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  • Articles  (28)
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  • Optimal control  (28)
  • 1980-1984  (28)
  • Mathematics  (28)
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  • Articles  (28)
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  • 1
    Electronic Resource
    Electronic Resource
    Analysis of a sterile insect release model with predation (1982)
    Springer
    Journal of mathematical biology 16 (1982), S. 33-48 
    Details
    ISSN: 1432-1416
    Keywords: Sterile insect release ; Predation ; Stability ; Limit cycles ; Optimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A model for the sterile insect release method of pest control in which the target species is under predatory or parasitic regulation is analyzed. The equations are nondimensionalized and the rescaled parameters are interpreted. There are four types of equilibria, whose existence and stability depend on which of ten regions of parameter space contain the rescaled parameters, and in turn give minimal release rates to achieve eradication of the pest. In at least one region, Hopf bifurcation theory shows the existence of limit cycles, but they are found to be unstable. In addition, the optimal release rate to minimize a total cost functional for pest control by the sterile release method is studied. Both approaches show that when predation accounts for a large fraction of the natural deaths, the necessary release rate and total cost are higher than for weak predation. If the predators are removed without being replaced by any other source of mortality, the cost rises in all cases but rises much more dramatically for cases with strong predation. A definite danger of the sterile release method when some predatory control exists is that the predators are frequently driven extinct before the prey, so that the target species could explode to much higher levels and be more difficult to eradicate again after the sterile release is terminated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00275159
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  • 2
    Electronic Resource
    Electronic Resource
    Some remarks on the existence of optimal controls for quasilinear systems (1981)
    Springer
    Journal of optimization theory and applications 33 (1981), S. 393-399 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; nonlinear systems ; existence theorems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let a quasilinear control system having the state space $$\bar X \subseteq R^n $$ be governed by the vector differential equation $$\dot x = G(u(t))x,$$ wherex(0) =x 0 andU is the family of all bounded measurable functions from [0,T] intoU, a compact and convex subset ofR m.LetG:U ⇑R be a bounded measurable nonlinear function, such thatG(U) is compact and convex.G −1 can be convex onG(U) or concave. The main results of the paper establish the existence of a controlu ∈U which minimizes the cost functional $$I(u) = \int_0^T {L(u(t))x(t)dt,} $$ whereL(·) is convex. A practical example of application for chemical reactions is worked out in detail.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935251
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  • 3
    Electronic Resource
    Electronic Resource
    Sufficient conditions for the optimal control of a class systems with continuous lags (1982)
    Springer
    Journal of optimization theory and applications 38 (1982), S. 153-154 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; maximum principle ; sufficient conditions ; integro-differential equations ; path constraints ; economic applications
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Notational errors in Theorem 5.2 of Ref. 1 are corrected.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934332
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  • 4
    Electronic Resource
    Electronic Resource
    On the optimal control problem of a single-server queueing system (1983)
    Springer
    Journal of optimization theory and applications 41 (1983), S. 317-325 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; queueing theory ; phase type distributions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For a single-server queueing system (with a finite waiting room) with phase type arrivals and exponential service times, an optimal control for the service rate is derived. This generalizes the result of Scott and Jefferson for theM/M/1/1 queueing model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935227
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  • 5
    Electronic Resource
    Electronic Resource
    Near-optimum design of nonstationary linear systems with state and control delays (1980)
    Springer
    Journal of optimization theory and applications 30 (1980), S. 73-88 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; suboptimal control ; time-delay systems ; linear systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A computationally efficient method based on a sensitivity approach is developed to obtain suboptimal control for nonstationary linear systems with multiple state and control delays and with quadratic cost. The proposed suboptimal control includes some truncated series whose terms are calculated in a recursive manner from nondelay system optimization.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934590
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  • 6
    Electronic Resource
    Electronic Resource
    Suboptimal control of systems with multiple delays (1980)
    Springer
    Journal of optimization theory and applications 30 (1980), S. 621-633 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; time-delay systems ; linear systems ; multiple-delay systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The application of Pontryagin's maximum principle to the optimization of linear systems with time delays results in a system of coupled two-point boundary-value problems involving both delay and advance terms. The exact solution of this system of TPBV problems is extremely difficult, if not impossible. In this paper, a fast-converging iterative approach is developed for obtaining the suboptimal control for nonstationary linear systems with multiple state and control delays and with quadratic cost. At each step of the proposed method, a linear nondelay system with an extra perturbing input must be optimized. The procedure can be extended for the optimization of nonlinear systems with multiple time-varying delays, provided that some of the nonlinearities satisfy the Lipschitz condition.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01686725
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  • 7
    Electronic Resource
    Electronic Resource
    Solution of nonlinear optimal control problems in Hilbert spaces by means of linear programming techniques (1980)
    Springer
    Journal of optimization theory and applications 30 (1980), S. 643-661 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; measures ; Hilbert spaces ; linear programming ; approximation techniques
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Optimal control problems in Hilbert spaces are considered in a measure-theoretical framework. Instead of minimizing a functional defined on a class of admissible trajectory-control pairs, we minimize one defined on a set of measures; this set is defined by the boundary conditions and the differential equation of the problem. The new problem is an infinite-dimensionallinear programming problem; it is shown that it is possible to approximate its solution by that of a finite-dimensional linear program of sufficiently high dimensions, while this solution itself can be approximated by a trajectory-control pair. This pair may not be strictly admissible; if the dimensionality of the finite-dimensional linear program and the accuracy of the computations are high enough, the conditions of admissibility can be said to be satisfied up to any given accuracy. The value given by this pair to the functional measuring the performance criterion can be about equal to theglobal infimum associated with the classical problem, or it may be less than this number. It appears that this method may become a useful technique for the computation of optimal controls, provided the approximations involved are acceptable.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01686727
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  • 8
    Electronic Resource
    Electronic Resource
    Junction phenomena for optimal control with state-variable inequality constraints of third order (1980)
    Springer
    Journal of optimization theory and applications 31 (1980), S. 85-99 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; junction conditions ; calculus of variations ; inequality constraints
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is known that extremal arcs governed by inequality constraints of third order (constraint relations that must be differentiated three times to generate a control equation) cannot join an unconstrained arc, except in special cases. But a control problem is exhibited, for which every extremal includes a constrained arc of third order. The constrained arc joins the end of an infinite sequence of consecutive unconstrained arcs of finite total duration. Evidence (but not proof) is given that this phenomenon is typical, rather than exceptional. An analogous phenomenon is well known for optimal control problems with singular arcs of second order.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934790
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  • 9
    Electronic Resource
    Electronic Resource
    Existence and global asymptotic stability of optimal trajectories for a class of infinite-horizon, nonconvex systems (1980)
    Springer
    Journal of optimization theory and applications 31 (1980), S. 515-533 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; economic systems ; stability ; existence theory ; turnpike property
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Sufficient conditions for the existence of optimal trajectories and for the global asymptotic stability of these trajectories are given for a class of nonconvex and nonautonomous systems controlled over an infinite-time horizon. The concept ofG-supported trajectory is introduced. It is shown that, under some assumptions, aG-supported trajectory is overtaking and is globally asymptotically stable. The concept of overtaking trajectory has been previously defined as a notion of optimality on an infinite-time domain. For autonomous systems, under weaker conditions, one guarantees the existence of weakly overtaking trajectories. Finally, it is shown howG-supported trajectories can be obtained, and an application to the study of a pre-predator ecosystem optimally harvested is sketched.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934475
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  • 10
    Electronic Resource
    Electronic Resource
    On optimal control problems with state constraints (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 75-80 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; state constraints ; multipliers ; perturbation theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is concerned with necessary conditions for a general optimal control problem developed by Russak and Tan. It is shown that, in most cases, a further relation between the multipliers holds. This result is of interest in particular for the investigation of perturbations of the state constraint.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934843
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