1,721,365 research outputs found
III. Mobilités urbaines durables : les apports d'une recherche finalisée
No full textFusco Giovanni. III. Mobilités urbaines durables : les apports d'une recherche finalisée. In: Annuaire des collectivités locales. Tome 25, 2005. Le financement des politiques locales. pp. 595-608
Gap Phenomena in Optimal Control with State Constraints
Get PDFWhen existence of minimizers of an optimal control problem is not guaranteed, it is a common practice in Control Theory to extend the set of admissible solutions, so that to construct an auxiliary optimization problem that admits minimizers. The first fundamental requirement of such an auxiliary problem for it to be well posed is the density (e.g. in the L∞-norm) of the set of trajectories of the original system into that of the auxiliary one. Nevertheless, due to the presence of constraints, it might happen that the minimum of the auxiliary problem is strictly smaller than the infimum of the original one. We refer to this phenomenon as infimum gap.
In the literature, sufficient conditions for no gap are sometimes expressed in terms of normality of the sets of multipliers of the Maximum Principle. However, in the common situation of active state constraints at the initial point, there always exist degenerate – consequently, abnormal – sets of multipliers.
In this thesis, we establish a gap-abnormality relation for a general auxiliary prob- lem that comprehends as special cases both the compactification of the control set and the convexification of the dynamics in a novel unified framework. Furthermore, we provide refined no infimum gap conditions in order to deal with the presence of state constraints. In particular, under a suitable constraint qualification condition, we prove that if the minimizer of the auxiliary problem is a nondegenerate normal extremal, i.e. it is normal in the subset of nondegenerate multipliers only, then there is no infimum gap.
We highlight the relevance and novelties of our results with several examples, and we analyze in detail the special case of control-polynomial impulsive optimization problems.When existence of minimizers of an optimal control problem is not guaranteed, it is a common practice in Control Theory to extend the set of admissible solutions, so that to construct an auxiliary optimization problem that admits minimizers. The first fundamental requirement of such an auxiliary problem for it to be well posed is the density (e.g. in the L∞-norm) of the set of trajectories of the original system into that of the auxiliary one. Nevertheless, due to the presence of constraints, it might happen that the minimum of the auxiliary problem is strictly smaller than the infimum of the original one. We refer to this phenomenon as infimum gap.
In the literature, sufficient conditions for no gap are sometimes expressed in terms of normality of the sets of multipliers of the Maximum Principle. However, in the common situation of active state constraints at the initial point, there always exist degenerate – consequently, abnormal – sets of multipliers.
In this thesis, we establish a gap-abnormality relation for a general auxiliary prob- lem that comprehends as special cases both the compactification of the control set and the convexification of the dynamics in a novel unified framework. Furthermore, we provide refined no infimum gap conditions in order to deal with the presence of state constraints. In particular, under a suitable constraint qualification condition, we prove that if the minimizer of the auxiliary problem is a nondegenerate normal extremal, i.e. it is normal in the subset of nondegenerate multipliers only, then there is no infimum gap.
We highlight the relevance and novelties of our results with several examples, and we analyze in detail the special case of control-polynomial impulsive optimization problems
L’évaluation "pragmatique" de la durabilité de la mobilité urbaine
No full textThis paper presents a research projet for a thesis : Elaboration of a systemic model of urban sustainability. The example of daily mobility in Nice and Genoa areas in respect for a international comparison (dir. A. Dauphiné, Nice-Sophia Antipolis University and G. Rabino, Polytechnic of Milan).Il s’agit ici de présenter un projet de recherche dans le cadre d’une thèse de doctorat intitulée : Élaboration d’un modèle systémique d’indicateurs de durabilité urbaine. Le cas de la mobilité quotidienne à Nice et à Gênes dans une comparaison internationale, sous la direction d’André Dauphiné (Université de Nice-Sophia Antipolis) et de Giovanni Rabino (Polytechnique de Milan).Fusco Giovanni. L’évaluation "pragmatique" de la durabilité de la mobilité urbaine. In: Cahiers Nantais, n°60, 2003. Transports, environnement et pratiques territoriales. pp. 167-169
No Infimum Gap and Normality in Optimal Impulsive Control Under State Constraints
Get PDFIn this paper we consider an impulsive extension of an optimal control problem with unbounded controls, subject to endpoint and state constraints. We show that the existence of an extended-sense minimizer that is a normal extremal for a constrained Maximum Principle ensures that there is no gap between the infima of the original problem and of its extension. Furthermore, we translate such relation into verifiable sufficient conditions for normality in the form of constraint and endpoint qualifications. Links between existence of an infimum gap and normality in impulsive control have previously been explored for problems without state constraints. This paper establishes such links in the presence of state constraints and of an additional ordinary control, for locally Lipschitz continuous data
Impulsive optimal control problems with time delays in the drift term
Get PDFWe introduce a notion of bounded variation solution for a new class of nonlinear control systems with ordinary and impulsive controls, in which the drift function depends not only on the state, but also on its past history, through a finite number of time delays. After proving the well-posedness of such solutions and the continuity of the corresponding input-output map with respect to suitable topologies, we establish necessary optimality conditions for an associated optimal control problem. The approach, which involves approximating the problem by a non-impulsive optimal control problem with time delays and using Ekeland’s principle combined with a recent, nonsmooth version of the Maximum Principle for conventional delayed systems, allows us to deal with mild regularity assumptions and a general endpoint constraint
Nondegenerate Abnormality, Controllability, and Gap Phenomena in Optimal Control with State Constraints
Get PDFIn optimal control theory, infimum gap means that there is a gap between the infimum values of a given minimum problem and an extended problem, obtained by enlarging the set of original solutions and controls. The gap phenomenon is somewhat ``dual"" to the problem of the controllability of the original control system to an extended solution. In this paper we present sufficient conditions for the absence of an infimum gap and for controllability for a wide class of optimal control problems subject to endpoint and state constraints. These conditions are based on a nondegenerate version of the nonsmooth constrained maximum principle, expressed in terms of subdifferentials. In particular, under some new constraint qualification conditions, we prove that (i) if an extended minimizer is a nondegenerate normal extremal, then no gap shows up; (ii) given an extended solution verifying the constraints, either it is a nondegenerate abnormal extremal or the original system is controllable to it. An application to the impulsive extension of a free end-time, nonconvex optimization problem with control-polynomial dynamics illustrates the results
Optimal impulse control problems with time delays: An illustrative example
Get PDFFor impulse control systems described by a measure driven differential equation, depending linearly on the measure, it is customary to interpret the state trajectory corresponding to an impulse control, specified by a measure, as the limit of state trajectories associated with some sequence of conventional controls approximating the measure. It is known that, when the measure is vector valued, it is possible that different choices of approximating sequences for the measure give rise to different limiting state trajectories. If the measure is scalar valued, however, there is a unique limiting trajectory. Now consider impulse control systems, in which the right side of the measure driven differential equation depends on both the current and delayed states. In recent work by the authors it has been shown that, for such impulse control systems with time delay, the state trajectory corresponding to a given measure may be non-unique, even when the measure is scalar valued. It was also shown that each limiting state trajectory can be identified with the unique state trajectory associated with some measure together with a family of ‘attached controls’. (The attached controls capture the nature of the measure approximation.) The authors also derived a maximum principle governing minimizers for a general class of impulse optimal control problems with time delay, in which the domain of the optimization problem comprises measures coupled with a family of ‘attached controls’. The purpose of this paper is both to illustrate, by means of an example, this newly discovered non-uniqueness phenomenon and to provide the first application of the new maximum principle, to investigate minimizers for scalar input impulse optimal control problems with time delay, in circumstances when limiting state trajectories associated with a given measure control are not unique. The example is an optimal control problem, for which the underlying control system is a forced harmonic oscillator, with scalar impulse control, in which the control gain is a nonlinear function of the current and delayed states
Abnormality and Strict-Sense Minimizers That Are Not Extended Minimizers
Get PDFWe consider a constrained optimal control problem and an extension of it, in which the set
of strict sense trajectories is enlarged. Extension is a common procedure in optimal control, used to derive necessary and sufficient optimality conditions for the original problem from the extended one, which usually admits a minimizer and has a more regular structure. However, this procedure fails if the two problems have different infima. It is therefore relevant to identify such situations. Following on from earlier work by Warga but adopting perturbation techniques developed in nonsmooth analysis, we investigate the relation between the occurrence of an infimum gap and abnormality of necessary conditions. For a notion of local minimizer based on control distance and an extension including the impulsive one, we prove that (i) a local extended minimizer which is not a local minimizer of the original problem and (ii) a local strict sense minimizer which is not a local minimizer of the extended problem, both satisfy the extended maximum principle in abnormal form. The main novelty is result (ii), as until now it had only been shown that a strict sense minimizer which is not an extended minimizer is abnormal for an `averaged version' of the maximum principle
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe 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
- …
