Discrete-time CMAC NN control of feedback linearizable nonlinear systems under a persistence of excitation

This paper attempts to provide a controller design for closed-loop control applications using cerebellar model articulation controller (CMAC) neural networks (NN) instead of feedforward NNs due to its increased structure. This increased local structure of CMAC NN result in better and faster controllers for nonlinear dynamical systems. For a class of multi-input multi-output (MIMO) nonlinear systems, a CMAC neural network-based controller in discrete-time which feedback linearizes the system is presented. A localized and efficient weight addressing scheme for the CMAC NNs is described using an appropriate choice of the B-spline receptive field functions that form a basis. A uniform ultimate boundedness of the closed-loop system is given in the sense of Lyapunov. The notions of discrete-time passive CMAC NN, a dissipative CMAC NN are defined and used with persistency of excitation condition to show the boundedness of CMAC NN weight estimates.