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  • Articles  (11)
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  • control theory  (11)
  • 1970-1974  (11)
  • Mathematics  (11)
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  • Articles  (11)
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  • Mathematics  (11)
  • 1
    Electronic Resource
    Electronic Resource
    On sensitivity in optimal control problems (1974)
    Springer
    Journal of optimization theory and applications 13 (1974), S. 56-73 
    Details
    ISSN: 1573-2878
    Keywords: Sensitivity analysis ; control theory ; mathematical programming ; method of multipliers ; Banach spaces
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Two types of interpretations of multipliers in both static and dynamic optimization problems are described. It is snown that the Lagrange multipliers encountered in mathematical programming problems and the auxiliary functions arising in Pontryagintype optimal control problems sometimes have highly analogous interpretations as rates of change of the optimal attainable value of an objective function, or in some cases as bounds on average rates of change.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935609
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  • 2
    Electronic Resource
    Electronic Resource
    An integral formulation of the ɛ-problem and a new computational approach to control function optimization (1974)
    Springer
    Journal of optimization theory and applications 13 (1974), S. 553-581 
    Details
    ISSN: 1573-2878
    Keywords: Epsilon technique ; computing methods ; control theory ; penalty function methods ; optimal strategies
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A version of Balakrishnan's ε-technique is developed using an integrated description of the system equations. The associated necessary conditions for optimality of theintegral ε-technique appear as integral equations and lead to computational algorithms which are largely independent of the penalty function characteristics of the ε-technique. The merits and shortcomings of this approach are discussed, alternative solution methods are proposed, and some computational results are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933045
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  • 3
    Electronic Resource
    Electronic Resource
    Geometric and analytic views in existence theorems for optimal control in Banach spaces. Part 1. Distributed parameters (1974)
    Springer
    Journal of optimization theory and applications 14 (1974), S. 505-520 
    Details
    ISSN: 1573-2878
    Keywords: Existence theorems ; optimal control ; control theory ; Banach spaces ; distributed parameters
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Existence theorems for optimal control problems in Banach spaces are stated and proved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00932845
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  • 4
    Electronic Resource
    Electronic Resource
    Some sufficient conditions for the observability of nonlinear systems (1974)
    Springer
    Journal of optimization theory and applications 13 (1974), S. 660-669 
    Details
    ISSN: 1573-2878
    Keywords: Observability ; nonlinear systems ; sufficient conditions ; control theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Some sufficient conditions are presented for the observability of systems described by nonlinear, ordinary differential equations with linear observations. The point which the authors especially emphasize is the fact that the results obtained are global in some sense. In the beginning, the observability problem is reduced to the uniqueness problem of solutions of some nonlinear integral equations for general nonlinear systems with linear observations. Then, for some restricted systems, a simple sufficient condition is derived. The relation between global and local observability for nonlinear systems is also considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933623
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  • 5
    Electronic Resource
    Electronic Resource
    Second-variation methods in periodic optimization (1974)
    Springer
    Journal of optimization theory and applications 14 (1974), S. 31-49 
    Details
    ISSN: 1573-2878
    Keywords: Calculus of variations ; control theory ; Hamilton-Jacobi equation ; periodic processes ; Riccati equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The periodic optimization of continuous dynamical systems is considered in this paper. Sufficient conditions for the optimality of a control function are established first. Then, the problem of finding the perturbations to be given to the nominal optimal control in order to preserve optimality under small parameter variations is stated and solved. Finally, the existence of periodic solution of the Riccati-type equations which are involved in the above problems is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933173
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  • 6
    Electronic Resource
    Electronic Resource
    A lower closure theorem for abstract control problems withL p-bounded controls (1974)
    Springer
    Journal of optimization theory and applications 14 (1974), S. 521-528 
    Details
    ISSN: 1573-2878
    Keywords: Lower closure theorems ; generalized control theory ; control theory ; calculus of variations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A lower closure theorem for an abstract control problem is proved. The functional isJ(ϕ,u)=∝ G f 0(t, (Mϕ)(t),u(t))dt and the state equations areNϕ(t)=f(t, (Mϕ)(t),u(t)). It is shown that, if {(ϕ k ,u k)} is a sequence of admissible controlsu k and corre-sponding trajectories ϕ k such that lim infJ(ϕ k ,u k)〈+∞ and such that ϕ k → ϕ weakly,Mϕ k →Mϕ strongly,Nϕ k →Nϕ weakly, and {u k} is bounded in someL p norm, then there is a controlu such that (ϕ,u) is admissible and lim infJ(ϕ k ,u k)≧J(ϕ,u).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00932846
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  • 7
    Electronic Resource
    Electronic Resource
    Optimal institutional advertising: Minimum-time problem (1974)
    Springer
    Journal of optimization theory and applications 14 (1974), S. 213-231 
    Details
    ISSN: 1573-2878
    Keywords: Management science ; time-optimal control ; Green's theorem approach ; advertising ; control theory ; bang-bang control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper considers the problem of optimizing the institutional advertising expenditure for a firm which produces two products. The problem is formulated as a minimum-time control problem for the dynamics of an extended Vidale-Wolfe advertising model, the optimal control being the rate of institutional advertising that minimizes the time to attain the specified target market shares for the two products. The attainable set and the optimal control are obtained by applying the recent theory developed by Hermes and Haynes extending the Green's theorem approach to higher dimensions. It is shown that the optimal control is a strict bang-bang control. An interesting side result is that the singular arc obtained by the Green's theorem application turns out to be a maximum-time solution over the set of all feasible controls. The result clarifies the connection between the Green's theorem approach and the maximum principle approach.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00932941
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  • 8
    Electronic Resource
    Electronic Resource
    Status of periodic optimization of dynamical systems (1974)
    Springer
    Journal of optimization theory and applications 14 (1974), S. 1-20 
    Details
    ISSN: 1573-2878
    Keywords: Periodic processes ; control theory ; mathematical programming ; maximum principle
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The problem of the periodic optimization of dynamical systems, recently considered to some extent in the literature, is reviewed here. The most interesting results among those available are illustrated. Mention is made of the most significant and open aspects of the problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933171
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  • 9
    Electronic Resource
    Electronic Resource
    Hamilton-Jacobi theory for periodic control problems (1974)
    Springer
    Journal of optimization theory and applications 14 (1974), S. 21-29 
    Details
    ISSN: 1573-2878
    Keywords: Calculus of variations ; control theory ; Hamilton-Jacobi equation ; periodic processes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The general problem of periodic optimization is considered in this paper. The contribution consists in stating sufficient conditions for the optimality of a control satisfying the periodicity constraint. The result has been achieved by means of the classical Hamilton-Jacobi equation, suitably modified in order to consider the peculiar constraint of the problem. Finally, an interesting application of the theory to the case of linear, time-invariant systems is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933172
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  • 10
    Electronic Resource
    Electronic Resource
    Controllability of nonlinear systems with restrained controls (1974)
    Springer
    Journal of optimization theory and applications 14 (1974), S. 251-262 
    Details
    ISSN: 1573-2878
    Keywords: Controllability ; nonlinear systems ; linearization methods ; control variable constraints ; control theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we examine the controllability of nonlinear differential systems which are perturbations of systems of the formx=A(t)x+g(t, u). Under appropriate assumptions, we show that integrably bounded perturbations preserve the controllability properties of the base system in the case when the control values are restrained. Our approach is based on the necessary and sufficient growth condition for controllability developed earlier by the author.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00932609
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