Shrinking Horizon Model Predictive Control with chance-constrained signal temporal logic specifications

Abstract

We present Shrinking Horizon Model Predictive Control (SHMPC) for linear dynamical systems, under stochastic disturbances, with probabilistic constraints encoded as Signal Temporal Logic (STL) specifications. The control objective is to minimize a cost function under the restriction that the given STL specification be satisfied with some minimum probability. The presented approach utilizes the knowledge of the disturbance distribution to synthesize the controller in SHMPC. We show that this synthesis problem can be (conservatively) transformed into sequential optimizations involving linear constraints. We experimentally demonstrate the effectiveness of our proposed approach by evaluating its performance on room temperature control of a building.