Model Predictive Control for Systems With Partially Unknown Dynamics Under Signal Temporal Logic Specifications

In this letter, we design a model predictive controller (MPC) for systems to satisfy Signal Temporal Logic (STL) specifications when the system dynamics are partially unknown, and only a nominal model and past runtime data are available. Our approach uses Gaussian process regression to learn a stochastic, data-driven model of the unknown dynamics, and manages uncertainty in the STL specification resulting from the stochastic model using Probabilistic Signal Temporal Logic (PrSTL). The learned model and PrSTL specification are then used to formulate a chance-constrained MPC. For systems with high control rates, we discuss a modification for improving the solution speed of the control optimization. In simulation case studies, our controller increases the frequency of satisfying the STL specification compared to controllers that use only the nominal dynamics model.