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  • 1
    Digitale Medien
    Digitale Medien
    On the necessary conditions for optimal control of retarded systems (1990)
    Springer
    Applied mathematics & optimization 22 (1990), S. 117-145 
    Details
    ISSN: 1432-0606
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract In this paper we derive necessary conditions, in the form of a maximum principle, for the optimal control of nonlinear, finitely retarded functional differential equations with function-space boundary conditions. We establish these conditions in a setting which guarantees the existence of regular multipliers, admits pointwise control constraints, and, with added restrictions, ensures nontriviality of the multipliers.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01447323
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  • 2
    Digitale Medien
    Digitale Medien
    Existence of optimal control without convexity and a bang-bang theorem for linear volterra equations (1976)
    Springer
    Journal of optimization theory and applications 19 (1976), S. 63-79 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Existence theorems ; linear equations ; Volterra equations ; bang-bang control ; convexity
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract We consider a Mayer problem of optimal control monitored by an integral equation of Volterra type: $$x(t) = x(t_1 ) + \int_{t_1 }^t { [h(t,s)x(s) + g(t, s)f(s, u(s))] ds,} $$ where the measurable control functionu satisfies a constraint of the formu(t) ∈U(t) ⊂E m,t 1≤t≤t 2, andg is a continuous kernel. Using the resolvent kernel associated with the kernelh, we prove the existence of an optimal usual solution for orientor fields without convexity assumptions. Further, ifU is a fixed compact set, we show the existence of an optimal bang-bang control.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934052
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  • 3
    Digitale Medien
    Digitale Medien
    On the optimal control of systems governed by nonlinear volterra equations (1976)
    Springer
    Journal of optimization theory and applications 19 (1976), S. 29-45 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Existence theorems ; nonlinear Volterra equations ; usual solutions ; lower closure theorems ; control theory ; initial-value problems
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract Existence theorems are stated and proved for optimal control problems monitored by a nonlinear Volterra-type integral equation. Growth conditions are taken into consideration which ensure the needed compactness on the set of trajectories and entail the existence of the usual optimal solutions for the given problem. Weak or approximate solutions are taken into consideration in a subsequent paper.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934050
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  • 4
    Digitale Medien
    Digitale Medien
    Existence of solutions of multi-valued Urysohn integral equations (1985)
    Springer
    Journal of optimization theory and applications 46 (1985), S. 129-151 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Urysohn equations ; delay systems ; set-valued mappings ; Kakutani's theorem ; semicontinuity
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract We prove the existence of a solution of an integral inclusion of Urysohn type with delay. By imposing standard boundedness, convexity, and semicontinuity conditions on the set-valued mapping defining the integral inclusion, we show that the right-hand side of the relation constitutes a mapping defined on a suitable Banach space and satisfying the conditions of Kakutani's theorem for the existence of a fixed point of a set-valued mapping. By introducing the notion of generalized or chattering state solutions, we show how the convexity requirements may be relaxed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00938420
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  • 5
    Digitale Medien
    Digitale Medien
    Generalized exterior boundary-value problems and optimization for the Helmholtz equation (1982)
    Springer
    Journal of optimization theory and applications 37 (1982), S. 469-497 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal surface currents ; maximal radiated power ; optimal solutions of the Helmholtz equation ; optimal antenna patterns
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract A class of radiation problems is considered for the Helmholtz equation in exterior domains bounded by a smooth surface on which Dirichlet, Neumann, or Robin boundary conditions are imposed. The problem of finding the boundary data which maximizes far field power in a restricted subset of far field directions is formulated as a constrained maximization problem. Existence of an optimal solution in a variety of control domains is established. The particular case when the boundary is circular and the control domain is the unit ball inL 2 is treated in detail. An algorithm for constructing the optimal solution is derived and used to obtain explicit numerical results.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934952
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  • 6
    Digitale Medien
    Digitale Medien
    The controllability problem for nonlinear Volterra systems (1983)
    Springer
    Journal of optimization theory and applications 41 (1983), S. 9-35 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Nonlinear controllability ; Volterra integral equations ; fixed point theorems for set-valued mappings ; semicontinuity conditions ; seminormality conditions ; generalized solutions
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract We discuss the controllability of systems whose dynamics are governed by a large class of nonlinear Volterra integral equations. The property of controllability is shown to be equivalent to the existence of a fixed point of a certain set-valued map. We show that convexity and seminormality conditions intimately related to those assumed in proofs of existence theorems for optimal controls are sufficient to guarantee controllability. Approximate controllability results are obtained by first introducing generalized solutions and then showing, under only mild additional restrictions, that ordinary solutions are dense in this broader class of trajectories.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934434
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  • 7
    Digitale Medien
    Digitale Medien
    Some remarks on existence of optimal controls for Mayer problems with singular components (1981)
    Springer
    Annali di matematica pura ed applicata 127 (1981), S. 13-24 
    Details
    ISSN: 1618-1891
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary This paper proves an existence theorem for optimal controls for systems governed by ordinary differential equations and a large class of functional differential equations of neutral type. Extensions beyond earlier work are made as a result of employing a new closure theorem originally used by Cesari and Suryanarayana in their study of Pareto optima and which is, in turn, based on the Fatou lemma for vector-valued functions as proved by Schmeidler. The use of these techniques simplifies the standard arguments for existence in the presence of singular components and allows the use of very weak semi-normality conditions. It also permits the consideration of a significantly larger class of hereditary systems than has been treated in the existing literature.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01811716
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  • 8
    Digitale Medien
    Digitale Medien
    L2-boundary integral equations for the robin problem (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 345-352 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper we study an integral equation method for the exterior Robin problem for the Helmholtz equation where the boundary condition is interpreted in the L2-sense. In particular, we derive a composite integral equation from Green's theorem which is uniquely solvable for all wave numbers.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060121
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  • 9
    Digitale Medien
    Digitale Medien
    Boundary integral equations for the Helmholtz equation: The third boundary value problem (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 164-193 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper we study the application of boundary integral equation methods for the solution of the third, or Robin, boundary value problem for the exterior Helmholtz equation. In contrast to earlier work, the boundary value problem is interpreted here in a weak sense which allows data to be specified in L∞ (∂D), ∂D being the boundary of the exterior domain which we assume to be Lyapunov of index 1. For this exterior boundary value problem, we employ Green's theorem to derive a pair of boundary integral equations which have a unique simultaneous solution. We then show that this solution yields a solution of the original exterior boundary value problem.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670040112
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  • 10
    Digitale Medien
    Digitale Medien
    An optimal design problem for submerged bodies (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 50-76 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The problem of finding the shape of a smooth body submerged in a fluid of finite depth which minimizes added mass or damping is considered. The optimal configuration is sought in a suitably constrained class so as to be physically meaningful and for which the mathematical problem of a submerged body with linearized free surface condition is uniquely solvable. The problem is formulated as a constrained optimization problem whose cost functional (e.g. added mass) is a domain functional. Continuity of the solution of the boundary value problem with respect to variations of the boundary is established in an appropriate function space setting and this is used to establish existence of an optimal solution. A variational inequality is derived for the optimal shape and it is shown how finite dimensional approximate solutions may be found.
    Zusätzliches Material: 5 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670080105
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