Non-linear multi-objective Bayesian MPC of water reservoir systems

Addressing multiple conflicting objectives in online control problems is a challenge. Traditional causal approaches optimize cost functions defined as a weighted sum of cost contributions, each representing a control objective. However, the way cost weights are chosen is traditionally heuristic, based at most on sensitivity analyses. In the literature, some solutions optimize weights based on multi-objective genetic algorithms (NSGA-II). Still, these strategies inherit the well-known deterioration phenomenon in which NSGA-II occurs. Here, we introduce a novel Non-Linear Model Predictive Control (NLMPC) formulation that automatically selects the optimal weight combination, i.e., the one resulting in the best-aggregated performance. We run NLMPC controllers simultaneously at each time step, calibrating their cost function weights using a Bayesian Optimization that optimizes the Pareto frontier's Hypervolume and Additive Epsilon Indicator. We then select the controller, minimizing the trade-off between objectives. We apply our approach to the Red River system, a highly non-linear and multipurpose water resource system in Vietnam. The proposed tuning algorithm overcomes the literature deterioration issue and validation over six years of observational data shows that our method minimizes the aggregated normalized cost, with and without disturbance knowledge assumption. The back-test of experimental data finally validates our control strategy, demonstrating a dominating solution against historical control.