Title: Shrinking Horizon Model Predictive Control with Signal Temporal Logic Constraints under Stochastic Disturbances,
Abstract: 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.