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  • Articles  (11)
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  • Springer  (11)
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  • American Institute of Physics (AIP)
  • American Physical Society
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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Meccanica 32 (1997), S. 555-565 
    ISSN: 1572-9648
    Keywords: Spacecraft dynamics ; Optimal control ; Hamilton principle ; Vibrations (structures)
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Modern space vehicles structure requisites are getting more and more stringent and complex as mission tasks become more sophisticated. This leads to the necessity of developing analysis methods that take into account structure flexibility and the need of reducing manoeuvre time as much as possible. In this work, a method based on the Hamilton Principle in its weak mixed form is developed, in which co-ordinates derivatives do not appear, but only their virtual variations. The proposed formulation is able to take into account system flexibility and saturation constraints on control torques and forces. A non-linear variational condition is obtained, which can be solved by means of a time-finite-element technique to give the minimum-time solutions of the control problem. The solutions for slewing manoeuvres are given, along with a new solution of the distributed optimal control problem.
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of mathematical biology 35 (1997), S. 775-792 
    ISSN: 1432-1416
    Keywords: Key words: Chemotherapy ; HIV ; Optimal control ; Ordinary differential equation system
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract.  Using an existing ordinary differential equation model which describes the interaction of the immune system with the human immunodeficiency virus (HIV), we introduce chemotherapy in an early treatment setting through a dynamic treatment and then solve for an optimal chemotherapy strategy. The control represents the percentage of effect the chemotherapy has on the viral production. Using an objective function based on a combination of maximizing benefit based on T cell counts and minimizing the systemic cost of chemotherapy (based on high drug dose/strength), we solve for the optimal control in the optimality system composed of four ordinary differential equations and four adjoint ordinary differential equations.
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Acta mathematicae applicatae sinica 13 (1997), S. 425-437 
    ISSN: 1618-3932
    Keywords: Optimal control ; tandem queueing system
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider a two-station tandem queue with no intermediate buffer. Jobs at the first station may be blocked when the following station is occupied by another job. The objective is to control the arrival and departure processes, subject to some capacity limits, so that an expected discounted profit function is maximized. We prove that the optimal control policy is of a threshold type, and the characterization of the threshold is provided.
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Mathematics of control, signals, and systems 10 (1997), S. 247-264 
    ISSN: 1435-568X
    Keywords: Descriptor systems ; Differential algebraic equations ; Optimal control ; Strangeness index ; Riccati differential-algebraic equations ; Euler-Lagrange equations ; Linear feedback
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Mathematics , Technology
    Notes: Abstract We study linear quadratic optimal control problems for linear variable coefficient descriptor systems. Generalization from the case of standard control problems leads to several difficulties. We discuss a behavioral approach that solves some of these difficulties. Furthermore, an analysis of general rectangular systems is given and generalized Euler-Lagrange equations and Riccati differential algebraic equations are discussed.
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 95 (1997), S. 101-126 
    ISSN: 1573-2878
    Keywords: Optimal control ; Lagrange multipliers ; augmented Lagrangians ; variational inequalities
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We investigate optimal control problems governed by variational inequalities involving constraints on the control, and more precisely the example of the obstacle problem. In this paper, we discuss some augmented Lagrangian algorithms to compute the solution.
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical methods of operations research 45 (1997), S. 63-79 
    ISSN: 1432-5217
    Keywords: Optimal control ; Markov decision processes ; light traffic ; discounted cost ; average cost
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We consider Markov Decision Processes under light traffic conditions. We develop an algorithm to obtain asymptotically optimal policies for both the total discounted and the average cost criterion. This gives a general framework for several light traffic results in the literature. We illustrate the method by deriving the asymptotically optimal control of a simple ATM network.
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 93 (1997), S. 103-119 
    ISSN: 1573-2878
    Keywords: Optimal control ; variational convergence ; functional differential equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The paper deals with the variational convergence of a sequence of optimal control problems for functional differential state equations with deviating argument. Variational limit problems are found under various conditions of convergence of the input data. It is shown that, upon sufficiently weak assumptions on convergence of the argument deviations, the limit problem can assume a form different from that of the whole sequence. In particular, it can be either an optimal control problem for an integro-differential equation or a purely variational problem. Conditions are found under which the limit problem preserves the form of the original sequence.
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 93 (1997), S. 597-607 
    ISSN: 1573-2878
    Keywords: Optimal control ; gradient flows ; optimization ; decentralized systems ; performance index
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, the problem of computing the suboptimal output feedback gains of decentralized control systems is investigated. First, the problem is formulated. Then, the gradient matrices based on the index function are derived and a new algorithm is established based on some nice properties. This algorithm shows that a suboptimal gain can be computed by solving several ordinary differential equations (ODEs). In order to find an initial condition for the ODEs, an algorithm for finding a stabilizing output feedback gain is exploited, and the convergence of this algorithm is discussed. Finally, an example is given to illustrate the proposed algorithm.
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 94 (1997), S. 273-309 
    ISSN: 1573-2878
    Keywords: Optimal control ; Euler flow equations ; sequential quadratic programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we study a design problem for a duct flow with a shock. The presence of the shock causes numerical difficulties. Good shock-capturing schemes with low continuity properties often cannot be combined successfully with efficient optimization methods requiring smooth functions. A remedy studied in this paper is to introduce the shock location as an explicit variable. This allows one to fit the shock and yields a problem with sufficiently smooth functions. We prove the existence of optimal solutions, Fréchet differentiability, and the existence of Lagrange multipliers. In the second part, we introduce and investigate the discrete problem and study the relations between the optimality conditions for the infinite-dimensional problem and the discretized one. This reveals important information for the numerical solution of the problem. Numerical examples are given to demonstrate the theoretical findings.
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 94 (1997), S. 155-168 
    ISSN: 1573-2878
    Keywords: Optimal control ; Bellman function ; value function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, time-optimal control problems with closed terminal sets are considered. We give conditions which guarantee the Bellman function to be Hölder and Lipschitz continuous. We then prove that the condition for Lipschitz continuity is also necessary.
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  • 11
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 95 (1997), S. 323-346 
    ISSN: 1573-2878
    Keywords: Optimal control ; sequential quadratic programming ; dynamic programming ; Newton method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Efficient sequential quadratic programming (SQP) implementations are presented for equality-constrained, discrete-time, optimal control problems. The algorithm developed calculates the search direction for the equality-based variant of SQP and is applicable to problems with either fixed or free final time. Problem solutions are obtained by solving iteratively a series of constrained quadratic programs. The number of mathematical operations required for each iteration is proportional to the number of discrete times N. This is contrasted by conventional methods in which this number is proportional to N 3. The algorithm results in quadratic convergence of the iterates under the same conditions as those for SQP and simplifies to an existing dynamic programming approach when there are no constraints and the final time is fixed. A simple test problem and two application problems are presented. The application examples include a satellite dynamics problem and a set of brachistochrone problems involving viscous friction.
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