Tube-Based Model Predictive Control with a Complementary Control Law Based on Algebraic Methods

This paper presents a control framework based on Tube-Based Model Predictive Control (MPC). Tube-based MPC is a robust control strategy that integrates MPC with a complementary robust control law. The nonlinear robust control law defines an invariant tube that encapsulates all possible trajectories of the actual system under bounded disturbances. A robust control law is derived using algebraic methods and sliding mode control to manage uncertainties and disturbances, combined with a linear MPC scheme to efficiently track the nominal system. This approach ensures system robustness while maintaining computational efficiency by leveraging the linearized dynamics of the nominal system for optimization. The linear MPC component computes the optimal control inputs for the nominal system, focusing on minimizing a defined objective function subject to input constraints. By decoupling the robust control design from the optimization process, the proposed method significantly reduces computational complexity compared to fully nonlinear MPC approaches. Experimental results on a benchmark nonlinear system demonstrate the method’s efficiency in achieving robust performance and constraint satisfaction, even in the presence of significant disturbances and model uncertainties. This approach bridges the gap between nonlinear control theory and practical MPC implementation, offering a scalable and efficient solution for controlling complex systems with real-world constraints. The results are discussed in detail.