# Recursively Feasible Stochastic Model Predictive Control using Indirect Feedback

## TL;DR

This paper introduces a stochastic MPC method for linear systems with unbounded, correlated disturbances, ensuring recursive feasibility and providing performance bounds, demonstrated through building control examples.

## Contribution

The paper proposes a recursive feasibility initialization scheme for stochastic MPC that handles correlated disturbances and guarantees chance constraint satisfaction.

## Key findings

- Recursive feasibility is maintained in stochastic MPC with correlated disturbances.
- The method achieves an average asymptotic performance bound under i.i.d. disturbance assumptions.
- Illustrative examples demonstrate the approach's effectiveness in building control scenarios.

## Abstract

We present a stochastic model predictive control (MPC) method for linear discrete-time systems subject to possibly unbounded and correlated additive stochastic disturbance sequences. Chance constraints are treated in analogy to robust MPC using the concept of probabilistic reachable sets for constraint tightening. We introduce an initialization of each MPC iteration which is always recursively feasibility and thereby allows that chance constraint satisfaction for the closed-loop system can readily be shown. Under an i.i.d. zero mean assumption on the additive disturbance, we furthermore provide an average asymptotic performance bound. Two examples illustrate the approach, highlighting feedback properties of the novel initialization scheme, as well as the inclusion of time-varying, correlated disturbances in a building control setting.