Efficient Performance-based MPC Tuning in High Dimensions using Bayesian Optimization over Sparse Subspaces

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.