Strong local optimality for generalized L1 optimal control problems

In this paper, we analyse control affine optimal control problems with a cost functional involving the absolute value of the control. The Pontryagin extremals associated with such systems are given by (possible) concatenations of bang arcs with singular arcs and with inactivated arcs, that is, arcs where the control is identically zero. Here we consider Pontryagin extremals given by a bang-inactive-bang concatenation. We establish sufficient optimality conditions for such extremals, in terms of some regularity conditions and of the coercivity of a suitable finite-dimensional second variation.Comment: Journal of Optimization Theory and Applications, Springer Verlag, In pres

Asymptotic ensemble stabilizability of the Bloch equation

In this paper we are concerned with the stabilizability to an equilibrium point of an ensemble of non interacting half-spins. We assume that the spins are immersed in a static magnetic field, with dispersion in the Larmor frequency, and are controlled by a time varying transverse field. Our goal is to steer the whole ensemble to the uniform "down" position. Two cases are addressed: for a finite ensemble of spins, we provide a control function (in feedback form) that asymptotically stabilizes the ensemble in the "down" position, generically with respect to the initial condition. For an ensemble containing a countable number of spins, we construct a sequence of control functions such that the sequence of the corresponding solutions pointwise converges, asymptotically in time, to the target state, generically with respect to the initial conditions. The control functions proposed are uniformly bounded and continuous

An investigation of the use of otolith microchemistry to discriminate reef fish populations and assess the movement of individuals.

The main objective of this thesis was to assess the degree of connectivity among populations of two highly abundant Caribbean reef fish (Stegasies partitus, Bicolor damselfish, and Haemulon flovolineatum , French grunt) at specific, but different portions of their life history; pelagic and demersal stages. In Chapter 2 (Section A) I assessed the classification of individuals to the site and time they were collected. The classification of S. partitus to their collection sites, separated by as little as 5 km, was moderately successful, while investigations of the temporal variability revealed substantial variability at the scale of two weeks. This spatial and temporal variability in otolith microchemistry suggested that investigations of connectivity were possible, but would require frequent recalibration of chemical signatures. Because the connectivity analysis of Chapter 2 relied upon the spatial variability in otolith chemistry, I investigated how the discrimination of populations could be improved in Chapter 3. An assumption of the connectivity analysis used in Chapter 2 was that otolith elemental concentrations did not differ between fish of different life stages (i.e., larval/pelagic stage with its core chemistry versus juvenile/demersal stage with its edge chemistry). In Chapter 4, I assessed whether there was ontogenetic variability in otolith microchemistry by comparing the otolith chemistry of pre-hatch embryos to that of post-settlement juveniles collected at the same site and time. Results indicated that elemental concentrations of embryo otoliths were between 2 and 325 times greater than that of juvenile edge chemistry (and 2 to 94 times greater than water chemistry) for Mn, Zn, Ba, Ce, and Pb. In Chapter 5 of Section B, I focused on the demersal stage of reef fish and whether otolith microchemistry could be used to discriminate H. flavolineatum caged in adjacent mangrove and coral reef sites in Belize and Bahamas. Significant variability in otolith trace elemental chemistry was detected among sites and habitats, which resulted in the classification of individuals separated by as little as 0.25 km (average correct classifications was between 68% and 85%). In Chapter 6, I expanded the sampling of H. favolineatum (19 sites throughout Turneffe Atoll: 9 mangrove and 11 reef sites, separated by 0.8 to 20m kms) to assess the extent to which individuals could be correctly assigned to the sites from which they were collected when natural movements were permitted (i.e., in the absence of cages, see Chapter 5). In Chapter 7, I discuss the findings of each of these chapters in the context of using otolith microchemistry in ecological investigations. (Abstract shortened by UMI.)Dept. of Biological Sciences. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2005 .C45. Source: Dissertation Abstracts International, Volume: 66-11, Section: B, page: 5776. Thesis (Ph.D.)--University of Windsor (Canada), 2005

Hyperbolicity and curvature in dynamics and control

In this thesis, we will use some techniques developed in the frame of Optimal Control Theory and some tools of Hyperbolic Dynamics to investigate problems of Hamiltonian dynamics and infinite horizon optimal control. The intimate relation between Optimal Control Theory and Hamiltonian Dynamics became clear after the publication of Pontryagin Maximum Principle (PMP) in the 50s ([24]): this result in fact shows that the extremals of an optimal control problem have to be seeked among the solutions of a certain Hamiltonian system associated to the problem..

Minimum-time strong optimality of a singular arc: the multi-input non involutive case

We consider the minimum-time problem for a multi-input control-affine system, where we assume that the controlled vector fields generate a non-involutive distribution of constant dimension, and where we do not assume a-priori bounds for the controls. We use Hamiltonian methods to prove that the coercivity of a suitable second variation associated to a Pontryagin singular arc is sufficient to prove its strong-local optimality. We provide an application of the result to a generalization of Dubins problem

Passive and active navigation of virtual environments vs. traditional printed evacuation maps: A comparative evaluation in the aviation domain

Printed maps are the most common tool to prepare people for emergency evacuation in contexts such as public buildings or transportation. Unfortunately, they are poorly understood and often ignored by people. Virtual environments (VEs) could be a more effective method to support people in acquiring spatial knowledge about the real-world environment to evacuate. This paper pursues three main goals. First, we propose a VE-based tool to support spatial knowledge acquisition for evacuation purposes, using aviation as a real-world domain in which such knowledge is crucial for passengers' safety. Second, we study in detail one of the VE design choices (active or passive navigation), comparing a version of our tool in which users navigate by actively controlling their position with another version in which users are passively led along pre-defined routes. Third, we contrast the two versions of the tool with the traditional, printed diagrammatic map provided to passengers by airlines. Results of our study show that the VE-based approach produces objectively better spatial knowledge when users are asked to pinpoint their assigned position in the environment, and that active navigation produces a performance improvement in a subsequent virtual evacuation. Moreover, the VE-based approach is perceived as more enjoyable, easier to comprehend and more effective than printed maps when active navigation is available