Adaptive Relaxation-Based Nonconservative Chance Constrained Stochastic MPC

Chance constrained stochastic model predictive controllers (CC-SMPCs) tradeoff full constraint satisfaction for economical plant performance under uncertainty. Previous CC-SMPC works are over-conservative in constraint violations leading to worse economic performance. Other past works require a priori information about the uncertainty set, limiting their application. This article considers a discrete linear time-invariant (LTI) system with hard constraints on inputs and chance constraints on states, with unknown uncertainty distribution, statistics, or samples. This work proposes a novel adaptive online update rule to relax the state constraints based on the time average of past constraint violations, to achieve reduced conservativeness in closed-loop. Under an ideal control policy assumption, it is proven that the time average of constraint violations asymptotically converges to the maximum allowed violation probability. The method is applied for optimal battery energy storage system (BESS) dispatch in a grid-connected microgrid (MG) with photovoltaic (PV) generation and load demand, with chance constraints on BESS state of charge (SOC). Realistic simulations show the superior electricity cost-saving potential of the proposed method as compared with the traditional economic model predictive control (EMPC) without chance constraints, and a state-of-the-art approach with chance constraints. We satisfy the chance constraints nonconservatively in closed-loop, effectively trading off increased cost savings with minimal adverse effects on BESS lifetime.