Equivalent Conditions for the Solvability of Nonstandard and Singular LQ-Problems with Application to Parabolic Equations

C. A. McMillan
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C. A. McMillan: Virginia Polytechnic Institute and State University

Journal of Optimization Theory and Applications, 1999, vol. 101, issue 2, No 5, 329-354

Abstract: Abstract We consider an optimal control problem with indefinite cost for an abstract model, which covers, in particular, parabolic systems in a general bounded domain. Necessary and sufficient conditions are given for the synthesis of the optimal control, which is given in terms of the Riccati operator arising from a nonstandard Riccati equation. The theory extends also a finite-dimensional frequency theorem to the infinite-dimensional setting. Applications include the heat equation with Dirichlet and Neumann controls, as well as the strongly damped Euler–Bernoulli and Kirchhoff equations with the control in various boundary conditions.

Keywords: Algebraic Riccati equations; parabolic equations; optimal control (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1023/A:1021789510611

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