Abstract
The quadratic criterion problem for systems governed by functional differential equations has been tackled using dynamic programming arguments in a space of continuous functions in several papers such as [10], [15], [2], [9], [1] and [15]. The solution is obtained in feedback form and the gain matrices satisfy a coupled set of first order partial differential equations. Working in the 2 Hilbert space M2 (see [4]) and using the direct method of Lions [12], Delfour and Mitter [5] have obtained the solution in terms of a M2 operator which satisfies (analogously to the ordinary differential equation case) an abstract Riccati differential operator equation. From this equation it is possible to deduce the coupled set of first order partial differential equations satisfied by the gain matrices [13], [7].
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References
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McCalla, C.A.W. (1974). The Quadratic Criterion Problem for Systems Governed by Retarded Functional Differential Equations and a Modal Analysis Approximation Procedure. In: Kirby, B.J. (eds) Optimal Control Theory and its Applications. Lecture Notes in Economics and Mathematical Systems, vol 106. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-48290-8_11
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DOI: https://doi.org/10.1007/978-3-642-48290-8_11
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