An example in linear quadratic optimal control

George Weiss, Hans Zwart*

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademicpeer-review

    30 Citations (Scopus)


    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.
    Original languageEnglish
    Pages (from-to)339-349
    Number of pages11
    JournalSystems and control letters
    Issue number5
    Publication statusPublished - 1998


    • Infinite-dimensional systems
    • Linear quadratic optimal control
    • Shift semigroups
    • Spectral factorization
    • Riccati equations
    • 2023 OA procedure

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