An example in linear quadratic optimal control


Weiss, George and Zwart, Hans (1998) An example in linear quadratic optimal control. Systems & Control Letters, 33 (5). pp. 339-349. ISSN 0167-6911

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Abstract:We construct a simple example of a quadratic optimal control problem for an infinite-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. Staffans (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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Copyright:© 1998 Elsevier
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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