Adaptive neural network output tracking control of uncertain switched nonlinear systems: An improved multiple Lyapunov function method

For a class of uncertain switched nonlinear systems, the adaptive neural network(NN) output tracking control problem is investigated by using the neural network technique in this paper. The considered switched nonlinear systems involve unknown control coefficients, external disturbances, and unmodeled dynamics merged in the full-states. An improved multiple Lyapunov function method is developed through relaxing the traditional multiple Lyapunov function conditions. A feasible state-dependent switching signal and an adaptive NN output tracking switching controller are designed such that the output tracking error converges to an arbitrarily small neighborhood of the origin, and all the signals in the closed-loop system remain within a bounded region. It is proved that the positive definiteness of Lyapunov functions and the solvability assumption of the adaptive NN output tracking control problem for all the subsystems are unnecessary. An application example of the mass-spring-damper system and a numerical example are given to illustrate the effectiveness of the proposed algorithm.