Adaptive Neural Networks Control for Markov Jump Nonlinear Systems with Nonstrict-Feedback Form and Uncertain Transition Rate

This paper studies the adaptive neural networks control for Markov jump nonlinear system with nonstrict-feedback form. To overcome the uncertainty of transition rate, the state space of Markov process is divided into two subsets: completely know and unknown but with known upper bound, and a special feedback gain is adopted. By applying the backstepping method and the property of radial basis function neural networks, a novel adaptive controller and the updating laws of parameters are proposed. The adaptive laws is only involved in the last step of backstepping, which sharply reduces the online computation burden. In the end of paper, a numerical example is given to illustrate the effectiveness of designed controller.