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  • Infinite-horizon optimal control  (3)
  • 1
    Electronic Resource
    Electronic Resource
    Uniformly overtaking and weakly overtaking optimal solutions in infinite-horizon optimal control: When optimal solutions are agreeable (1990)
    Springer
    Journal of optimization theory and applications 64 (1990), S. 55-69 
    Details
    ISSN: 1573-2878
    Keywords: Infinite-horizon optimal control ; overtaking optimal solutions ; decision-horizon optimal solutions ; agreeable plans ; sufficient conditions for optimality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we investigate the relationship between two classes of optimality which have arisen in the study of dynamic optimization problems defined on an infinite-time domain. We utilize an optimal control framework to discuss our results. In particular, we establish relationships between limiting objective functional type optimality concepts, commonly known as overtaking optimality and weakly overtaking optimality, and the finite-horizon solution concepts of decision-horizon optimality and agreeable plans. Our results show that both classes of optimality are implied by corresponding uniform limiting objective functional type optimality concepts, referred to here as uniformly overtaking optimality and uniformly weakly overtaking optimality. This observation permits us to extract sufficient conditions for optimality from known sufficient conditions for overtaking and weakly overtaking optimality by strengthening their hypotheses. These results take the form of a strengthened maximum principle. Examples are given to show that the hypotheses of these results can be realized.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00940022
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Infinite-horizon optimal controls for problems governed by a volterra integral equation with state-and-control-dependent discount factor (1990)
    Springer
    Journal of optimization theory and applications 66 (1990), S. 311-336 
    Details
    ISSN: 1573-2878
    Keywords: Infinite-horizon optimal control ; Volterra integral equations ; recursive objective functionals
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this work, we concern ourselves with the existence of optimal solutions to optimal control problems defined on an unbounded time interval with states governed by a nonlinear Volterra integral equation. These results extend both the work of Baum and others in infinite-horizon control of ordinary differential equations as well as the work of Angell concerning integral equations. In addition, we incorporate into the objective functional (described by an improper integral) a discount factor which reflects a hereditary dependence on both state and control. In this manner, we are able to generalize the recent results of Becker, Boyd, and Sung in which they establish an existence theorem in the calculus of variations with objective functionals of the so-called recursive type. Our results are obtained through the use of appropriate lower-closure theorems and compactness conditions. Examples are presented in which the applicability of our results is demonstrated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00939541
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Nonconvex and relaxed infinite-horizon optimal control problems (1993)
    Springer
    Journal of optimization theory and applications 78 (1993), S. 465-491 
    Details
    ISSN: 1573-2878
    Keywords: Infinite-horizon optimal control ; overtaking optimality ; economic growth ; chattering states
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we consider the Lagrange problem of optimal control defined on an unbounded time interval in which the traditional convexity hypotheses are not met. Models of this form have been introduced into the economics literature to investigate the exploitation of a renewable resource and to treat various aspects of continuous-time investment. An additional distinguishing feature in the models considered is that we do not assume a priori that the objective functional (described by an improper integral) is finite, and so we are led to consider the weaker notions of overtaking and weakly overtaking optimality. To treat these models, we introduce a relaxed optimal control problem through the introduction of chattering controls. This leads us naturally to consider the relationship between the original problem and the convexified relaxed problem. In particular, we show that the relaxed problem may be viewed as a limiting case for the original problem. We also present several examples demonstrating the applicability of our results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00939878
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    Paper (German National Licenses)
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