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  • Artikel  (26)
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  • Biologie  (1)
  • 1
    Digitale Medien
    Digitale Medien
    Analysis of a sterile insect release model with predation (1982)
    Springer
    Journal of mathematical biology 16 (1982), S. 33-48 
    Details
    ISSN: 1432-1416
    Schlagwort(e): Sterile insect release ; Predation ; Stability ; Limit cycles ; Optimal control
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00275159
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  • 2
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): Optimal control ; maximum principle ; sufficient conditions ; integro-differential equations ; path constraints ; economic applications
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract Notational errors in Theorem 5.2 of Ref. 1 are corrected.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934332
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  • 3
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): Optimal control ; suboptimal control ; time-delay systems ; linear systems
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934590
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  • 4
    Digitale Medien
    Digitale Medien
    Suboptimal control of systems with multiple delays (1980)
    Springer
    Journal of optimization theory and applications 30 (1980), S. 621-633 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; time-delay systems ; linear systems ; multiple-delay systems
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01686725
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  • 5
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): Optimal control ; measures ; Hilbert spaces ; linear programming ; approximation techniques
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01686727
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  • 6
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): Optimal control ; junction conditions ; calculus of variations ; inequality constraints
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934790
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  • 7
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): Optimal control ; economic systems ; stability ; existence theory ; turnpike property
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934475
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  • 8
    Digitale Medien
    Digitale Medien
    On optimal control problems with state constraints (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 75-80 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; state constraints ; multipliers ; perturbation theory
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934843
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  • 9
    Digitale Medien
    Digitale Medien
    A property of an autonomous minimax optimal control problem (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 81-87 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; minimax problems ; maximum principle ; Hamiltonian function
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract A control system $$\dot x = f\left( {x,u} \right)$$ ,u) with cost functional $$\mathop {ess \sup }\limits_{T0 \leqslant t \leqslant T1} G\left( {x\left( t \right),u\left( t \right)} \right)$$ is considered. For an optimal pair $$\left( {\bar x\left( \cdot \right),\bar u\left( \cdot \right)} \right)$$ ,ū(·)), there is a maximum principle of the form $$\eta \left( t \right)f\left( {\bar x\left( t \right),\bar u\left( t \right)} \right) = \mathop {\max }\limits_{u \in \Omega \left( t \right)} \eta \left( t \right)f\left( {\bar x\left( t \right),u} \right).$$ By means of this fact, it is shown that $$\eta \left( t \right)f\left( {\bar x\left( t \right),\bar u\left( t \right)} \right)$$ is equal to a constant almost everywhere.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934844
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  • 10
    Digitale Medien
    Digitale Medien
    An exact penalty function algorithm for optimal control problems with control and terminal equality constraints, part 1 (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 211-246 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; control constraints ; terminal equality constraints ; exact penalty function ; convergence
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The presence of control constraints, because they are nondifferentiable in the space of control functions, makes it difficult to cope with terminal equality constraints in optimal control problems. Gradient-projection algorithms, for example, cannot be employed easily. These difficulties are overcome in this paper by employing an exact penalty function to handle the cost and terminal equality constraints and using the control constraints to define the space of permissible search directions in the search-direction subalgorithm. The search-direction subalgorithm is, therefore, more complex than the usual linear program employed in feasible-directions algorithms. The subalgorithm approximately solves a convex optimal control problem to determine the search direction; in the implementable version of the algorithm, the accuracy of the approximation is automatically increased to ensure convergence.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934725
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  • 11
    Digitale Medien
    Digitale Medien
    Sufficient conditions for asymptotic optimal control (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 307-325 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; asymptotic optimal control ; calculus of variations ; Lagrange problems ; global minima ; absolute minima ; necessary conditions ; sufficient conditions
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract For a selected family of Lagrange-type control problems involving a nonnegative integral costJ T (y,u) over the interval [0,T], 0〈T〈∞, with system conditions consisting of differential inequalities and/or equalities, the following material is treated: (i) a resumé of relevant necessary conditions and sufficient conditions for a pair (y T ,u T ) to minimizeJ T (y,u); (ii) conditions sufficient for the convergence asT→∞ of minimizing pairs (y T ,u T ) over [0,T] to a limit pair (y ∞,u ∞) over the infinite-time interval [0, ∞); (iii) conditions sufficient for (y ∞,u ∞) to minimize the costJ ∞(y,u) over [0, ∞); and (iv) conditions sufficient for the optimal cost per unit timeJ T (y T ,u T )/T to have a limit asT→∞.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934555
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  • 12
    Digitale Medien
    Digitale Medien
    An exact penalty function algorithm for optimal control problems with control and terminal equality constraints, part 2 (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 345-364 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; control constraints ; terminal equality constraints ; exact penalty functions ; convergence ; relaxed control
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract In Part 1 of this paper, implementable and conceptual versions of an algorithm for optimal control problems with control constraints and terminal equality constraints were presented. It was shown that anyL ∞ accumulation points of control sequences generated by the algorithms satisfy necessary conditions of optimality. Since such accumulation points need not exist, it is shown in this paper that control sequences generated by the algorithms always have accumulation points in the sense of control measure, and these accumulation points satisfy optimality conditions for the corresponding relaxed control problem.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934557
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  • 13
    Digitale Medien
    Digitale Medien
    On the order of singular optimal control problems (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 479-489 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; singular control ; junction conditions ; singular control order
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract In singular optimal control problems, the functional form of the optimal control function is usually determined by solving the algebraic equation which results by successively differentiating the switching function until the control appears explicitly. This process defines the order of the singular problem. Order-related results are developed for singular linear-quadratic problems and for a bilinear example which gives new insights into the relationship between singular problem order and singular are order.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934035
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  • 14
    Digitale Medien
    Digitale Medien
    On the general inverse problem of optimal control theory (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 491-497 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; inverse problems ; dynamic programming
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The general inverse problem of optimal control is considered from a dynamic programming point of view. Necessary and sufficient conditions are developed which two integral criteria must satisfy if they are to yield the same optimal feedback law, the dynamics being fixed. Specializing to the linear-quadratic case, it is shown how the general results given here recapture previously obtained results for quadratic criteria with linear dynamics.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934036
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  • 15
    Digitale Medien
    Digitale Medien
    Optimal control of continuous-time deterministic systems with incomplete discrete feedback (1990)
    Springer
    Journal of optimization theory and applications 64 (1990), S. 557-571 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; deterministic systems ; discrete incomplete information ; sufficient conditions for optimality ; feedback systems
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract Sufficient conditions for optimality are obtained for controls that depend on the current time and values of known functions of the state vector at finite points of the time interval. The equations for finding the required control laws are derived. An example is given for which an exact solution of the problem can be obtained.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00939424
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  • 16
    Digitale Medien
    Digitale Medien
    On a student-related optimal control problem (1990)
    Springer
    Journal of optimization theory and applications 65 (1990), S. 129-138 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; mathematical modelling ; study strategies
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract In a recent paper (Ref. 1), Cheng and Teo discussed some further extensions of a student-related optimal control problem which was originally proposed by Raggettet al. (Ref. 2) and later on modified by Parlar (Ref. 3). In this paper, we treat further extensions of the problem.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00941164
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  • 17
    Digitale Medien
    Digitale Medien
    Additional necessary conditions for optimal control with state-variable inequality constraints (1982)
    Springer
    Journal of optimization theory and applications 38 (1982), S. 241-250 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; state constraints ; necessary conditions for optimality
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract It is shown that, when the set of necessary conditions for an optimal control problem with state-variable inequality constraints given by Bryson, Denham, and Dreyfus is appropriately augmented, it is equivalent to the (different) set of conditions given by Jacobson, Lele, and Speyer. Relationships among the various multipliers are given.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934086
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  • 18
    Digitale Medien
    Digitale Medien
    Discrete approximation of relaxed optimal control problems (1990)
    Springer
    Journal of optimization theory and applications 65 (1990), S. 395-407 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; nonlinear systems ; discretization ; nonconvexity ; relaxed controls ; approximation
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract We consider a general nonlinear optimal control problem for systems governed by ordinary differential equations with terminal state constraints. No convexity assumptions are made. The problem, in its so-called relaxed form, is discretized and necessary conditions for discrete relaxed optimality are derived. We then prove that discrete optimality [resp., extremality] in the limit carries over to continuous optimality [resp., extremality]. Finally, we prove that limits of sequences of Gamkrelidze discrete relaxed controls can be approximated by classical controls.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00939558
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  • 19
    Digitale Medien
    Digitale Medien
    Optimal production mix (1990)
    Springer
    Journal of optimization theory and applications 66 (1990), S. 255-273 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; state constraints ; production problems
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract This paper deals with a production plant in which two different products can be produced. The plant consists of three subsystemsS i . Before or after a phase of separate processing in subsystemsS 1 andS 2, the two products have to be processed in subsystemS 3. Each of these subsystems has a limited capacity. In the first part, we assume empty stocks at the beginning; at a fixed timeT in the future, certain quantitiesX i of the two products have to be delivered to the customers. Facing linear holding costs, convex production costs, and stringent capacity constraints, the problem is to decide when to produce which product at what rate. It is shown that the optimal solution consists of up to six different regimes and that the time paths of the production rates need not be monotonic. These results, which can be obtained analytically, are also illustrated in several numerical examples. Finally, the case is considered where the terminal demand at timeT is replaced by a continuous and seasonally fluctuating demand rate. It is demonstrated that the optimal production rates show an interesting and nontrivial behavior. In particular, it may happen that, on intervals where the demand for the one product increases, the optimal production rate decreases. This is also demonstrated by computer plots in some numerical examples.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00939538
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  • 20
    Digitale Medien
    Digitale Medien
    Small penalty control of the end temperature in a long rod (1990)
    Springer
    Journal of optimization theory and applications 66 (1990), S. 443-454 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; heat transfer ; singularly perturbed integral equations
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The problem considered is that of maintaining the end temperature of a long rod near a prescribed level over a fixed time interval. Control is achieved via the heat flux at the near end, and it is optimal in the sense that it minimizes a given performance index of quadratic form. The performance index contains a penalty parameter associated with the magnitude of the control. Particular attention is given to the determination of the optimal control when the penalty parameter is small (i.e., cheap control). This gives rise to a singularly perturbed integral equation, which is solved asymptotically by a methodology which has recently been developed for a related class of problems.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00940931
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  • 21
    Digitale Medien
    Digitale Medien
    On the optimal control of minimum film thickness (1990)
    Springer
    Journal of optimization theory and applications 67 (1990), S. 17-41 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; existence ; numerical approximation ; piston rings ; journal bearings ; hydrodynamic lubrication theory
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The present paper is concerned with the study of controlling the motion of a bearing so that the thin film of lubricant separating it from its container will have the largest possible thickness. Explicit equations are derived, and the control problem is solved explicitly in some simple cases.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00939733
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  • 22
    Digitale Medien
    Digitale Medien
    Time-axis decomposition of large-scale optimal control problems (1990)
    Springer
    Journal of optimization theory and applications 67 (1990), S. 259-277 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; time-axis decomposition ; Stackelberg games ; bilevel programming
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract Continuous-time optimal control problems can rarely be solved directly but have to be approximated with discrete analogues. Shorter time steps lead to more accurate approximations, but result in formulations that are often too big for computer memory. This paper presents a technique for decomposing the problem along the time axis and iterating toward a solution in a leader-follower framework. In the model, the leader controls a set of coordination parameters, which he passes to the followers, who then solve their individual subproblems. State and sensitivity information is returned to the leader, who attempts to minimize an unconstrained problem in the coordination space. Parameters are updated and the process continues until improvement ceases. Two advantages of this technique are that feasible solutions to the original problem are available at each iteration and that the optimal coordination parameters obtained provide some measure of feedback control. Computational results are presented for a comprehensive set of test problems.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00940476
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  • 23
    Digitale Medien
    Digitale Medien
    Optimal control of time-delay systems with distributed parameters (1990)
    Springer
    Journal of optimization theory and applications 67 (1990), S. 567-585 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; parabolic partial differential equations ; time-delay systems ; necessary conditions ; sufficient conditions ; maximum principle
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract An optimal control problem with a prescribed performance index for parabolic systems with time delays is investigated. A necessary condition for optimality is formulated and proved in the form of a maximum principle. Under additional conditions, the maximum principle gives sufficient conditions for optimality. It is also shown that the optimal control is unique. As an illustration of the theoretical consideration, an analytic solution is obtained for a time-delayed diffusion system.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00939650
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  • 24
    Digitale Medien
    Digitale Medien
    Dynamic programming using singular perturbations (1982)
    Springer
    Journal of optimization theory and applications 38 (1982), S. 221-230 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; dynamic programming ; singular perturbations ; system order reduction
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The singular perturbation method is used in dynamic programming to reduce the order and the computational requirements of linear systems composed of slow and fast modes. After the fast modes are separated, a near-optimum solution is computed at two different iteration rates determined by the slow and fast subsystem dynamics. The result is a reduction in the order of the computational requirement of the given system to that of the slow subsystem.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934084
    Standort Signatur Erwartet Verfügbarkeit
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  • 25
    Digitale Medien
    Digitale Medien
    Maximum principle, dynamic programming, and their connection in deterministic control (1990)
    Springer
    Journal of optimization theory and applications 65 (1990), S. 363-373 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; maximum principle ; dynamic programming ; viscosity solutions ; superdifferential ; subdifferential
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract Two major tools for studying optimally controlled systems are Pontryagin's maximum principle and Bellman's dynamic programming, which involve the adjoint function, the Hamiltonian function, and the value function. The relationships among these functions are investigated in this work, in the case of deterministic, finite-dimensional systems, by employing the notions of superdifferential and subdifferential introduced by Crandall and Lions. Our results are essentially non-smooth versions of the classical ones. The connection between the maximum principle and the Hamilton-Jacobi-Bellman equation (in the viscosity sense) is thereby explained by virtue of the above relationship.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01102352
    Standort Signatur Erwartet Verfügbarkeit
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  • 26
    Digitale Medien
    Digitale Medien
    Optimal control of linear time-varying systems via Fourier series (1990)
    Springer
    Journal of optimization theory and applications 65 (1990), S. 375-384 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; time-varying systems ; Fourier series operational matrix ; Fourier series approximation
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The optimal control of linear time-varying systems with quadratic cost functional is obtained by Fourier series approximation. The properties of Fourier series are first briefly presented and the operational matrix of backward integration together with the product operational matrix are utilized to reduce the optimal control problem to a set of simultaneous linear algebraic equations. An illustrative example is included to demonstrate the validity and applicability of the technique.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01102353
    Standort Signatur Erwartet Verfügbarkeit
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    Artikel (Nationallizenzen)
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