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Colombo, Leonardo
Publications (4 of 4) Show all publications
Colombo, L. & Dimarogonas, D. V. (2018). Optimal Control of Left-Invariant Multi-Agent Systems with Asymmetric Formation Constraints. In: 2018 European Control Conference, ECC 2018: . Paper presented at 16th European Control Conference, ECC 2018, Limassol, Cyprus, 12 June 2018 through 15 June 2018 (pp. 1728-1733). Institute of Electrical and Electronics Engineers (IEEE), Article ID 8550238.
Open this publication in new window or tab >>Optimal Control of Left-Invariant Multi-Agent Systems with Asymmetric Formation Constraints
2018 (English)In: 2018 European Control Conference, ECC 2018, Institute of Electrical and Electronics Engineers (IEEE), 2018, p. 1728-1733, article id 8550238Conference paper, Published paper (Refereed)
Abstract [en]

In this work we study an optimal control problem for a multi-agent system modeled by an undirected formation graph with nodes describing the kinematics of each agent, given by a left invariant control system on a Lie group. The agents should avoid collision between them in the workspace. Such a task is done by introducing some potential functions into the cost functional for the optimal control problem, corresponding to fictitious forces, induced by the formation constraint among agents, that break the symmetry of the individual agents and the cost functions, and rendering the optimal control problem partially invariant by a Lie group of symmetries. Reduced necessary conditions for the existence of normal extremals are obtained using techniques of variational calculus on manifolds. As an application we study an optimal control problem for multiple unicycles.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2018
National Category
Control Engineering
Identifiers
urn:nbn:se:kth:diva-241506 (URN)10.23919/ECC.2018.8550238 (DOI)2-s2.0-85059809247 (Scopus ID)9783952426982 (ISBN)
Conference
16th European Control Conference, ECC 2018, Limassol, Cyprus, 12 June 2018 through 15 June 2018
Funder
Swedish Research CouncilKnut and Alice Wallenberg Foundation
Note

QC 20190124

Available from: 2019-01-24 Created: 2019-01-24 Last updated: 2019-01-24Bibliographically approved
Colombo, L., Clark, W. & Bloch, A. (2018). Time reversal symmetries and zero dynamics for simple hybrid Hamiltonian control systems. In: 2018 Annual American Control Conference (ACC): . Paper presented at 2018 Annual American Control Conference, ACC 2018, Wisconsin Center / Hilton Milwauke City CenterMilwauke, United States, 27 June 2018 through 29 June 2018 (pp. 2218-2223). Institute of Electrical and Electronics Engineers (IEEE)
Open this publication in new window or tab >>Time reversal symmetries and zero dynamics for simple hybrid Hamiltonian control systems
2018 (English)In: 2018 Annual American Control Conference (ACC), Institute of Electrical and Electronics Engineers (IEEE), 2018, p. 2218-2223Conference paper, Published paper (Refereed)
Abstract [en]

This paper studies Hamel's formalism for simple hybrid mechanical control systems and explores the role of time-reversal symmetries and hybrid zero dynamics to predict the existence of periodic orbits in these control system. A time reversal symmetry in the phase-space permits us to construct a time reversible hybrid Hamiltonian system. If the Hamiltonian function describing the continuous dynamics and the impact map are invariants under a time reversal symmetry on the zero hybrid dynamics, under some mild conditions, we find sufficient conditions for the existence of periodic solutions for the class of simple hybrid Hamiltonian control systems.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2018
Series
Proceedings of the American Control Conference, ISSN 0743-1619
National Category
Control Engineering
Identifiers
urn:nbn:se:kth:diva-234868 (URN)10.23919/ACC.2018.8431672 (DOI)2-s2.0-85052550147 (Scopus ID)9781538654286 (ISBN)
Conference
2018 Annual American Control Conference, ACC 2018, Wisconsin Center / Hilton Milwauke City CenterMilwauke, United States, 27 June 2018 through 29 June 2018
Note

QC 20180912

Available from: 2018-09-12 Created: 2018-09-12 Last updated: 2018-09-12Bibliographically approved
Clark, W., Bloch, A., Colombo, L. & Rooney, P. (2017). Optimal Control of Quantum Purity for n=2 Systems. In: 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017: . Paper presented at 56th IEEE Annual Conference on Decision and Control, CDC 2017; Melbourne Convention and Exhibition Centre (MCEC)Melbourne; Australia; 12 December 2017 through 15 December 2017 (pp. 1317-1322). IEEE
Open this publication in new window or tab >>Optimal Control of Quantum Purity for n=2 Systems
2017 (English)In: 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017, IEEE , 2017, p. 1317-1322Conference paper, Published paper (Refereed)
Abstract [en]

The objective of this work is to study time-minimum and energy-minimum global optimal control for dissipative open quantum systems whose dynamics is governed by the Lindblad equation. The controls appear only in the Hamiltonian. Using recent results regarding the decoupling of such dissipative dynamics into intra- and inter-unitary orbits, we transform the control system into a bi-linear control system on the Bloch ball (the unitary sphere together with its interior). We then design a numerical algorithm to construct an optimal path to achieve a desired point given initial states close to the origin (the singular point) of the Bloch ball. This is done both for the minimum-time and minimum-energy control problems.

Place, publisher, year, edition, pages
IEEE, 2017
Series
IEEE Conference on Decision and Control, ISSN 0743-1546
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-223847 (URN)10.1109/CDC.2017.8263837 (DOI)000424696901055 ()2-s2.0-85046146518 (Scopus ID)978-1-5090-2873-3 (ISBN)
Conference
56th IEEE Annual Conference on Decision and Control, CDC 2017; Melbourne Convention and Exhibition Centre (MCEC)Melbourne; Australia; 12 December 2017 through 15 December 2017
Note

QC 20180306

Available from: 2018-03-06 Created: 2018-03-06 Last updated: 2018-11-19Bibliographically approved
Bloch, A., Clark, W. & Colombo, L. (2017). Quasivelocities and Symmetries in Simple Hybrid Systems. In: 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017: . Paper presented at IEEE 56th Annual Conference on Decision and Control (CDC), DEC 12-15, 2017, Melbourne, AUSTRALIA (pp. 1529-1534). IEEE
Open this publication in new window or tab >>Quasivelocities and Symmetries in Simple Hybrid Systems
2017 (English)In: 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017, IEEE , 2017, p. 1529-1534Conference paper, Published paper (Refereed)
Abstract [en]

This paper discusses Hamel's formalism for simple hybrid systems and explores the role of reversing symmetries in these system with a continuous-discrete combined dynamics. By extending Hamel's formalism to the class of simple hybrid systems with impulsive effects, we derive, under some conditions, the dynamics of Lagrangian hybrid systems and Hamiltonian hybrid systems. In particular, we derive Euler-Poincare and Lie-Poisson equations for systems with impulsive effects as a simple hybrid system. A reversing symmetry in the phase-space permits one to construct a time reversible hybrid Hamiltonian system. Based on the invariance of a Hamiltonian function by a reversing symmetry, we can find sufficient conditions for the existence of periodic solutions for these simple hybrid systems.

Place, publisher, year, edition, pages
IEEE, 2017
Series
IEEE Conference on Decision and Control, ISSN 0743-1546
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-223844 (URN)10.1109/CDC.2017.8263869 (DOI)000424696901087 ()2-s2.0-85046279283 (Scopus ID)978-1-5090-2873-3 (ISBN)
Conference
IEEE 56th Annual Conference on Decision and Control (CDC), DEC 12-15, 2017, Melbourne, AUSTRALIA
Note

QC 20180306

Available from: 2018-03-06 Created: 2018-03-06 Last updated: 2018-11-14Bibliographically approved
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