Abstract
In this paper we consider the problem under which conditions there is, for a discrete-time system and an arbitrary finite planning horizon, a unique control that minimizes a general quadratic cost functional. The cost functional differs from the usual one considered in optimal control theory in the sense that we do not assume that the considered weight matrices are (semi) positive definite. The system is described by a linear time-invariant recurrence equation and has an exogenous component. For single input, single output systems both necessary and sufficient conditions are derived.
Zusammenfassung
Diese Arbeit behandelt die Frage unter welche Bedingungen die Optimierung einer quadratischen Kostenfunktion in einem Zeitdiscreten System mit endlichem Planungshorizont, eine eindeutige Lösung hat. Die Kostenfunktion unterscheidet sich von der Standardsituation dadurch, daβ nur vorausgesetzt wird daβ die Gewichtmatrizen symmetrisch sind. Für single input, single output Systeme wird eine komplette Charakterisierung der Existenzfrage gegeben.
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© 1993 Springer-Verlag Heidelberg
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Engwerda, J.C. (1993). The Indefinite LQ-Problem: Existence of a Unique Solution. In: Hansmann, KW., Bachem, A., Jarke, M., Katzenberger, W.E., Marusev, A. (eds) DGOR / ÖGOR. Operations Research Proceedings 1992, vol 1992. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-78196-4_75
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DOI: https://doi.org/10.1007/978-3-642-78196-4_75
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