Complexity Reduction for Parameter-Dependent Linear Systems

TL;DR

This paper introduces a sum-of-squares optimization-based algorithm for reducing the complexity of parameter-dependent linear systems, effectively approximating the original system with fewer parameters or states.

Contribution

It proposes a novel complexity reduction method for parameter-dependent systems using sum-of-squares optimization, applicable to both continuous and discrete-time systems.

Findings

Effective reduction of system complexity demonstrated on numerical examples.

Minimizes H-infinity-norm difference between original and reduced systems.

Applicable to systems with parameters in semi-algebraic sets.

Abstract

We present a complexity reduction algorithm for a family of parameter-dependent linear systems when the system parameters belong to a compact semi-algebraic set. This algorithm potentially describes the underlying dynamical system with fewer parameters or state variables. To do so, it minimizes the distance (i.e., H-infinity-norm of the difference) between the original system and its reduced version. We present a sub-optimal solution to this problem using sum-of-squares optimization methods. We present the results for both continuous-time and discrete-time systems. Lastly, we illustrate the applicability of our proposed algorithm on numerical examples.