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Linear Quadratic Optimal Control of Time-Varying Systems with Indefinite Costs on Hilbert Spaces

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Abstract.

In this paper we consider time-varying linear systems on Hilbert spaces and study the linear quadratic optimal control problem with an indefinite performance criterion over an infinite time interval. An example shows that in contrast to the finite-dimensional situation, in general, the solvability of the optimal control problem does not imply the solvability of the associated integral Riccati equation. Using an operator theoretic approach towards the time-varying integral Riccati equation, we derive equivalent conditions for the solvability of both problems.

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Authors and Affiliations

  1. School of Mathematics, University of Leeds, Leeds LS2 9JT, England. birgit@amsta.leeds.ac.uk., , , , , , GB

    Birgit Jacob

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  1. Birgit Jacob
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Date received: October 8, 1997. Date revised: August 10, 1998.

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Jacob, B. Linear Quadratic Optimal Control of Time-Varying Systems with Indefinite Costs on Hilbert Spaces. Math. Control Signals Systems 12, 196–218 (1999). https://doi.org/10.1007/PL00009850

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  • DOI: https://doi.org/10.1007/PL00009850

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