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  • 1
    Electronic Resource
    Electronic Resource
    A Carathéodory-Hamilton-Jacobi theory for infinite-horizon optimal control problems (1986)
    Springer
    Journal of optimization theory and applications 48 (1986), S. 265-287 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; Hamilton-Jacobi theory ; infinite horizon ; equivalent variational problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we extend Carathéodory's concept of equivalent variational problems to infinite-horizon optimal control problems. In such a setting, the usual concept of a minimum need not exist, and we therefore consider a weaker definition of optimality, known as catching up optimality. The extension presented here leads us to a Hamilton-Jacobi theory for infinite-horizon optimal control problems that closely parallels the classical work of Carathéodory as well as providing sufficient conditions for optimality. Finally, we show that the results given here subsume several previously known results as a special case.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00940673
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On the existence of catching-up optimal solutions for Lagrange problems defined on unbounded intervals (1986)
    Springer
    Journal of optimization theory and applications 49 (1986), S. 207-225 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; existence theory ; catching-up optimal solutions ; infinite-horizon problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we are concerned with the question of the existence of optimal solutions for infinite-horizon optimal control problems of Lagrange type. In such problems, the objective or cost functional is described by an improper integral. As dictated by applications arising in mathematical economics, we do nota priori assume that this improper integral converges. This leads us to consider a weaker type of optimality, known as catching-up optimality. The results presented here utilize the classical convexity and seminormality conditions typically imposed in the existence theory for the case of finite intervals. These conditions are significantly weaker than those imposed by other authors; as a consequence, their existence results are contained as special cases of the results presented here. The method of proof utilizes the Carathéodory-Hamilton-Jacobi theory previously developed by the author for infinite-horizon optimal control problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00940757
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    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Existence of finitely optimal solutions for infinite-horizon optimal control problems (1986)
    Springer
    Journal of optimization theory and applications 51 (1986), S. 41-62 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; existence theory ; finite optimality ; infinite horizons ; continuous dependence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we investigate the existence of finitely optimal solutions for the Lagrange problem of optimal control defined on [0, ∞) under weaker convexity and seminormality hypotheses than those of previous authors. The notion of finite optimality has been introduced into the literature as the weakest of a hierarchy of types of optimality that have been defined to permit the study of Lagrange problems, arising in mathematical economics, whose cost functions either diverge or are not bounded below. Our method of proof requires us to analyze the continuous dependence of finite-interval Lagrange problems with respect to a prescribed terminal condition. Once this is done, we show that a finitely optimal solution can be obtained as the limit of a sequence of solutions to a sequence of corresponding finite-horizon optimal control problems. Our results utilize the convexity and seminormality hypotheses which are now classical in the existence theory of optimal control.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00938602
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    On the existence of sporadically catching-up optimal solutions for infinite-horizon optimal control problems (1987)
    Springer
    Journal of optimization theory and applications 53 (1987), S. 219-235 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; existence theory ; sporadically catching-up optimality ; infinite-horizon optimal control problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we extend the existence theory of Brock and Haurie concerning the existence of sporadically catching-up optimal solutions for autonomous, infinite-horizon optimal control problems. This notion of optimality is one of a hierarchy of types of optimality that have appeared in the literature to deal with optimal control problems whose cost functionals, described by an improper integral, either diverge or are unbounded below. Our results rely on the now classical convexity and seminormality hypotheses due to Cesari and are weaker than those assumed in the work of Brock and Haurie. An example is presented where our results are applicable, but those of the above-mentioned authors do not.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00939215
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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