Shrinking Horizon Model Predictive Control With Signal Temporal Logic Constraints Under Stochastic Disturbances

Samira S. Farahani*, Rupak Majumdar, Vinayak S. Prabhu, Sadegh Soudjani

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

16 Citations (Scopus)


We present shrinking horizon model predictive control for discrete-time linear systems under stochastic disturbances with constraints encoded as signal temporal logic (STL) specification. The control objective is to satisfy a given STL specification with high probability against stochastic uncertainties while maximizing the robust satisfaction of an STL specification with minimum control effort. We formulate a general solution, which does not require precise knowledge of probability distributions of (possibly dependent) stochastic disturbances; only the bounded support of the density functions and moment intervals are used. For the specific case of disturbances that are normally distributed, we optimize the controllers by utilizing knowledge of the probability distribution of the disturbance. 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 a heating, ventilation, and air conditioning system.

Original languageEnglish
Article number8528869
Pages (from-to)3324-3331
Number of pages8
JournalIEEE Transactions on Automatic Control
Issue number8
Publication statusPublished - 2019


  • HVAC system
  • predictive control
  • signal temporal logic
  • stochastic disturbance

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