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Dissipativity in nonautonomous linear-quadratic control processes
Multi angle
Authors : Núñez, Carmen (Author of the conference)
CIRM (Publisher )
49N10 - Linear-quadratic problems
93C15 - Control systems governed by ODE
37B55 - Nonautonomous dynamical systems
CIRM (Publisher )
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Abstract :
This talk concerns the concept of dissipativity in the sense of Willems for nonautonomous linear-quadratic (LQ) control systems. A nonautonomous system of Hamiltonian ODEs can be associated with such an LQ system, and the analysis of the corresponding symplectic dynamics provides valuable information on the dissipativity properties. The presence of exponential dichotomy, the occurrence of weak disconjugacy, and the existence of nonnegative solutions of the Riccati equation provided by the Hamiltonian system are closely related to the presence of (normal or strict) dissipativity and to the definition of the (normal or strong) storage functions.
This is a joint work with: Roberta Fabbri, Russell Johnson, Sylvia Novo and Rafael Obaya.
MSC Codes : This is a joint work with: Roberta Fabbri, Russell Johnson, Sylvia Novo and Rafael Obaya.
49N10 - Linear-quadratic problems
93C15 - Control systems governed by ODE
37B55 - Nonautonomous dynamical systems
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 07/04/16 Conference Date : 22/03/16 Subseries : Research talks arXiv category : Optimization and Control ; Dynamical Systems Mathematical Area(s) : Dynamical Systems & ODE ; Control Theory & Optimization Format : MP4 (.mp4) - HD Video Time : 00:28:19 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2016-03-22_Nunez.mp4 
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Information on the Event
Event Title : Dynamics of evolution equations / Systèmes dynamiques et problèmes d'évolutionEvent Organizers : Joly, Romain ; Raugel, Geneviève ; Yi, Yingfei Dates : 21/03/16 - 25/03/16 Event Year : 2016 Event URL : http://conferences.cirm-math.fr/1335.html
Citation Data
DOI : 10.24350/CIRM.V.18949403Cite this video as: Núñez, Carmen (2016). Dissipativity in nonautonomous linear-quadratic control processes. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18949403 URI : http://dx.doi.org/10.24350/CIRM.V.18949403 |
See Also
- [Multi angle] Geometric control and dynamics / Author of the conference Rifford, Ludovic.
- [Multi angle] Dichotomy, the closed range theorem and optimal control / Author of the conference Brunovsky, Pavel.
- [Multi angle] Dynamics of bounded solutions of parabolic equations on the real line - Part 1 / Author of the conference Polacik, Peter.
- [Post-edited] Perturbative techniques of the dynamics in the $C^1$-topology / Author of the conference Crovisier, Sylvain.
Bibliography
- Fabbri, R., Johnson, R., Novo, S., & Núñez, C. (2013). On linear-quadratic dissipative control processes with time-varying coefficients. Discrete and Continuous Dynamical Systems, 33(1), 193-210 - http://dx.doi.org/10.3934/dcds.2013.33.193
- Johnson, R., Núñez, C., & Obaya, R. (2013). Dynamical methods for linear Hamiltonian systems with applications to control processes. Journal of Dynamics and Differential Equations, 25(3), 679-713 - http://dx.doi.org/10.1007/s10884-013-9300-y
- Johnson, R., Obaya, R., Novo, S., Núñez, C., & Fabbri, R. (2016). Nonautonomous linear Hamiltonian systems: oscillation, spectral theory and control. Cham: Springer - http://dx.doi.org/10.1007/978-3-319-29025-6
