Minimization of a functional over the set of causal operators of causal Hilbert space
The minimization problem for a quadratic functional defined on the set of nonwarning (causal) operators acting in a causal Hilbert space can be regarded as an abstract analog of the Wiener problem on constructing the optimal nonwarning filter. A similar problem also arises in the linear control problem with the quadratic performance criterion (in this case the transfer operators of a closed control system serve as causal ones). The introduction of causal operators in filtering theory and control theory is a mathematical expression of the causality principle, which must be taken into account for a number of problems. In the present paper we attempt to systematize the mathematical foundations of the abstract linear filtering theory, for which its basic results are expressed in terms of operators describing the filtering problem. We introduce and study a class of finite operators a natural generalization of the class of causal operators, and give a solution of the minimization problem for a quadratic positive functional defined on the set of causal operators acting in a discrete causal space.
- Sponsoring Organization:
- USDOE
- OSTI ID:
- 210112
- Journal Information:
- Journal of Mathematical Sciences, Vol. 77, Issue 4; Other Information: PBD: 5 Dec 1995; TN: Translated from Problemy Matematicheskogo Analiza; No. 14, 143-187(1995)
- Country of Publication:
- United States
- Language:
- English
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