Shrinking Horizon Model Predictive Control with Signal Temporal Logic Constraints under Stochastic Disturbances
It provides a practical control framework for safety-critical systems where probabilistic satisfaction of temporal logic specifications is required under uncertainty.
This paper introduces a Shrinking Horizon Model Predictive Control method for linear systems under stochastic disturbances that ensures Signal Temporal Logic specifications are satisfied with high probability. The approach is validated on an HVAC system, showing effective control without requiring full knowledge of disturbance distributions.
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.