Shrinking Horizon Model Predictive Control with Signal Temporal Logic Constraints under Stochastic Disturbances
Abstract
We present Shrinking Horizon Model Predictive Control (SHMPC) for discretetime 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.
 Publication:

arXiv eprints
 Pub Date:
 May 2017
 DOI:
 10.48550/arXiv.1705.02152
 arXiv:
 arXiv:1705.02152
 Bibcode:
 2017arXiv170502152F
 Keywords:

 Computer Science  Systems and Control;
 Computer Science  Logic in Computer Science;
 Mathematics  Optimization and Control;
 Mathematics  Probability
 EPrint:
 11 pages, 1 figure, 1 table, Submitted to IEEE Transaction on Automatic Control. A limited subset of the results of this paper is accepted for presentation at American Control Conference 2017