Adaptive Scenario-Based Predictive Control: A Set Membership Learning Approach

This paper explores using the Set Membership estimation approach within a scenario-based Model Predictive Control framework to robustly control unknown constrained systems. By assuming unknown-but-bounded noises, a set of models compatible with available data is derived at each time step. Then, a stochastic predictive control scheme regulates the system, ensuring probabilistic operational constraint satisfaction. The combined strategy allows to iteratively refine the set of feasible models that explain the system dynamics, enhancing closed-loop performance as the system operates, while its computational complexity remains lower than that of similar solutions, requiring solving a quadratic program with a set of linear constraints that grows linearly with the risk level, and a set of linear programs when new information allows to update the models set for adaptation. Simulations related to depth tracking of a diving system demonstrate the effective operation of the strategy, reducing uncertainty while satisfying constraints. An initial unconstrained phase is also considered to further improve the identification phase, yielding notable performance gains while satisfying all constraints.