Adaptive neural inverse optimal control for uncertain switched nonlinear systems: an improved predefined-time method

Abstract

For the first time, this paper introduces an improved predefined-time inverse optimal method to address the adaptive tracking control problem of a class of uncertain switched nonlinear systems. The proposed approach enables the system to achieve optimal performance without resorting to the HJB equation. Firstly, we design two-time constants to improve the traditional predefined-time lemma. The improved predefined-time lemma exhibits faster convergence. Subsequently, to realise the design of a predefined-time inverse optimal controller, a specific form of the auxiliary controller is designed using Sontag functions and nonsingular functions. Furthermore, the stability of the system and the optimality of the inverse are proven through the use of a common Lyapunov function method, ensuring that tracking errors converge to the neighbourhood of zero within the predefined time. Finally, the rationality of the proposed control structure is demonstrated through the example results.