Adaptive neural network control for uncertain dual switching nonlinear systems

Dual switching system is a special hybrid system that contains both deterministic and stochastic switching subsystems. Due to its complex switching mechanism, few studies have been conducted for dual switching systems, especially for systems with uncertainty. Usually, the stochastic subsystems are described as Markov jump systems. Based upon the upstanding identity of RBF neural network on approaching nonlinear data, the tracking models for uncertain subsystems are constructed and the neural network adaptive controller is designed. The global asymptotic stability almost surely (GAS a.s.) and almost surely exponential stability (ES a.s.) of dual switching nonlinear error systems are investigated by using the energy attenuation theory and Lyapunov function method. An uncertain dual switching system with two subsystems, each with two modes, is studied. The uncertain functions of the subsystems are approximated well, and the approximation error is controlled to be below 0.05. Under the control of the designed adaptive controller and switching rules, the error system can obtain a good convergence rate. The tracking error is quite small compared with the original uncertain dual switching system.