A Geometric Method for Passivation and Cooperative Control of Equilibrium-Independent Passivity-Short Systems
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2019
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| _version_ | 1866915133218881536 |
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| author | Sharf, Miel Jain, Anoop Zelazo, Daniel |
| author_facet | Sharf, Miel Jain, Anoop Zelazo, Daniel |
| contents | Equilibrium-independent passive-short (EIPS) systems are a class of systems that satisfy a passivity-like dissipation inequality with respect to any forced equilibria with non-positive passivity indices. This paper presents a geometric approach for finding a passivizing transformation for such systems, relying on their steady-state input-output relation and the notion of projective quadratic inequalities (PQIs). We show that PQIs arise naturally from passivity-shortage characteristics of an EIPS system, and the set of their solutions can be explicitly expressed. We leverage this connection to build an input-output mapping that transforms the steady-state input-output relation to a monotone relation, and show that the same mapping passivizes the EIPS system. We show that the proposed transformation can be implemented through a combination of feedback, feed-through, post- and pre-multiplication gains. Furthermore, we consider an application of the presented passivation scheme for the analysis of networks comprised of EIPS systems. Numerous examples are provided to illustrate the theoretical findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1901_06512 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | A Geometric Method for Passivation and Cooperative Control of Equilibrium-Independent Passivity-Short Systems Sharf, Miel Jain, Anoop Zelazo, Daniel Systems and Control Equilibrium-independent passive-short (EIPS) systems are a class of systems that satisfy a passivity-like dissipation inequality with respect to any forced equilibria with non-positive passivity indices. This paper presents a geometric approach for finding a passivizing transformation for such systems, relying on their steady-state input-output relation and the notion of projective quadratic inequalities (PQIs). We show that PQIs arise naturally from passivity-shortage characteristics of an EIPS system, and the set of their solutions can be explicitly expressed. We leverage this connection to build an input-output mapping that transforms the steady-state input-output relation to a monotone relation, and show that the same mapping passivizes the EIPS system. We show that the proposed transformation can be implemented through a combination of feedback, feed-through, post- and pre-multiplication gains. Furthermore, we consider an application of the presented passivation scheme for the analysis of networks comprised of EIPS systems. Numerous examples are provided to illustrate the theoretical findings. |
| title | A Geometric Method for Passivation and Cooperative Control of Equilibrium-Independent Passivity-Short Systems |
| topic | Systems and Control |
| url | https://arxiv.org/abs/1901.06512 |