Stochastic Model Predictive Control with adaptive constraint tightening for non-conservative chance constraints satisfaction

Most stochastic Model Predictive Control (MPC) formulations allow constraint violations via the use of chance constraints, thus increasing control authority and improving performance when compared to their robust MPC counterparts. However, common stochastic MPC methods handle chance constraints conservatively: constraint violations are often smaller than allowed by design, thus limiting the potential improvements in control performance. This is a consequence of enforcing chance constraints overlooking the past behavior of the system and/or of an over tightening of the constraints on the predicted sequences. This work presents a stochastic MPC strategy that uses the observed amount of constraint violations to adaptively scale the tightening parameters, thus eliminating the aforementioned conservativeness. It is proven using Stochastic Approximation that, under suitable conditions, the amount of constraint violations converges in probability when using the proposed method. The effectiveness and benefits of the approach are illustrated by a simulation example.