Model predictive control of stochastic hybrid systems with signal temporal logic constraints

This paper investigates the control synthesis problem for stochastic hybrid systems with multiple tasks. The given tasks are characterized using signal temporal logic (STL) specifications, with the control goal being to execute them with specified probabilities. A deterministic model predictive control (MPC) problem is then derived by employing the unscented transformation (UT) and properties of STL. For scenarios where tasks overlap in time, we utilize dynamic weighting along with the inherent space robustness of each task to address a multi-objective MPC problem. We further propose a control strategy to ensure the recursive feasibility of deterministic MPC. Additionally, we apply the main results to a stochastic hybrid system with discrete dynamics represented by probabilistic Boolean control networks (PBCNs) and compare the results with existing research. The effectiveness of the proposed method is illustrated through a numerical example. © 2024 Elsevier Ltd