Extended Projected Dynamical Systems with Applications to Hybrid Integrator-Gain Systems

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Abstract

The class of projected dynamical systems (PDS) has proven to be a powerful framework for modeling dynamical systems of which the trajectories are constrained to a set by means of projection. However, PDS fall short in modeling systems in which the constraint set does not satisfy certain regularity conditions and only part of the dynamics can be projected. This poses limitations in terms of the phenomena that can be described in this framework especially in the context of systems and control. Motivated by hybrid integrator-gain systems (HIGS), which are recently proposed control elements in the literature that aim at overcoming fundamental limitations of linear time-invariant feedback control, a new class of discontinuous dynamical systems referred to as extended projected dynamical systems (ePDS) is introduced in this paper. Extended projected dynamical systems include PDS as a special case and are well-defined for a wider variety of constraint sets as well as partial projections of the dynamics. In this paper, the ePDS framework is connected to the classical PDS literature and is subsequently used to provide a formal mathematical description of a HIGS-controlled system, which was lacking in the literature so far. Based on the latter result, HIGS-controlled systems are shown to be well-posed, in the sense of global existence of solutions.

Original languageEnglish
Title of host publication2019 IEEE 58th Conference on Decision and Control, CDC 2019
PublisherInstitute of Electrical and Electronics Engineers
Pages5773-5778
Number of pages6
ISBN (Electronic)9781728113982
DOIs
Publication statusPublished - Dec 2019
Event58th IEEE Conference on Decision and Control, CDC 2019 - Nice, France
Duration: 11 Dec 201913 Dec 2019

Conference

Conference58th IEEE Conference on Decision and Control, CDC 2019
CountryFrance
CityNice
Period11/12/1913/12/19

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  • Cite this

    Sharif, B., Heertjes, M. F., & Heemels, W. P. M. H. (2019). Extended Projected Dynamical Systems with Applications to Hybrid Integrator-Gain Systems. In 2019 IEEE 58th Conference on Decision and Control, CDC 2019 (pp. 5773-5778). [9028882] Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/CDC40024.2019.9028882