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

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