1,721,006 research outputs found
On the metric regularity of affine optimal control problems
No full textThe paper establishes properties of the type of (strong) metric regularity of the set-valued map associated with the system of necessary optimality conditions for optimal control problems that are affine with respect to the control (shortly, affine problems). It is shown that for such problems it is reasonable to extend the standard notions of metric regularity by involving two metrics in the image space of the map. This is done by introducing (following an earlier paper by the first and the third named author) the concept of (strong) bi-metric regularity in a general space setting. Lyusternik-Graves-type theorems are proved for (strongly) bi-metrically regular maps, which claim stability of these regularity properties with respect to “appropriately small” perturbations. Based on that, it is proved that in the case of a map associated with affine optimal control problems, the strong bi-metric regularity is invariant with respect to linearization. This result is complemented with a sufficient condition for strong bi-metric regularity for linear-quadratic affine optimal control problems, which applies to the “linearization” of a nonlinear affine problem. Thus the same conditions are also sufficient for strong bi-metric regularity in the nonlinear affine problem
Higher-order numerical scheme for linear quadratic problems with bang–bang controls
Full text linkThis paper considers a linear-quadratic optimal control problem where the control function appears linearly and takes values in a hypercube. It is assumed that the optimal controls are of purely bang-bang type and that the switching function, associated with the problem, exhibits a suitable growth around its zeros. The authors introduce a scheme for the discretization of the problem that doubles the rate of convergence of the Euler's scheme. The proof of the accuracy estimate employs some recently obtained results concerning the stability of the optimal solutions with respect to disturbances
Gradient methods on strongly convex feasible sets and optimal control of affine systems
No full textThe paper presents new results about convergence of the gradient projection and the conditional gradient methods for abstract minimization problems on strongly convex sets. In particular, linear convergence is proved, although the objective functional does not need to be convex. Such problems arise, in particular, when a recently developed discretization technique is applied to optimal control problems which are affine with respect to the control. This discretization technique has the advantage to provide higher accuracy of discretization (compared with the known discretization schemes) and involves strongly convex constraints and possibly non-convex objective functional. The applicability of the abstract results is proved in the case of linear-quadratic affine optimal control problems. A numerical example is given, confirming the theoretical findings
Metric Regularity Properties in Bang-Bang Type Linear-Quadratic Optimal Control Problems
Full text linkThe paper investigates the Lipschitz/Hölder stability with respect to perturbations of the solutions of linear-quadratic optimal control problems where the control variable appears linearly and the optimal one is of bang-bang type. Conditions for bi-metric regularity and (Hölder) metric sub-regularity are established, involving only the order of the zeros of the associated switching function and smoothness of the data. The results provide a basis for investigation of various approximation methods and are applied in this paper for convergence analysis of a Newton-type method
High Order Discrete Approximations to Mayer's Problems for Linear Systems
No full textThis paper presents a discretization scheme for Mayer's type optimal control problems of linear systems. The scheme is based on second order Volterra--Fliess approximations, and on an augmentation of the control variable in a control set of higher dimension. Compared with the existing results, it has the advantage of providing a higher order accuracy, which may make it more efficient when aiming for a certain precision. Error estimations (depending on the controllability index of the system at the solution) are proved by using a recent result about stability of the optimal solution with respect to disturbances. Numerical results are provided which show the sharpness of the error estimations.
Read More: http://epubs.siam.org/doi/abs/10.1137/16M107914
On the Regularity of Linear-Quadratic Optimal Control Problems with Bang-Bang Solutions
No full textThe paper investigates the stability of the solutions of linear-
quadratic optimal control problems with bang-bang controls in terms of
metric sub-regularity and bi-metric regularity. New sufficient conditions for these properties are obtained, which strengthen the known conditions for sub-regularity and extend the known conditions for bi-metric regularity to Bolza-type problems
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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