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  • Articles  (4)
  • control theory  (4)
  • 1975-1979  (4)
  • 1945-1949
  • 1979  (4)
  • Mathematics  (4)
  • Sociology
  • Architecture, Civil Engineering, Surveying
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  • Articles  (4)
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  • 1975-1979  (4)
  • 1945-1949
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  • Mathematics  (4)
  • Sociology
  • Architecture, Civil Engineering, Surveying
  • 1
    Electronic Resource
    Electronic Resource
    Control problems with intermediate constraints: A sufficient condition (1979)
    Springer
    Journal of optimization theory and applications 29 (1979), S. 253-290 
    Details
    ISSN: 1573-2878
    Keywords: Sufficient optimality conditions ; indirect control proof ; intermediate constraints ; E-dominance ; control theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A sufficient condition is given for an arc to be optimal in a general control problem with intermediate constraints. The method of proof is indirect, a la Hestenes, and requires the functionH of the maximum principle to satisfy a concavity property in the control variable, called localE-dominance.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00937171
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  • 2
    Electronic Resource
    Electronic Resource
    Unique winning policies for linear differential pursuit games (1979)
    Springer
    Journal of optimization theory and applications 29 (1979), S. 629-658 
    Details
    ISSN: 1573-2878
    Keywords: Differential games ; pursuit-evasion problems ; optimal strategies ; control theory ; duality theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study optimal control problems which are the duals, in a specified sense, to a certain class of linear differential games. Directly verifiable conditions, in terms of the data of the game, for uniqueness of solutions of the dual problem and thus for uniqueness of winning policies for the differential game, are derived. As a byproduct, in the particular context of two-dimensional problems, a strong result concerning normality is obtained. As a second byproduct, several geometrical and topological properties of thestar difference are derived. This set operation is of paramount importance for the study of rich classes of differential and difference games extending far beyond that treated here.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934455
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  • 3
    Electronic Resource
    Electronic Resource
    Optimal control of systems with multiple criteria when disturbances are present (1979)
    Springer
    Journal of optimization theory and applications 27 (1979), S. 135-146 
    Details
    ISSN: 1573-2878
    Keywords: Differential games ; Pareto optimality ; multicriteria optimization ; control theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Optimal control problems with a vector performance index and uncertainty in the state equations are investigated. Nature chooses the uncertainty, subject to magnitude bounds. For these problems, a definition of optimality is presented. This definition reduces to that of a minimax control in the case of a scalar cost and to Pareto optimality when there is no uncertainty or disturbance present. Sufficient conditions for a control to satisfy this definition of optimality are derived. These conditions are in terms of a related two-player zero-sum differential game and suggest a technique for determining the optimal control. The results are illustrated with an example.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933331
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  • 4
    Electronic Resource
    Electronic Resource
    Existence of an optimal control for stochastic systems governed by ito equations (1979)
    Springer
    Journal of optimization theory and applications 27 (1979), S. 377-398 
    Details
    ISSN: 1573-2878
    Keywords: Stochastic control problems ; existence theorems ; probability theory ; control theory ; stochastic differential equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We give existence theorems for stochastic control problems with a lower semicontinuous cost functional and governed by Ito equations. We prove that two formulations of the fundamental problem are equivalent, one involving nonanticipative controls and the other involving (measurable) feedback controls. We then use the concept ofconvergence in distribution to prove existence for the first problem, and hence for the second as well. While our work has certain similarities with a paper of Kushner, our techniques are different and lead to more general results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933031
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