Adaptive backstepping control of time-delayed nonlinear Markovian jump systems

In this note, an adaptive control scheme is developed for the time-delayed nonlinear Markovian jump systems. The explosion of complexity in traditional backstepping design is avoided by utilizing dynamic surface control. Filters are constructed to provide the proper auxiliary signals. Neural networks are employed to estimate the unknown continuous functions. A novel Lyapunov function is proposed, which contains the stochastically jumping parameters. New features of neural networks approximation in Markovian jump systems are revealed. It is proved that the closed-loop system is bounded in probability. The theoretic result is illustrated through a simulation example.