Linear-Quadratic Control and Quadratic Differential Forms
| Authors: | Willems Jan C., K.U. Leuven, Belgium
Valcher Maria Elena, Universita di Padova, Italy |
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| Topic: | 2.2 Linear Control Systems |
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| Session: | Control in a Behavioral Setting |
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| Keywords: | Linear-quadratic control, behaviors, stationarity, quadratic differential forms, Hurwitz factorization, state representations, behavioral control. |
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Abstract
We consider the infinite time linear-quadratic control problem from a behavioral point of view. The performance functional is the integral of a quadratic differential form. A characterization of thestationary trajectories and of the local minima with respect to (left) compact support variations, as well as their relation to stability, are obtained. Finally, several theorems are derived that describe the optimal LQ trajectories with specified initial, and possibly terminal, conditions.
