Automatic Control Software Synthesis for Quantized Discrete Time Hybrid Systems

TL;DR

This paper introduces a formal model-based method for automatically synthesizing control software for discrete-time hybrid systems, ensuring controllers designed for linear approximations are valid for the original nonlinear systems, demonstrated on an inverted pendulum.

Contribution

It proposes a novel overapproximation technique transforming nonlinear hybrid systems into linear ones for control synthesis, with verified applicability on a benchmark inverted pendulum.

Findings

Successful control software synthesis for the inverted pendulum

Guarantees controllers for linear models are valid for original nonlinear systems

Demonstrates effectiveness of the overapproximation approach

Abstract

Many Embedded Systems are indeed Software Based Control Systems, that is control systems whose controller consists of control software running on a microcontroller device. This motivates investigation on Formal Model Based Design approaches for automatic synthesis of embedded systems control software. This paper addresses control software synthesis for discrete time nonlinear systems. We present a methodology to overapproximate the dynamics of a discrete time nonlinear hybrid system H by means of a discrete time linear hybrid system L(H), in such a way that controllers for L(H) are guaranteed to be controllers for H. We present experimental results on the inverted pendulum, a challenging and meaningful benchmark in nonlinear Hybrid Systems control.