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.
|
|