An implicit function based control scheme for discrete-time non-canonical form neural network systems

This paper develops an implicit function based control scheme for discrete-time non-canonical form neural network systems which do not have explicit relative degrees and cannot be directly dealt with by using feedback linearization. Different from time-differentiation operation for continuous-time systems leading to linear input dependence of output dynamics in the process of feedback linearization, time-advance operation for discrete-time non-canonical form neural network systems results in nonlinear input dependence of output dynamics, which brings a difficulty to specify explicit relative degrees. In order to solve this problem, this paper derives new results for relative degrees of such systems using the implicit function theory, based on which a normal form is derived. Based on the normal form, the paper develops a feedback control scheme for systems with implicit relative degrees. A detailed design procedure using implicit function theory is derived to ensure stable precise output tracking. A numerical solution algorithm is also given to ensure stable output tracking with any degree of accuracy. Simulation results are shown to show effectiveness of the proposed control scheme.