Adaptive Relaxation based Non-Conservative Chance Constrained Stochastic MPC

Abstract

Chance constrained stochastic model predictive controllers (CC-SMPC) trade off 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 paper considers a discrete 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 with 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 to the traditional economic MPC without chance constraints, and a state-of-the-art approach with chance constraints. We satisfy the chance constraints non-conservatively in closed-loop, effectively trading off increased cost savings with minimal adverse effects on BESS lifetime.