Model predictive control with deep neural network based integral sliding modes generation for a class of uncertain nonlinear systems

In this paper, a Model Predictive Control (MPC) scheme incorporating Integral Sliding Mode (ISM) is presented to deal with a class of uncertain nonlinear systems. Classical design of ISM control components requires the knowledge of the system nominal dynamics. In the present paper, it is assumed that the nominal dynamics is unknown, and that matched disturbances affect the system state evolution. In the proposed approach, two Deep Neural Networks (DNNs) are employed to estimate the drift dynamics and control effectiveness matrix of the system. The approximation errors introduced by the DNNs, along with the matched disturbances acting on the system, are compensated by the DNN-based ISM control. The weights of the DNNs are tuned relying on adaptation laws derived from Lyapunov analysis, providing theoretical guarantees. A solution to the considered control problem based on the joint use of the DNN-based ISM control and MPC is discussed. The proposal is assessed in simulation on the classical Duffing oscillator with satisfactorily results.