Accurate Approximate Regulation of Nonlinear Delay Differential Control Systems

E. Aulisa, J. A. Burns, D. S. Gilliam, S. Paruchuri

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


In this paper we present an approximate controller design methodology for tracking/disturbance-rejection problems governed by nonlinear delay differential control systems. The method considered here is a version of the practical regulation approach developed by the authors in a series of articles. It is important to note that this approach to regulation does not require the existence of an exo-system to define disturbances and signals to be tracked. Therefore, this control law enables tracking and disturbance rejection for general reference and disturbance signals. The idea is similar to the inclusion of a cascade controller design providing a sequence of increasingly more accurate and better preforming controllers. The underlying principle derives from well known geometric methods which rely on the existence of an attractive invariant manifold in the case when the reference and disturbance signals are outputs of an autonomous, linear, neutrally stable exo-system. However, we are able accomplish high performance tracking without this assumption. References in the literature are provided for the history of the methodology and proofs of the error estimates for general systems. We show, in our included example, that the tracking error can be significantly enhanced using a single extra step in the sequence of controllers. In particular, at each step in the cascade controller the error from the previous step provides the reference signal for the next step. In this way, at each step the errors are reduced geometrically.

Original languageEnglish
Title of host publication60th IEEE Conference on Decision and Control, CDC 2021
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781665436595
StatePublished - 2021
Event60th IEEE Conference on Decision and Control, CDC 2021 - Austin, United States
Duration: Dec 13 2021Dec 17 2021

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370


Conference60th IEEE Conference on Decision and Control, CDC 2021
Country/TerritoryUnited States


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