State estimation and fuzzy sliding mode control of nonlinear Markovian jump systems via adaptive neural network

This paper deals with the problem of Takagi-Sugeno fuzzy model-based state estimation and sliding mode control for nonlinear systems through an adaptive neural network, in which the system parameters follow the Markovian switching rules. In order to deal with the unknown local nonlinearity, a multi-layer neural network is used for the nonlinear function approximation. First, a Lebesgue fuzzy observer with adaptive compensator is designed based on state-dependent fuzzy rules. Second, an integral sliding surface is proposed, based on which the obtained sliding mode dynamics has good property of sliding mode manifold. Third, an H_∞ performance with stochastic stability of the sliding mode dynamics and error dynamics are developed in the form of linear matrix inequality. Moreover, reachability of sliding surface in finite-time and maintenance of sliding motion are realized by constructing a fuzzy sliding mode controller. Finally, a simulation study is added to show the validity of the proposed results on the robot manipulator model.