Efficient Performance-based MPC Tuning in High Dimensions using Bayesian Optimization over Sparse Subspaces
Akshay Kudva, Melanie T. Huynh, Ali Mesbah, Joel A. Paulson · IFAC-PapersOnLine · 2024
Model predictive control (MPC) is one of the most effective technologies for optimal control of constrained multivariable systems. The closed-loop performance of MPC, however, can be sensitive to the choice of several tuning parameters that can appear in the prediction model, constraints, and/or cost function. Due to inherent limitations of manual tuning and the performance function depends on these parameters in an unknown manner, there has been increasing interest in “auto-tuning” using derivative-free optimization (DFO) methods. Bayesian optimization (BO) is a particularly powerful framework for data-efficient DFO of noisy, black-box functions Several recent works have shown the effectiveness of BO for MPC tuning when the number of tuning parameters is relatively small; however, MPC problems often involve a much larger number of parameters for which BO tends to struggle. In this paper, we propose to exploit a new type of Gaussian process surrogate model defined on sparse axis-aligned subspaces to mitigate the curse of dimensionality in BO. The approach is effective when closed-loop performance is sensitive to a small subset of tuning parameters, which is often the case in task-specific tuning problems. We demonstrate an order-of-magnitude performance improvement can be obtained with the proposed method compared to standard BO on a benchmark inverted pendulum on a cart problem controlled by MPC with twenty independent tuning parameters.