Learning from direct adaptive neural control

This paper studies deterministic learning for nonlinear systems in the sense that an appropriately designed adaptive neural controller is shown to be capable of learning the unknown system dynamics while attempting to control the system. Following an earlier result for a simple class of systems, it is shown that this "deterministic learning" ability can still be implemented for direct adaptive neural control (ANC) of more general nonlinear systems. Specifically, for direct ANC of nonlinear systems in the strict-feedback form, accurate learning of system dynamics in certain desired control occur when all the NN inputs, including the system states and the intermediate variables, become periodic or periodic-like (recurrent) signals such that a partial persistence of excitation condition is satisfied. Further, it is also revealed that the direct ANC has advantages over the indirect ANC concerning the learning ability.