An Iterative Abstraction Algorithm for Reactive Correct-by-Construction Controller Synthesis

TL;DR

This paper introduces an iterative abstraction algorithm that generates dual over- and under-approximations of a dynamical system to improve the synthesis of correct-by-construction controllers, demonstrated through numerical examples.

Contribution

It proposes a novel iterative abstraction scheme using dual FTSs and winning sets to enhance controller synthesis for discrete-time systems.

Findings

The new algorithm efficiently synthesizes controllers with improved accuracy.

Numerical examples demonstrate the effectiveness of the dual abstraction approach.

Abstract

In this paper, we consider the problem of synthesizing correct-by-construction controllers for discrete-time dynamical systems. A commonly adopted approach in the literature is to abstract the dynamical system into a Finite Transition System (FTS) and thus convert the problem into a two player game between the environment and the system on the FTS. The controller design problem can then be solved using synthesis tools for general linear temporal logic or generalized reactivity(1) specifications. In this article, we propose a new abstraction algorithm. Instead of generating a single FTS to represent the system, we generate two FTSs, which are under- and over-approximations of the original dynamical system. We further develop an iterative abstraction scheme by exploiting the concept of winning sets, i.e., the sets of states for which there exists a winning strategy for the system. Finally, the efficiency of the new abstraction algorithm is illustrated by numerical examples.