Some Computational Tools for Solving a Selection of Problems in Control Theory

TL;DR

This paper introduces PACE.jl, a Julia package that employs symbolic elimination and interval computations to solve control theory problems like stability analysis and optimization.

Contribution

The paper presents a novel computational tool, PACE.jl, integrating symbolic elimination and multi-precision interval methods for control theory applications.

Findings

Effective in stability analysis

Supports parameter-dependent systems

Enables optimization in control problems

Abstract

This paper demonstrates how certified computational tools can be used to address various problems in control theory. In particular, we introduce PACE.jl, a Julia package that implements symbolic elimination techniques, including (among others) discriminant varieties and Rational Univariate Representation, while also supporting multi-precision interval computations. We showcase its applications to key control theory problems, including identification, stability analysis, and optimization, for both parameter-dependent and parameter-free systems.