Control Co-Design With Performance-Robustness Trade-Off Using Tube-Based Stochastic Model Predictive Control

Abstract Control co-design (CCD) has been demonstrated to achieve superior solutions for closed-loop systems. However, limited work has addressed CCD problems under probabilistic disturbances. This article addresses this gap by formulating a finite-horizon optimal control problem with chance constraints and proposing a novel CCD approach. This approach integrates tube-based stochastic model predictive control with constraint-tightening techniques to optimize performance and robustness while preventing instability and infeasibility. A nested CCD framework is introduced, along with a constrained multi-objective optimization algorithm that enables the performance-robustness trade-off. A method for quantifying the robustness of closed-loop systems under stochastic disturbances is presented. The proposed CCD approach is demonstrated on a numerical example and an engineering case of the satellite attitude control system. Results show that CCD can generate more well-spread Pareto fronts that cannot be reached by other design strategies. This helps designers explore more potential solutions with different dynamic characteristics. Selected nondominated solution trajectories are visualized for qualitative comparisons. Future work will extend this to nonlinear applications.