Intelligent dynamic practical-sliding-mode control for singular Markovian jump systems

This paper is concerned with the problems of dynamic practical-sliding-mode control (SMC) and estimation of unknown functions for singular Markovian jump systems (MJSs) with system perturbations, by using an ellipsoidal-type interval type-2 fuzzy neural networks (FNNs). For the interval type-2 FNN, both the system states and control inputs are utilized as its inputs. Then, by using respectively the linear and the integral sliding variables depending on both the system state and control input, the design of novel interval type-2 FNN-integrated intelligent dynamic practical SMCs to achieve practical sliding modes in finite time is presented. The resulting practical sliding motions are proved to be semi-global practical finite-time stochastic stable based on the Lyapunov function. Furthermore, by exploring some adaptive laws based on the interval type-2 FNN, the unknown function can be approximated, and even the bound of the approximation errors of the interval type-2 FNN can be estimated, under the system perturbation. Finally, an application example is introduced to illustrate the validity of the presented intelligent dynamic practical SMC techniques.