Learning From Neural Control of Strict-feedback Systems

In this paper, we study deterministic learning from adaptive neural control (ANC) of nonlinear strict-feedback systems, with the affine terms as unknown functions of system states. Through system decomposition and state transformation, the problem caused by the strict-feedback structure and affine terms is transformed into the stability analysis of a class of cascade LTV subsystems, for which exponential stability can be guaranteed when the PE condition is satisfied. Specifically, when the state tracking to a periodic reference orbit is achieved, the closed-loop signals, which are taken as the inputs to the employed radial basis function (RBF) networks, will become periodic one, such that the partial PE condition for each subsystem can be satisfied in an iterative manner. The contribution of this paper is that for strict-feedback plants, locally-accurate learning of the closed-loop control system dynamics is achieved along periodic orbits of closed-loop signals. Simulation studies are included to demonstrate the effectiveness of the approach.