A Data-Driven Automatic Tuning Method for MPC under Uncertainty using Constrained Bayesian Optimization

Abstract

The closed-loop performance of model predictive controllers (MPCs) is sensitive to the choice of prediction models, controller formulation, and tuning parameters. However, prediction models are typically optimized for prediction accuracy instead of performance, and MPC tuning is typically done manually to satisfy (probabilistic) constraints. In this work, we demonstrate a general approach for automating the tuning of MPC under uncertainty. In particular, we formulate the automated tuning problem as a constrained black-box optimization problem that can be tackled with derivative-free optimization. We rely on a constrained variant of Bayesian optimization (BO) to solve the MPC tuning problem that can directly handle noisy and expensive-to-evaluate functions. The benefits of the proposed automated tuning approach are demonstrated on a benchmark continuously stirred tank reactor example.

Zeroth-order optimisation on subsets of symmetric matrices with application to MPC tuning

“…We now perform numerical simulations to show the advantage of our proposed MPC tuning framework with respect to other available gradient-free algorithms in the literature. Particularly, we compare our approach to the dividing rectangles (DIRECT) algorithm [17], particle swarm optimisation algorithms [18], and Bayesian optimisation algorithms [22,37]. DIRECT is a sample-based global optimisation method for Lipschitz continuous functions defined over multidimensional domains.…”

“…This translates into running 20 to 50 closed-loop experiments per iteration, which is not practical for applications where the plant is in the loop. Gradient-based methods [8] and Bayesian optimisation (BO) methods [22,37] can also be used as an alternative with less experiments per iteration, but existent results are presented only for vectors of parameters (i.e. diagonal tuning matrices).…”

“…The optimisation framework presented in this paper, when applied to the context of MPC tuning, offers a more general approach with respect to available literature, and it also comes with convergence guarantees. Particularly, it can deal with MPC tuning over trajectories in a general setting as opposed to [16,32,38,40,43], and it provides MPC weighting matrices that satisfy the required constraints of being symmetric and positive (semi) definite, and thus provide more degrees of freedom than the usual diagonal choices in [8,18,22,37].…”

Performance-based Trajectory Optimization for Path Following Control Using Bayesian Optimization

“…to the limits only if the plant under control is accurately modeled, alternatively, the performance degrades due to imposed robustness constraints. Instead of adapting the controller for the worst case scenarios, the prediction model can be selected to provide the best closed-loop performance by tuning the parameters in the MPC optimization objective for maximum performance [8]- [10]. Using Bayesian optimizationbased tuning for enhanced performance has been further demonstrated for cascade controllers of linear axis drives, where data-driven performance metrics have been used to specifically increase the traversal time and the tracking accuracy while reducing vibrations in the systems [11], [12].…”

COBALT: COnstrained Bayesian optimizAtion of computationaLly expensive grey-box models exploiting derivaTive information

“…A key ingredient in BO is the choice of the acquisition function that should be designed in a way that tradeoffs exploration of regions where the surrogate model is uncertain and exploitation of the model's confidence in good solutions. Although the basic BO framework can be traced back to the 1970s [21], its popularity has substantially grown in recent years due to advances in computer power, algorithms, and software as well as successes in a variety of application areas including hyperparameter optimization in machine learning models [22], material design and discovery [23], aircraft design [24], and automated controller design [25,26].…”