Incremental Control Synthesis in Probabilistic Environments with Temporal Logic Constraints

TL;DR

This paper introduces an incremental control synthesis method for deterministic plants interacting with probabilistic agents in graph environments, optimizing the probability of satisfying temporal logic specifications efficiently.

Contribution

It presents a novel incremental approach that reduces computational costs for control synthesis under temporal logic constraints in probabilistic settings.

Findings

The incremental method is faster than classical approaches.

It uses less memory during synthesis.

Case-study demonstrates practical efficiency improvements.

Abstract

In this paper, we present a method for optimal control synthesis of a plant that interacts with a set of agents in a graph-like environment. The control specification is given as a temporal logic statement about some properties that hold at the vertices of the environment. The plant is assumed to be deterministic, while the agents are probabilistic Markov models. The goal is to control the plant such that the probability of satisfying a syntactically co-safe Linear Temporal Logic formula is maximized. We propose a computationally efficient incremental approach based on the fact that temporal logic verification is computationally cheaper than synthesis. We present a case-study where we compare our approach to the classical non-incremental approach in terms of computation time and memory usage.