Predictive Control Co-Design: A Single-Level Optimization Framework for Computationally-Efficient Approximation of Recursive Model Predictive Control in Control Co-Design

Abstract

Control co-design (CCD) offers a promising solution for coordinating plant and control design of complex systems to better meet next generation demands. Most CCD algorithms optimize open-loop control signals that solve the problem with a single horizon, yet yield system designs lacking robustness to uncertainties. Recent work has integrated modern model predictive control (MPC) policies into CCD. While this results in systems that are more robust, the recursive nature of receding-horizon MPC is computationally expensive and necessitates a bi-level (nested) optimization process to solve sequential MPC problems over smaller horizons. In this work, I present a single-level predictive control co-design (pCCD) optimization framework that approximates the solution to optimizing a recursive MPC within CCD within a single optimization horizon without the need for nested optimization. The pCCD framework leverages elements of static gain matrices as decision variables to integrate a predictive controller into the algorithm that approximates the benefits afforded by embedding a MPC policy in CCD. The formulation reduces algorithm computational complexity by optimizing over the entire operating horizon at once while retaining key robustness and constraint-handling advantages of MPC. Through a comparative case study for a dual-tank thermal management system, this work shows the pCCD algorithm yields superior robustness to disturbance uncertainties compared to an analogous open-loop CCD system while converging on an optimal system/control design with a 92% reduction in run time compared to an analogous system optimized using a recursive MPC policy within the same CCD algorithm.