ISSN:
1573-2878
Keywords:
Quadratic control problems
;
minimum effort problem
;
Mosco convergence
;
extremals of an element
;
adjoint operators
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract This paper belongs to the class of works about perturbations of linear-quadratic control problems. Given a linear, bounded, surjective operatorL o:B→V, between Banach spaces, the problem of minimizing |u−ũ|,ũ ∈ B, among all the elementsu satisfying the constraintsL o u=y, has unique solutions under suitable hypotheses onB. The same occurs if we consider a sequence of operatorsL n :B→V, which represent perturbations of theL o-operator. Ifu n (ũ, y) andu o(ũ, y) are the minima of the perturbed problem and the original problems, respectively, convergence ofu n tou o is characterized by means of convergences ofL n and their adjoint operators, in the case whenV≡ℝ l . A sufficiency criterion is given whenB andV are Hilbert spaces. Finally, we study an example problem governed by an ordinary differential equation, in which convergence of the minima is characterized in terms of control coefficients.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00935499
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