17th International Symposium on
Mathematical Theory of Networks and Systems
Kyoto International Conference Hall, Kyoto, Japan, July 24-28, 2006

MTNS 2006 Paper Abstract

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Paper MoP13.5

Quadrat, Alban (INRIA Sophia Antipolis, France), Robertz, Daniel (RWTH Aachen, Germany)

On the Monge Problem and Multidimensional Optimal Control

Scheduled for presentation during the Mini-Symposium "Symbolic Methods in Multidimensional Systems Theory" (MoP13), Monday, July 24, 2006, 17:00−17:25, Room 101

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on March 29, 2024

Keywords Multidimensional systems, Integral quadratic constraints, Behavioral approach to systems theory

Abstract

Using new results on the general Monge parametrization recently obtained in A. Quadrat, D. Robertz, ``Parametrizing all solutions of uncontrollable multidimensional linear systems'', Proceedings of the 16th IFAC World Congress, Prague (Czech Republic) (04-08/07/05), i.e., on the possibility to extend the concept of the image representation for non-controllable multidimensional linear systems, we show that we can transform some quadratic variational problems (e.g., optimal control problems) with differential constraints into free variational ones directly solvable by means of the standard Euler-Lagrange equations. This result generalizes for non-controllable multidimensional linear systems the results obtained in H. K. Pillai, J. C. Willems, ``Lossless and dissipative distributed systems'', SIAM Journal of Control and Optimization, 40 (2002), 1406-1430, and in J.-F. Pommaret, A. Quadrat, ``A differential operator approach to multidimensional optimal control'', Int. J. Control, 77 (2004), 821-836, for controllable ones. In particular, in the 1-D case, this result allows us to avoid the controllability condition commonly used in the behavioural approach literature in the study of optimal control problems with a finite horizon and replace it by the stabilizability condition for the ones with an infinite horizon.