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Dissipativity in nonautonomous linear-quadratic control processes

By Carmen Núñez

Also appears in collection : Dynamics of evolution equations / Systèmes dynamiques et problèmes d'évolution

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.

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Citation data

  • DOI 10.24350/CIRM.V.18949403
  • Cite this video Núñez, Carmen (22/03/2016). Dissipativity in nonautonomous linear-quadratic control processes. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.18949403
  • URL https://dx.doi.org/10.24350/CIRM.V.18949403

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

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