Distributed Model Predictive Control for Probabilistic Signal Temporal Logic Specifications

This paper proposes a distributed model predictive control (DMPC) for a class of discrete-time stochastic multi-agent systems subject to partially coupled temporal logic tasks. For each agent, the given tasks are formulated as local and coupled probabilistic signal temporal logic (PrSTL) constraints in DMPC, and the control objective is to satisfy the PrSTL constraints against stochastic uncertainties and the coupled spatio-temporal relationship between agents. Considering that control under STL is historically dependent, a shrinking horizon DMPC framework is adopted and a probabilistic-tightening method is proposed to transform the complex form of PrSTL into deterministic constraints. Then, combining with the asynchronous update strategy, the satisfaction verification of coupled PrSTL tasks is achieved. Since large uncertainties may result in optimization infeasibility and affect the completion of the temporal logic tasks, a distributed PrSTL task softening method is further proposed, which can guarantee the softened tasks converge to the original ones and reduce the conservatism of the controller design. The recursive feasibility of the proposed PrSTL-DMPC strategy is proved and the efficiency of the algorithm is demonstrated by simulations.
Note to Practitioners
—With the increasing application of autonomous systems, more complex temporal logic tasks are imposed on system behaviors. This paper focuses on the distributed control problem for stochastic multi-agent systems under temporal logic tasks formulated as PrSTL specifications. A asynchronous DMPC controller is presented to improve task satisfaction against uncertainties and coupled spatial-temporal relationships between agents. The control performance including the recursive feasibility and soundness is formally guaranteed. For applications to autonomous systems, the practitioners can employ PrSTL for specifying spatial and temporal requirements on agents and employ the proposed PrSTL-DMPC algorithm for the task implementation.