Input Influence Matrix Design for MIMO Discrete-Time Ultra-Local Model

Sangli Teng, Amit K. Sanyal, Ram Vasudevan, Anthony Bloch, Maani Ghaffari

Research output: Chapter in Book/Entry/PoemConference contribution


Ultra-Local Models (ULM) have been applied to perform model-free control of nonlinear systems with unknown or partially known dynamics. Unfortunately, extending these methods to MIMO systems requires designing a dense input influence matrix which is challenging. This paper presents guidelines for designing an input influence matrix for discretetime, control-affine MIMO systems using an ULM-based controller. This paper analyzes the case that uses ULM and a model-free control scheme: the Hölder-continuous Finite-Time Stable (FTS) control. By comparing the ULM with the actual system dynamics, the paper describes how to extract the input-dependent part from the lumped ULM dynamics and finds that the tracking and state estimation error are coupled. The stability of the ULM-FTS error dynamics is affected by the eigenvalues of the difference (defined by matrix multiplication) between the actual and designed input influence matrix. Finally, the paper shows that a wide range of input influence matrix designs can keep the ULM-FTS error dynamics (at least locally) asymptotically stable. A numerical simulation is included to verify the result. The analysis can also be extended to other ULM-based controllers.

Original languageEnglish (US)
Title of host publication2022 American Control Conference, ACC 2022
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781665451963
StatePublished - 2022
Event2022 American Control Conference, ACC 2022 - Atlanta, United States
Duration: Jun 8 2022Jun 10 2022

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619


Conference2022 American Control Conference, ACC 2022
Country/TerritoryUnited States

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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