Tube-based integral sliding mode predictive control scheme for constrained uncertain nonlinear time-delay system

For a class of constrained uncertain nonlinear time-delay systems, how to achieve their stability and robustness is a crucial issue. To this end, this paper proposes a tube-based integral sliding mode predictive control scheme (ISMPC). The model predictive control (MPC) is designed as a nominal controller to generate an optimal ‘reference trajectory’ for the actual (controlled) system. The integral sliding mode control (ISMC) acts as an auxiliary controller to combat disturbances and ensure that the actual trajectory is restricted in a robust tube centred on the reference trajectory. In addition, during the design process, the practical constraints are satisfied through the sliding mode boundary layer, without the need for iterative computation of robust invariant sets. The proposed control scheme combines the advantages of model predictive control MPC and ISMC, ensuring the optimal performance and robustness of the controlled system, and effectively reducing the computational burden required for the control scheme. Finally, the stability of the closed-loop system is proved theoretically, and the effectiveness of the proposed method is verified by the simulation results of two examples.