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  • 1
    Monograph available for loan
    Monograph available for loan
    Sustainable management of natural resources : mathematical models and methods (2008)
    Berlin [u.a.] : Springer
    Details Availability
    Call number: PIK M 370-09-0045
    Description / Table of Contents: Contents: Sequential Decision Models ; Equilibrium and Stability ; Viable Sequential Decisions ; Optimal Sequential Decisions ; Sequential Decisions under Uncertainty ; Robust and Stochastic Viability ; Robust and Stochastic Optimization ; Sequential Decision under Imperfect Information ; Appendix: Mathematical Proofs ; Index
    Type of Medium: Monograph available for loan
    Pages: XI, 266 S. : graph. Darst.
    ISBN: 9783540790730
    Series Statement: Environmental science and engineering : Environmental science
    Location: A 18 - must be ordered
    Branch Library: PIK Library
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  • 2
    Electronic Resource
    Electronic Resource
    Mutational equations for shapes and vision-based control (1995)
    Springer
    Journal of mathematical imaging and vision 5 (1995), S. 99-109 
    Details
    ISSN: 1573-7683
    Keywords: vision-based control ; visual servoing ; shape gradient ; mutational equation ; shape regulation ; shape Lyapunov function ; Hausdorff's distance ; optical flow equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Basic idea of vision-based control in robotics is to include the vision system directly in the control servo loop of the robot. When images are binary, this problem corresponds to the control of the evolution of a geometric domain. The present paper proposes mathematical tools derived from shape analysis and optimization to study this problem in a quite general way, i.e., without any regularity assumptions or modelsa priori on the domains that we deal with. Indeed, despite the lackness of a vectorial structure, one can develop a differential calculus in the metric space of all non-empty compact subsets of a given domain ofR n , and adapt ideas and results of classical differential systems to study and control the evolution of geometric domains. For instance, a shape Lyapunov characterization allows to investigate the asymptotic behavior of these geometric domains using the notion of directional shape derivative. We apply this inR 2 to the visual servoing problem using the optical flow equations and some experimental simulations illustrate this approach.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01250522
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  • 3
    Electronic Resource
    Electronic Resource
    Storage and Viability of a Fishery with Resource and Market Dephased Seasonalities (2000)
    Springer
    Environmental and resource economics 15 (2000), S. 1-26 
    Details
    ISSN: 1573-1502
    Keywords: dynamic model ; fisheries economics ; storage regulation ; viability analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering , Economics
    Notes: Abstract In this study we analyse the role of the storageregulation in a fishery's production process when theresource exploited and the market to which theproduction is exported are characterized by seasonaldephased oscillations. For this purpose we built up adynamic model drawn from the French Guyana shrimpfishery example. The underlying objective of the modelis not the maximisation of a given criterion (as wouldbe in the optimal control approach), but merely themaintenance of the fishery's economical viability. Thefundamental principle is here to try to preserve asmany as possible viable control options. Theconditions to achieve and maintain this viability arecaptured in a certain number of constraints. Theanalysis points out periods and situations within theseason where the fishermen must anticipate theevolution of their storage to avoid violating thoseviability constraints. The study also indicates howthe fishery's viability can be ensured even if theexploitation costs exceed the commercial value of thelandings for a finite part of the year. However, whenthe resource's and/or market's oscillations are toolarge, the fishery may be not viable any longer and itappears that the crisis can not be removed byinvesting in larger storage capacities.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008336002697
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  • 4
    Electronic Resource
    Electronic Resource
    Lattice operators underlying dynamic systems (1996)
    Springer
    Set-valued analysis 4 (1996), S. 119-134 
    Details
    ISSN: 1572-932X
    Keywords: 06A23 ; 34A60 ; 68U10 ; 93C15 ; complete lattice ; algebraic dilation and erosion ; algebraic opening and closing ; semicontinuity ; differential inclusion ; contingent cone ; reachable set ; exit tube ; viability kernel ; invariance kernel
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper investigates algebraic and continuity properties of increasing set operators underlying dynamic systems. We recall algebraic properties of increasing operators on complete lattices and some topologies used for the study of continuity properties of lattice operators. We apply these notions to several operators induced by a differential equation or differential inclusion. We especially focus on the operators associating with any closed subset its reachable set, its exit tube, its viability kernel or its invariance kernel. Finally, we show that morphological operators used in image processing are particular cases of operators induced by constant differential inclusion.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00425961
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  • 5
    Electronic Resource
    Electronic Resource
    Lipschitz Kernel of a Closed Set-Valued Map (2000)
    Springer
    Set-valued analysis 8 (2000), S. 101-109 
    Details
    ISSN: 1572-932X
    Keywords: Lipschitz selection ; Lipschitz kernel ; Lipschitz extension ; discriminating kernel
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper deals with Lipschitz selections of set-valued maps with closed graphs. First, we characterize Lipschitzianity of a closed set-valued map in the differential games framework in terms of a discriminating property of its graph. This allows us to consider the λ-Lipschitz kernel of a given set-valued map as the largest λ-Lipschitz closed set-valued map contained in the initial one, to derive an algorithm to compute the collection of Lipschitz selections, and to extend the Pasch–Hausdorff envelope to set-valued maps.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008722524668
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  • 6
    Electronic Resource
    Electronic Resource
    Guaranteed Output Feedback Control for Uncertain Systems under Control and State Constraints (2000)
    Springer
    Set-valued analysis 8 (2000), S. 149-162 
    Details
    ISSN: 1572-932X
    Keywords: output regulation ; robust control problem ; state constraints ; guaranteed viability ; Hamilton–Jacobi–Isaac equation ; Lipschitz kernel
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper deals with output feedback control of uncertain nonlinear dynamic systems in the presence of state and control constraints. We provide necessary and sufficient conditions for the guaranteed viability property defined by the existence of a Lipschitz closed-loop that maintains exactly the state of the system in a given closed domain of constraints despite some bounded disturbances acting both on the dynamics and on the output. Using the notion of Lipschitz kernel of a closed set-valued map, we obtain some equivalent geometric and Hamilton–Jacobi–Isaac conditions for the guaranteed viability property. We derive an algorithm to build a guaranteed viable output feedback.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008734827394
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  • 7
    Electronic Resource
    Electronic Resource
    Filippov and invariance theorems for mutational inclusions of tubes (1993)
    Springer
    Set-valued analysis 1 (1993), S. 289-303 
    Details
    ISSN: 1572-932X
    Keywords: 34A99 ; 34G99 ; 49J99 ; 49N99 ; 494J52 ; 54G60 ; 46G05 ; Transitions ; mutations ; Filippov's theorem ; invariance ; contingent cone
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The framework of transitions and mutational calculus inspired by shape optimization allows the notions of derivative, tangent cone, and differential equation to be extended to a metric space and especially to the family of all nonempty compact subsets of a given domainE. It gives tools to study the evolution of tubes and fundamental theorems such as those of Cauchy-Lipschitz, Nagumo, or Lyapunov, well known in vector spaces, can be adapted to mutational equations. The present paper deals with mutational inclusions of tubes which include many tube control problems and an adaptation of the Filippov theorem is proved. As a consequence, an invariance theorem is stated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01027639
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  • 8
    Electronic Resource
    Electronic Resource
    Mutational equations of the morphological dilation tubes (1995)
    Springer
    Journal of mathematical imaging and vision 5 (1995), S. 219-230 
    Details
    ISSN: 1573-7683
    Keywords: mathematical morphology ; dilation tubes ; mutational calculus
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The present paper provides some differential results dealing with the morphological dilation of a compact set in the nonregular case. Indeed the evolution of dilated sets with respect to time is characterized through mutational equations which are new mathematical tools extending the concept of differential equations to the metric space of all nonempty compact sets of ℝ n . Using this new tool, we prove that the mutation of the dilation is the normal cone which is a generalization of the classical notion of normal. This result clearly establishes that the dilation transforms this initial set in the direction of the normal at any point of the set. Furthermore, it does not require any regularity assumptions on the compact set.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01248373
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  • 9
    Electronic Resource
    Electronic Resource
    Control of Uncertain Systems under Bounded Chattering (1998)
    Springer
    Dynamics and control 8 (1998), S. 163-176 
    Details
    ISSN: 1573-8450
    Keywords: robust stabilization ; differential games
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper, we propose a mathematical method to compute a robust control with bounded chattering enabling to stabilize a uncertain dynamical system around an equilibrium of the nominal system (non disturbed system) The idea is to consider the problem in the framework of differential games and to treat the stabilization problem as a state constraint inspired from a Lyapunov characterization. The notion of Leadership kernel then provides states and controls allowing the system to converge exponentially to a neighborhood of the equilibrium.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008271413337
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  • 10
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    Maximum Economic Yield Fishery Management in the Face of Global Warming (2018)
    Elsevier
    Details
    Publication Date: 2018-12-01
    Print ISSN: 0921-8009
    Electronic ISSN: 1873-6106
    Topics: Energy, Environment Protection, Nuclear Power Engineering , Economics
    Published by Elsevier
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