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

arXiv: https://arxiv.org/abs/1705.02152 · HTML: https://mlsanity.com/paper/1705.02152/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 May 2017.

## Built on by (most cited first, 3 of 3)

- [Risk-averse autonomous systems: A brief history and recent developments from the perspective of optimal control](https://mlsanity.com/paper/2109.08947/) (2021)
- [STL Robustness Risk over Discrete-Time Stochastic Processes](https://mlsanity.com/paper/2104.01503/) (2021)
- [Reward Machines for Signal Temporal Logic](https://mlsanity.com/paper/2608.13625/) (2026)

## Abstract (arXiv)

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.