Multi-objective Bayesian optimisation over sparse subspaces for model predictive control of wind farms

As model mismatch (uncertainty) is inevitable, fine-tuning control strategies with closed-loop performance data is critical. This is relevant for model predictive control (MPC) in wind farms (WFs), as inaccurate wake models affect performance. However, challenges such as conflicting control objectives, limited closed-loop data due to expensive experiments, and the high-dimensional design spaces of these MPC formulations make tuning non-trivial. Inspired by the notion of performance-oriented learning, we propose a multi-objective (MO) Bayesian optimisation (BO) framework over sparse subspaces to address these challenges systematically for increased closed-loop MPC performance. To show the efficacy of the BO approach, a simulation case study with a 3x3 WF is investigated where the control objective is to provide secondary frequency regulation while minimising dynamic loading for an MPC with 28 design parameters to auto-tune. Simulations show that the proposed framework achieves a good balance between two conflicting WF control objectives, where dynamic loading is reduced by 51.59% compared to a nominal MPC whose performance is not tuned using closed-loop data while still achieving similar tracking performance. The proposed method is general and can be applied regardless of a closed-loop control goal, WF specifications (complexity, topology, location), or controller formulation for multi-objective constrained control of WFs.