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  • 1
    Electronic Resource
    Electronic Resource
    On the optimal controls of a class of systems governed by second order parabolic partial delay-differential equations with first boundary conditions (1979)
    Springer
    Annali di matematica pura ed applicata 122 (1979), S. 61-82 
    Details
    ISSN: 1618-1891
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper we consider the question of existence of optimal controls for a class of systems governed by second order parabolic partial delay-differential equations with first boundary conditions and with controls appearing in the coefficients. In Theorems2.2 and2.3 we present existence and uniqueness of solutions of the first boundary problems. In Theorems3.1 and3.2 we prove that whenever the coefficients of the system converge in the w*-topology (L1 topology on L∞) the corresponding solutions converge weakly in an appropriate Sobolev space. Using these basic results we present two theorems (Theorems4.1 and4.2) on the existence of optimal controls.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02411688
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Comments on a selector theorem in Banach spaces (1976)
    Springer
    Journal of optimization theory and applications 19 (1976), S. 117-118 
    Details
    ISSN: 1573-2878
    Keywords: Set-valued mappings ; selection theorem ; reflexive Banach spaces ; weakly compact sets ; Cesari's Q-property ; optimal control theory ; existence of optimal controls
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Recently, Cole (Ref. 1) presented a selection theorem in reflexive Banach spaces under certain convexity assumptions. In this paper, we present a proof of Cole's selection theorem without imposing the convexity condition. This makes the result more powerful for application in optimal control theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934055
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Optimal control of systems governed by a class of nonlinear evolution equations in a reflexive Banach space (1978)
    Springer
    Journal of optimization theory and applications 25 (1978), S. 57-81 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; nonlinear evolution equations ; reflexive Banach spaces ; existence theorems ; time-optimal control ; Bolza problem ; terminal control ; velocity field ; set-valued map ; weak Cesari property
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The paper presents a closure theorem for the attainable trajectories of a class of control systems governed by a large class of nonlinear evolution equations in reflexive Banach spaces. Several existence theorems for optimal controls are proven that include a terminal control problem, a time-optimal control problem, and a special Bolza problem. Some results of independent interest are also presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933255
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    Paper (German National Licenses)
    Fulltext
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