This paper presents a new study on adaptive control of non-canonical discrete-time neural network systems which do not have explicit relative degrees and cannot be directly dealt with by using feedback linearization control. The paper derives new results for the relative degrees of such systems using the implicit function theory to solve the issue of implicit dependence on system input in the process of feedback linearization. Such implicit input dependence is typically caused by time-advance operation for discrete-time systems, different from their continunous-time counterparts under time-differentiation operation leading to explicit input dependence. New relative degree formulations are employed to achieve desired system reparametrization for adaptive control. It develops an adaptive control scheme with analysis for relative degree one systems and an adaptive control design for relative degree two systems with simulation results to show desired system performance and discussion on some technical issues.
['Yanjun Zhang', 'Gang Tao', 'Mou Chen']
An adaptive control scheme for non-canonical discrete-time neural network systems