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An example in linear quadratic optimal control

✍ Scribed by George Weiss; Hans Zwart

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
128 KB
Volume
33
Category
Article
ISSN
0167-6911

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✦ Synopsis

We construct a simple example of a quadratic optimal control problem for an inΓΏnite-dimensional linear system based on a shift semigroup. This system has an unbounded control operator. The cost is quadratic in the input and the state, and the weighting operators are bounded. Despite its extreme simplicity, this example has all the unexpected features discovered recently by O. Sta ans (and also by M. Weiss and G. Weiss). More precisely, in the formula linking the optimal feedback operator to the optimal cost operator, as well as in the Riccati equation, the weighting operator of the input has to be replaced by another operator, which can be derived from the spectral factorization of the Popov function.

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