Decomposition-Based MPC for Uncertain Systems With Nested Signal Temporal Logic Specifications

In this letter, we tackle the complex problem of control synthesis for uncertain systems with dynamically nested tasks represented by signal temporal logic (STL) specifications. Traditional temporal logic control approaches typically consider non-nested specifications under deterministic systems, thereby limiting their applicability in more complex environments. To overcome these limitations, we propose a decomposition-based model predictive control (MPC) framework designed for linear systems affected by additive, bounded stochastic disturbances. Our approach first decomposes each nested STL specification into a series of atomic subtasks through nested specification resolution (NSR) approach, then we adopt a distributed shrinking horizon MPC (dSHMPC) strategy for each subtask to improve computational efficiency. The efficacy of the proposed method is illustrated through a robot simulation scenario.