Output Feedback Adaptive Neural Control Without Seeking SPR Condition

For output-feedback adaptive control of affine nonlinear systems based on feedback linearization and function approximation, the observation error dynamics usually should be augmented by a low-pass filter to satisfy a strictly positive real (SPR) condition so that output feedback can be realized. Yet, this manipulation results in filtering basis functions of approximators, which makes the order of the controller dynamics very large. This paper presents a novel output-feedback adaptive neural control (ANC) scheme to avoid seeking the SPR condition. A saturated output-feedback control law is introduced based on a state-feedback indirect ANC structure. An adaptive neural network (NN) observer is applied to estimate immeasurable system state variables. The output estimation error rather than the basis functions is filtered and the filter output is employed to update NNs. Under given initial conditions and sufficient control parameter constraints, it is proved that the closed-loop system is uniformly ultimately bounded stable in the sense that both the state estimation errors and the tracking errors converge to small neighborhoods of zero. An illustrative example is provided to demonstrate the effectiveness of this approach.