On the Equivalence of Extended and Oblique Projected Dynamics with Applications to Hybrid Integrator-Gain Systems

B. Sharif; M.F. Heertjes; H. Nijmeijer; W.P.M.H. Heemels

doi:10.23919/ACC50511.2021.9483069

On the Equivalence of Extended and Oblique Projected Dynamics with Applications to Hybrid Integrator-Gain Systems

B. Sharif, M.F. Heertjes, H. Nijmeijer, W.P.M.H. Heemels

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

Abstract

The class of projected dynamical systems (PDS) provides a powerful framework for modeling dynamical systems of which the trajectories are constrained to a set by means of projection. This work is concerned with establishing equivalence results among two recent variations of PDS. These are (i) extended PDS (ePDS), which enable partial projection of dynamics, and (ii) oblique PDS, (oPDS) where projections can be done with respect to non-Euclidean norms. We present two sets of sufficient conditions for equivalence among these two system classes. These results enable the transfer of system theoretical properties and tools from one class to the other, which we illustrate in this paper. As an application, we study hybrid integrator-gain systems (HIGS), which are recently introduced hybrid control elements aiming at overcoming fundamental limitations of linear time-invariant control, and are formally described in the ePDS framework. We use our results to also describe these control elements as oPDS, thereby enabling the study of HIGS-controlled systems in this framework.

Original language	English
Title of host publication	2021 American Control Conference, ACC 2021
Publisher	Institute of Electrical and Electronics Engineers
Pages	3434-3439
Number of pages	6
ISBN (Electronic)	9781665441971
DOIs	https://doi.org/10.23919/ACC50511.2021.9483069
Publication status	Published - 28 Jul 2021
Event	2021 American Control Conference, ACC 2021 - Virtual, Virtual, New Orleans, United States Duration: 25 May 2021 → 28 May 2021 http://acc2021.a2c2.org/

Conference

Conference	2021 American Control Conference, ACC 2021
Abbreviated title	ACC 2021
Country/Territory	United States
City	Virtual, New Orleans
Period	25/05/21 → 28/05/21
Internet address	http://acc2021.a2c2.org/

Bibliographical note

Funding Information:
Marcel Heertjes is also with ASML Mechatronic Systems Development, Veldhoven, the Netherlands. E-mail corresponding author: b.sharif@tue.nl This work is carried out as part of the project “From PID to complex order controller (CLOC)” and is supported by the Netherlands Organization for Scientific Research (NWO) Domain for Applied and Engineering Sciences (TTW).

Keywords

Extended projected dynamical systems
hybrid integrator gain systems
oblique projected dynamical systems

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10.23919/ACC50511.2021.9483069

Cite this

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abstract = "The class of projected dynamical systems (PDS) provides a powerful framework for modeling dynamical systems of which the trajectories are constrained to a set by means of projection. This work is concerned with establishing equivalence results among two recent variations of PDS. These are (i) extended PDS (ePDS), which enable partial projection of dynamics, and (ii) oblique PDS, (oPDS) where projections can be done with respect to non-Euclidean norms. We present two sets of sufficient conditions for equivalence among these two system classes. These results enable the transfer of system theoretical properties and tools from one class to the other, which we illustrate in this paper. As an application, we study hybrid integrator-gain systems (HIGS), which are recently introduced hybrid control elements aiming at overcoming fundamental limitations of linear time-invariant control, and are formally described in the ePDS framework. We use our results to also describe these control elements as oPDS, thereby enabling the study of HIGS-controlled systems in this framework.",

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Sharif, B , Heertjes, MF , Nijmeijer, H & Heemels, WPMH 2021, On the Equivalence of Extended and Oblique Projected Dynamics with Applications to Hybrid Integrator-Gain Systems. in 2021 American Control Conference, ACC 2021., 9483069, Institute of Electrical and Electronics Engineers, pp. 3434-3439, 2021 American Control Conference, ACC 2021, Virtual, New Orleans, United States, 25/05/21. https://doi.org/10.23919/ACC50511.2021.9483069

On the Equivalence of Extended and Oblique Projected Dynamics with Applications to Hybrid Integrator-Gain Systems. / Sharif, B.; Heertjes, M.F.; Nijmeijer, H. et al.

2021 American Control Conference, ACC 2021. Institute of Electrical and Electronics Engineers, 2021. p. 3434-3439 9483069.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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N2 - The class of projected dynamical systems (PDS) provides a powerful framework for modeling dynamical systems of which the trajectories are constrained to a set by means of projection. This work is concerned with establishing equivalence results among two recent variations of PDS. These are (i) extended PDS (ePDS), which enable partial projection of dynamics, and (ii) oblique PDS, (oPDS) where projections can be done with respect to non-Euclidean norms. We present two sets of sufficient conditions for equivalence among these two system classes. These results enable the transfer of system theoretical properties and tools from one class to the other, which we illustrate in this paper. As an application, we study hybrid integrator-gain systems (HIGS), which are recently introduced hybrid control elements aiming at overcoming fundamental limitations of linear time-invariant control, and are formally described in the ePDS framework. We use our results to also describe these control elements as oPDS, thereby enabling the study of HIGS-controlled systems in this framework.

AB - The class of projected dynamical systems (PDS) provides a powerful framework for modeling dynamical systems of which the trajectories are constrained to a set by means of projection. This work is concerned with establishing equivalence results among two recent variations of PDS. These are (i) extended PDS (ePDS), which enable partial projection of dynamics, and (ii) oblique PDS, (oPDS) where projections can be done with respect to non-Euclidean norms. We present two sets of sufficient conditions for equivalence among these two system classes. These results enable the transfer of system theoretical properties and tools from one class to the other, which we illustrate in this paper. As an application, we study hybrid integrator-gain systems (HIGS), which are recently introduced hybrid control elements aiming at overcoming fundamental limitations of linear time-invariant control, and are formally described in the ePDS framework. We use our results to also describe these control elements as oPDS, thereby enabling the study of HIGS-controlled systems in this framework.

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BT - 2021 American Control Conference, ACC 2021

PB - Institute of Electrical and Electronics Engineers

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On the Equivalence of Extended and Oblique Projected Dynamics with Applications to Hybrid Integrator-Gain Systems

Abstract

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Bibliographical note

Keywords

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