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    Digitale Medien
    Digitale Medien
    Variational approximations in energy space for the regulator problem with time delay (1980)
    Springer
    Journal of optimization theory and applications 30 (1980), S. 293-307 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Spline approximation ; energy space ; time-delay systems ; Ritz-Trefftz method ; a priori error bounds ; a posteriori error bounds
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract We consider a variational procedure for approximating the solution of the state regulator problem with time delay. Motivated by a dual formulation of the problem, we introduce a positive-definite functionalF over a certain energy space of Mikhlin and obtain approximating solutions by the Ritz-Trefftz idea of minimizing it over finite-dimensional subspaces. The resulting approximating solutions, in turn, furnish suboptimal solutions which converge to the optimal solution of the regulator problem with time delay. A priori error bounds in terms of splines are given. A posteriori error bounds are also obtained.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934500
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  • 2
    Digitale Medien
    Digitale Medien
    Sufficient conditions for variational problems with delayed argument (1993)
    Springer
    Journal of optimization theory and applications 76 (1993), S. 131-144 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Calculus of variations ; delayed arguments ; sufficient conditions ; Riccati differential inequality
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract Various first-order and second-order sufficient conditions of optimality for calculus of variations problems with delayed argument are formulated. The cost functionals are not required to be convex. A second-order sufficient condition is shown to be related to the existence of solutions of a Riccati-type matrix differential inequality.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00952825
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