Input Synthesis for Sampled Data Systems by Program Logic

TL;DR

This paper introduces a method for synthesizing inputs for sampled data hybrid systems with imperative controllers, using program logic to efficiently reduce the search space for desired system behaviors.

Contribution

It presents a novel structural approach combining forward and backward reasoning in program logic for input synthesis in sampled data systems.

Findings

Prototype implementation demonstrates potential of the approach.

Method effectively reduces search space in input synthesis.

Applicable to systems with imperative controller programs.

Abstract

Inspired by a concrete industry problem we consider the input synthesis problem for hybrid systems: given a hybrid system that is subject to input from outside (also called disturbance or noise), find an input sequence that steers the system to the desired postcondition. In this paper we focus on sampled data systems--systems in which a digital controller interrupts a physical plant in a periodic manner, a class commonly known in control theory--and furthermore assume that a controller is given in the form of an imperative program. We develop a structural approach to input synthesis that features forward and backward reasoning in program logic for the purpose of reducing a search space. Although the examples we cover are limited both in size and in structure, experiments with a prototype implementation suggest potential of our program logic based approach.