Online learning based risk-averse stochastic MPC of constrained linear uncertain systems

This paper investigates the problem of designing data-driven stochastic Model Predictive Control (MPC) for linear time-invariant systems under additive disturbance, whose probability distribution is unknown but can be partially inferred from data. We propose a novel online learning based risk-averse MPC framework in which Conditional Value-at-Risk (CVaR) constraints on system states are required to hold family distributions called an ambiguity set. The set constructed disturbance data by leveraging Dirichlet process mixture model that self-adaptive underlying structure and complexity. Specifically, structural property multimodality exploited, so first- second-order moment information each component incorporated into A constraint tightening strategy then developed equivalent reformulation distributionally robust CVaR over proposed As more gathered during runtime controller, updated using real-time data, enables cope with time-varying distributions. variational inference algorithm employed does not require all collected learned scratch, therefore endowed guaranteed computational complexity learning. guarantees recursive feasibility closed-loop stability established via safe update scheme. Numerical examples used illustrate effectiveness advantages MPC.