2014
DOI: 10.2478/amcs-2014-0053
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On an infinite dimensional linear-quadratic problem with fixed endpoints: The continuity question

Abstract: In a Hilbert space setting, necessary and sufficient conditions for the minimum norm solution u to the equation Su = Rz to be continuously dependent on z are given. These conditions are used to study the continuity of minimum energy and linear-quadratic control problems for infinite dimensional linear systems with fixed endpoints.

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Cited by 3 publications
(3 citation statements)
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“…the latter satisfying (15). Indeed, by (28), B(s) ⊖ [ dy ds + A(s)y(s)] = B(s) ⊖ B(s)N −1 (s)B * (s)(χ zt (s)1I s<t − q zt (s)).…”
Section: Identifying the Kernel Of Lq Controlmentioning
confidence: 99%
See 1 more Smart Citation
“…the latter satisfying (15). Indeed, by (28), B(s) ⊖ [ dy ds + A(s)y(s)] = B(s) ⊖ B(s)N −1 (s)B * (s)(χ zt (s)1I s<t − q zt (s)).…”
Section: Identifying the Kernel Of Lq Controlmentioning
confidence: 99%
“…Notably the LQR problem (3) with terminal cost is a special case of (46). Moreover (46) can incorporate indicator functions, and thus handle a finite number state constraints, beside a terminal constraint as considered in [15]. For an infinite number of state constraints, e.g.…”
Section: More General Objectives: State Constraints and Intermediary ...mentioning
confidence: 99%
“…Przyşuski (2014) [26]), especially as there are more efficient numerical tools. Thanks to computers, nowadays, we can analyze complex mathematical models of distributed parameter systems, e.g.…”
Section: Introductionmentioning
confidence: 99%