Partial-State DADS Control for Matched Unmodeled Dynamics

TL;DR

This paper extends DADS control to systems with unmeasured dynamic uncertainties, including infinite-dimensional PDEs, achieving robust regulation without known bounds on disturbances or parameters.

Contribution

It introduces a DADS controller for partial-state adaptive feedback in systems with unmeasured dynamic uncertainties, including infinite-dimensional PDEs, bypassing small-gain conditions.

Findings

DADS controller achieves robust regulation despite unbounded interconnections.

No gain or state drift occurs regardless of disturbance size.

Effective control of infinite-dimensional PDE systems with unknown parameters.

Abstract

We extend the Deadzone-Adapted Disturbance Suppression (DADS) control to time-invariant systems with dynamic uncertainties that satisfy the matching condition and for which no bounds for the disturbance and the unknown parameters are known. This problem is equivalent to partial-state adaptive feedback, where the states modeling the dynamic uncertainty are unmeasured. We show that the DADS controller can bypass small-gain conditions and achieve robust regulation for systems in spite of the fact that the strength of the interconnections has no known bound. Moreover, no gain and state drift arise, regardless of the size of the disturbances and unknown parameters. Finally, the paper provides the detailed analysis of a control system where the unmeasured state (or the dynamic uncertainty) is infinite-dimensional and described by a reaction-diffusion Partial Differential Equation, where the diffusion coefficient and the reaction term are unknown. It is shown that even in the infinite-dimensional case, a DADS controller can be designed and guarantees robust regulation of the plant state.