×
Lenczner, Michel; Montseny, Gérard

Diffusive realization of operator solutions of certain operational partial differential equations. (English) Zbl 1080.49003

C. R., Math., Acad. Sci. Paris 341, No. 12, 737-740 (2005).
Summary: This note is focused on the derivation of state-realizations of diffusive type for linear operator solutions of some linear partial differential operational equations. It allows the implementation of a large class of linear operators on semi-decentralized architectures. The practical interest of this work relates, for example, to the realization of optimal control law for linear partial differential equations.

Cited in 2 Documents

MSC:

49J20 Existence theories for optimal control problems involving partial differential equations
93B36 \(H^\infty\)-control
93C20 Control/observation systems governed by partial differential equations
35B37 PDE in connection with control problems (MSC2000)

Keywords:

optimal control; linear operator solution; linear partial differential operator equation; causal operator; diffuse symbolic formulation

Software:

CNN
Cite Review PDF
Full Text: DOI Link

References:

[1] Bamieh, B.; Paganini, F.; Dahleh, M., Distributed control of spatially-invariant systems, IEEE Trans. Automatic Control, 47, 7, 1091-1107 (2002) · Zbl 1364.93363
[2] Chua, L. O.; Roska, T., Cellular Neural Networks and Visual Computing (2002), Cambridge University Press: Cambridge University Press Cambridge
[3] D’Andrea, R.; Dullerud, G. E., Distributed control design for spatially interconnected systems, IEEE Trans. Automatic Control, 48, 9, 1478-1495 (2003) · Zbl 1364.93206
[4] Kader, M.; Lenczner, M.; Mrcarica, Z., Distributed optimal control of vibrations: a high frequency approximation approach, Smart Materials and Structures, 12, 437 (2003)
[5] Lasiecka, I.; Triggiani, R., Control Theory for Partial Differential Equations I and II, Encyclopedia Math., vols. 74 and 75 (2000), Cambridge University Press · Zbl 0983.35032
[6] Mikkola, K., Infinite-dimensional linear systems: optimal control and Riccati equations, PhD Thesis, Helsinki University of Technology, Institute of Mathematics, 2002, available at · Zbl 1109.93002
[7] Montseny, G., Représentation diffusive (July 2005), Hermès-Science · Zbl 1251.47001
[8] Opmeer, M. R.; Curtain, R. F., New Riccati equation for well-posed linear systems, in press, available at · Zbl 1157.49316
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.