Adaptive neural arbitrary prescribed-time control for switched nonlinear systems

The adaptive neural arbitrary prescribed-time control problem is studied for switched nonlinear systems in this paper. The definition of arbitrary prescribed-time stability is supplied. Besides, by leveraging the properties of the non-autonomous differential equation, the sufficient Lyapunov-based conditions for ensuring the stability of nonlinear systems within an arbitrary prescribed-time are provided. The neural networks are introduced to approximate the unknown smooth nonlinear functions. An adaptive backstepping-based control scheme via the common Lyapunov function method is investigated to achieve arbitrary prescribed-time convergence for the signals of the controlled systems. The simulation section employs two practical switched systems to verify the effectiveness of the proposed method.