Robust Control Co-Design using Tube-Based Model Predictive Control

Control co-design (CCD) has received much attention since it can achieve superior system performance by optimizing physical and control systems simultaneously. Despite many successful examples from diverse engineering fields using CCD, a lack of attention toward accounting for uncertainty hinders application to real-world systems. This paper aims to solve CCD problems under uncertainty by proposing a robust CCD formulation and algorithm. A robust feedback controller using tube-based model predictive control (tube-based MPC) approach is incorporated into a bi-level optimization architecture. The use of the set invariance theory and an approximation algorithm helps identify the set of all possible states due to disturbances, this set is known as a tube, and quantify system robustness by calculating the tube size. It enables designers to make performance-robustness trade-offs with the approximate Pareto fronts. A numerical example and a simplified model of the satellite attitude control system are used to demonstrate the proposed method. Results show that the CCD solutions dominate most of the solutions from the traditional sequential design and control design only. This study will be extended into nonlinear applications in our future work.