Deterministic learning of a class of nonlinear systems with relaxed conditions

A deterministic learning theory was recently presented which states that all appropriately designed adaptive neural controller can learn the system internal dynamics while attempting to control a class of simple nonlinear systems in Brunovsky form. In this paper, we investigate deterministic learning from adaptive neural control of a class of nonlinear systems with mild assumptions on the lower and upper bounds of affine term g(x). To overcome the difficulties brought by the affine terms for learning, firstly, the tracking control and the stability of the closed-loop system are guaranteed by the use of ISS (Input-to-State Stability) analysis and SG (Small Gain) theorem. Secondly, without bound of the derivative of affine term, deterministic learning of the unknown system dynamics can be implemented when the exponential stability of a class of LTV systems is achieved. In addition, the utilization of knowledge learned is also investigated, i.e., a non-high gains controller is constructed to improve the control performance and reduce the control cost.