the proposed network is given. An e-modification updating law with projection for the weight matrix is employed to guarantee its boundedness and the stability of the network without the requirement of persistent excitation. Then a discrete-time multivariable neuro-adaptive variable structure control is designed to improve the system performances