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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Archive of applied mechanics 57 (1987), S. 16-24 
    ISSN: 1432-0681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Übersicht Es wird gezeigt, daß ein möglicherweise redundanter Roboter mit steifen Gliedern, welche in den Drehgelenken angetrieben werden, für jeden denkbaren gegebenen Weg der Drehpunkte stabilisiert werden kann. Dieses Resultat gilt ganz allgemein für Roboter mit steifen, jedoch flexiblen Gliedern. Die Lagrangeschen Bewegungsgleichungen werden zur Beschreibung des Roboters benutzt. Die Regelungen sind die polygenen generalisierten Kräfte, die den Lagrangeschen Koordinaten entsprechen. Die stabilisierenden Regelungen werden hergeleitet. Beispiele sind der Behandlung der allgemeinen Theorie vorangestellt.
    Notes: Summary It is shown that a possibly redundant robot with rigid links which is driven at the nodes can be stabilized for any feasible, given path of the nodes. This result is generalized to robots with stiff yet flexible links. The Lagrangean equations of motion are used as a description of the robot. The controls are the polygenic generalized forces corresponding to the Lagrangean coordinates. The stabilizing controls are exhibited. Examples precede the general theory.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    International journal of game theory 3 (1974), S. 47-66 
    ISSN: 1432-1270
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract A coplanar aerial dogfight is analyzed by assuming constant, not necessarily identical, speeds and individual maximum turning rates and lethal ranges. A combatant (A) is assumed to be victorious when his opponent (B) has been maneuvered into a relative position within A's lethal range and in the direction of A's velocity. Three variables are required to define the instantaneous “state” of the game, namely the relative position (2) and the angle (1) between their velocities. A computer program has been constructed to divide the 3-dimensional region of possible initial (and subsequent) states into regions corresponding to victory by one or the other combatant, and, if the faster combatant has the smaller lethal range, a “no contest” region corresponding to escape by the faster combatant. The critical separating surface (or surfaces) is composed of a number of pieces corresponding to initial conditions leading either to simultaneous kill or to “near miss” situations of one type or another. Optimal play is defined in the immediate neighborhood of the entire separating surface, guaranteeing victory (or escape) to one combatant or the other, depending on location on one side or the other of the separating surface.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Dynamics and control 2 (1992), S. 281-301 
    ISSN: 1573-8450
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The minimum-time problem is a well known problem in optimal control and several methods are available to solve this problem. In this article, an extension of the minimum-time problem will be considered. A specific optimal control problem will be treated and the so-called Isopone method to determine the optimal control is proposed. In this Isopone method, multi dimensional reachable subsets are computed repeatedly. This method is similar to dynamic programming in that it is a recursive algorithm, but is designed to reduce the amount of calculation time. The current algorithm yields, as a degenerate case, also the time optimal route.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 42 (1984), S. 551-560 
    ISSN: 1573-2878
    Keywords: Nash games ; linear-quadratic games
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Linear closed-loop no-memory strategies for the LQ Nash game are considered. We exhibit a class of such problems with the property that the solution exists for any finite time interval; for the infinite time case, there exist none or a unique or many solutions, depending on the choice of the parameters. In addition, the limit of the finite time solution as the time interval increases does not have to yield the infinite time case solution. A geometric formulation of the coupled algebraic Riccati equation is given. This formulation seems to be an interesting starting point for a thorough study of these equations.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 59 (1988), S. 467-486 
    ISSN: 1573-2878
    Keywords: Markov games ; zero-sum games ; incomplete information ; pursuit-evasion ; mixed strategies
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Two players, not knowing each other's position, move in a domain and can flash a searchlight. The game terminates when one player is caught within the area illuminated by the flash of the other. However, if this first player is not in this area, then the other player has disclosed his position to the former one, who may be able to exploit this information. The game is considered on a finite state space and in discrete time.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 27 (1979), S. 107-125 
    ISSN: 1573-2878
    Keywords: Differential games ; optimal strategies ; optimal trajectories ; singular surfaces ; solution concepts ; surveillance evasion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A surveillance-evasion differential game of degree with a detection zone in the shape of a two-dimensional cone is posed. The nature of the optimal strategies and the singular phenomena of the value function are described and correlated to subsets of the space of all possible parameter combinations, showing the relation of the singular phenomena in differential game theory and control theory.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 16 (1975), S. 497-517 
    ISSN: 1573-2878
    Keywords: Bang-bang control ; time-optimal control ; switching surfaces ; multidimensional control problems ; control theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This article deals with bang-bang solutions of linear time-optimal control problems. Linear multivariable systems are considered which have one or more control components. It is shown in which way the control components act together to make the system achieve the ultimate aim (namely, the origin in the state space) as quickly as possible. The theory only applies to initial positions sufficiently near the origin. Criteria are given which give the number of switches per control component. Asymptotic dependences of the switching times and the final time on the distance of the initial position from the origin are established. The theory provides a numerical procedure to calculate the time-optimal control. These calculations are very simple. Basic to the proof of these results is a generalized implicit function theorem due to Artin (Ref. 1).
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Journal of engineering mathematics 3 (1969), S. 137-150 
    ISSN: 1573-2703
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Summary The mathematical theory of optimal control is applied to the problem of steering a ship as quickly as possible to a new course. In the linearized theory such an optimal control exists for each change of course and will be discussed for stable as well as unstable ships.
    Type of Medium: Electronic Resource
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