Superstabilizing Control of Discrete-Time ARX Models under Error in Variables

TL;DR

This paper introduces a polynomial optimization framework using sum-of-squares methods to achieve superstabilizing control of ARX models with noisy data, addressing Error in Variables issues.

Contribution

It develops a novel SOS-based approach to design controllers that superstabilize all models consistent with noisy data in ARX systems.

Findings

Method successfully stabilizes example ARX models with noisy data

Converging hierarchy of semidefinite programs improves computational efficiency

Elimination of noise terms simplifies the control synthesis process

Abstract

This paper applies a polynomial optimization based framework towards the superstabilizing control of an Autoregressive with Exogenous Input (ARX) model given noisy data observations. The recorded input and output values are corrupted with L-infinity bounded noise where the bounds are known. This is an instance of Error in Variables (EIV) in which true internal state of the ARX system remains unknown. The consistency set of ARX models compatible with noisy data has a bilinearity between unknown plant parameters and unknown noise terms. The requirement for a dynamic compensator to superstabilize all consistent plants is expressed using polynomial nonnegativity constraints, and solved using sum-of-squares (SOS) methods in a converging hierarchy of semidefinite programs in increasing size. The computational complexity of this method may be reduced by applying a Theorem of Alternatives to eliminate the noise terms. Effectiveness of this method is demonstrated on control of example ARX models.