Adaptive Neural Control with Desired Approximation: An Integral Lyapunov Function Approach

The inherent approximation ability of neural networks plays an essential role in adaptive neural control, where the prerequisite for existence of the compact set is crucial in the control designs. Instead of using practical system state, in this paper, the desired approximation approach is characterized to tackle such a problem, where the desired state signal is required only as the input to the network. An integral Lyapunov function-based adaptive controller is designed, in the sense of the error tracking, where the treatment of the state-dependent input gain is adopted. Theoretical results for the performance analysis of the integral and incremental adaptation algorithms are presented in details. In particular, the boundedness of the variables in the closed-loop is characterized, while the transient performance of the output error is analytically quantified. It is shown that the proposed control schemes assure that the tracking error converges to an adjustable set without any requirement on the knowledge of the region that the practical variables evolve, and remove the requirement for the setting of initial conditions including system states and weight estimates.