# Shrinking Horizon Model Predictive Control with Signal Temporal Logic Constraints under Stochastic Disturbances

## TL;DR

This paper introduces a novel Shrinking Horizon Model Predictive Control method for discrete-time linear systems with STL constraints, effectively handling stochastic disturbances without requiring full distribution knowledge, demonstrated on HVAC systems.

## Contribution

It develops a general STL-constrained control approach under stochastic disturbances that does not need precise distribution information, extending to cases with known distributions for improved performance.

## Key findings

- Effective control synthesis for HVAC systems.
- Robust STL satisfaction under stochastic disturbances.
- Optimization problems with linear constraints at each step.

## Abstract

We present Shrinking Horizon Model Predictive Control (SHMPC) for discrete-time linear systems with Signal Temporal Logic (STL) specification constraints under stochastic disturbances. The control objective is to maximize an optimization function under the restriction that a given STL specification is satisfied with high probability against stochastic uncertainties. We formulate a general solution, which does not require precise knowledge of the probability distributions of the (possibly dependent) stochastic disturbances; only the bounded support intervals of the density functions and moment intervals are used. For the specific case of disturbances that are independent and normally distributed, we optimize the controllers further by utilizing knowledge of the disturbance probability distributions. We show that in both cases, the control law can be obtained by solving optimization problems with linear constraints at each step. We experimentally demonstrate effectiveness of this approach by synthesizing a controller for an HVAC system.