An Input-Output Simulation Approach to Controlling Multi-AffineSystems for Linear Temporal Logic Specifications

TL;DR

This paper introduces an input-output simulation method for controlling multi-affine systems to satisfy linear temporal logic specifications by partitioning the state space and synthesizing controllers through abstracted transition systems.

Contribution

It proposes a novel input-output simulation approach that enables LTL controller synthesis for multi-affine systems via state space partitioning and transition system abstraction.

Findings

Successfully synthesizes controllers satisfying LTL specifications.

Demonstrates input-output simulation preserves LTL properties.

Provides a systematic control design framework for multi-affine systems.

Abstract

This paper presents an input-output simulation approach to controlling multi-affine systems for linear temporal logic (LTL) specifications, which consists of the following steps. First, we partition the state space into rectangles, each of which satisfies atomic LTL propositions. Then, we study the control of multi-affine systems on rectangles including the control of driving all trajectories starting from a rectangle to exit through a facet and the control of stabilizing the system towards a desired point. With the proposed controllers, a finitely abstracted transition system is constructed which is shown to be input-output simulated by the rectangular transition system of the multi-affine system. Since input-output simulation preserves LTL properties, the controller synthesis of the multi-affine system for LTL specifications is achieved by designing a nonblocking supervisor for the abstracted transition system and by continuously implementing the resulting supervisor for the original multi-affine system.