846 research outputs found
Nonlocal Nonholonomic Source Seeking Despite Local Extrema
In this paper, we investigate the problem of source seeking with a unicycle
in the presence of local extrema. Our study is motivated by the fact that most
of the existing source seeking methods follow the gradient direction of the
signal function and thus only lead to local convergence into a neighborhood of
the nearest local extremum. So far, only a few studies present ideas on how to
overcome local extrema in order to reach a global extremum. None of them apply
to second-order (force- and torque-actuated) nonholonomic vehicles. We consider
what is possibly the simplest conceivable algorithm for such vehicles, which
employs a constant torque and a translational/surge force in proportion to an
approximately differentiated measured signal. We show that the algorithm steers
the unicycle through local extrema towards a global extremum. In contrast to
the previous extremum-seeking studies, in our analysis we do not approximate
the gradient of the objective function but of the objective function's local
spatial average. Such a spatially averaged objective function is expected to
have fewer critical points than the original objective function. Under suitable
assumptions on the averaged objective function and on sufficiently strong
translational damping, we show that the control law achieves practical uniform
asymptotic stability and robustness to sufficiently weak measurement noise and
disturbances to the force and torque inputs
An Efficient Global Optimization Method Based on Multi-Unit Extremum Seeking
RÉSUMÉ
Les problèmes d'optimisation industrielle, telle que la maximisation de la production de produits
chimiques et pétrochimiques, montrent généralement plusieurs points optimaux locaux. Le
développement de méthode pour la sélection du point optimal global a toujours fait l’objet de
nombreuses recherches. Plusieurs techniques dĂ©terministes et stochastiques ont Ă©tĂ© explorĂ©es Ă
cette fin. Les techniques stochastiques ne garantissent pas toujours la convergence vers la
solution globale, mais sont efficaces pour les dimensions supérieures. D'autre part, les méthodes
déterministes se rendent à l'optimum global, mais le défi est d'employer un cloisonnement
efficace de l'espace afin de réduire le nombre d'évaluations fonctionnelles.
Cette thèse propose une approche originale en matière d’optimisation globale, numérique et
déterministe basée sur des techniques d'optimisation locale en temps réel et en particulier, sur
des techniques sans modèle appelé les systèmes de commande extrémale. Pour les problèmes
sans contrainte, les systèmes de commande extrémale représente le problème d'optimisation
comme un contrôle du gradient. La façon dont le gradient est estimé constitue la différence
principale entre les différentes alternatives qui sont proposées dans la littérature scientifique. Pour
les méthodes de perturbation, un signal d'excitation temporelle est utilisé afin de calculer le
gradient. Une alternative existe dans le cadre d'optimisation multi-unité où le gradient est estimé
par la différence finie de la sortie de deux unités identiques, mais dont les données d’entré se
distinguent par un décalage.
Le point de départ de cette recherche a été motivée par les systèmes de commandes extrémales
locales. Ces commandes sont basées sur une perturbation qui peut être utilisée comme un outil
pour l'optimisation globale des polynômes scalaires du quatrième ordre avec un optimum global.
L'objectif de cette thèse est d'étendre ce concept et de développer une technique d'optimisation
globale déterministe pour une classe générale de systèmes multi-variables, statiques, non linéaires
et continus. Dans cette thèse, il est d'abord démontré que si le décalage est réduit à zéro pour une
optimisation multi-unité scalaire, le système converge vers l'optimum global. Le résultat est
également étendu aux problèmes scalaires avec contraintes qui sont caractérisés par des régions
non-convexes. Dans ce cas, une stratégie de commande de “Switching” est utilisée pour faire face
aux contraintes.----------ABSTRACT
Industrial optimization problems, e.g., maximizing production in chemical and petrochemical
facilities, typically exhibit multiple local optimal points and so choosing the global one has
always attracted many researchers. Many deterministic and stochastic techniques have been
explored towards this end. The stochastic techniques do not always guarantee convergence to the
global solution, but fare well computationally for higher dimensions. On the other hand, the
deterministic methods get to the global optimum, while the challenge therein is to employ an
efficient partitioning of the space in order to reduce the number of functional evaluations.
This thesis proposes an original approach to numerical deterministic global optimization based on
real-time local optimization techniques (in particular, model-free techniques termed the
extremum-seeking schemes). For unconstrained problems, extremum-seeking schemes recast the
optimization problem as the control of the gradient. The way the gradient is estimated forms the
main difference between different alternatives that are proposed in the literature. In perturbation
methods, a temporal excitation signal is used in order to compute the gradient. As an alternative,
in the multi-unit optimization framework, the gradient is estimated as the finite difference of the
outputs of two identical units driven with the inputs that differ by an offset.
The starting point of this research was motivated by the perturbation-based extremum seeking
schemes which can be used as a tool for global optimization of scalar fourth order polynomials,
with one local and one global optimum. The objective of this thesis is to extend this concept and
develop a deterministic global optimization technique for a general class of multi-variable, static,
nonlinear and continuous systems. In this thesis, it is first shown that in the scalar multi-unit
optimization framework, if the offset is reduced to zero, the scheme converges to the global
optimum. The result is also extended to scalar constrained problems, with possible non-convex
feasible regions, where a switching control strategy is employed to deal with the constraints.
The next step consists of extending the algorithm to more than one variable. For two-input
systems, univariate global optimization was repeated on the circumference of a circle of reducing
radius. With three variables, the two-variable optimization mentioned above is repeated on the
surface of a sphere of reducing radius. Time-scale separation between the various layer
Operations research investigations of satellite power stations
A systems model reflecting the design concepts of Satellite Power Stations (SPS) was developed. The model is of sufficient scope to include the interrelationships of the following major design parameters: the transportation to and between orbits; assembly of the SPS; and maintenance of the SPS. The systems model is composed of a set of equations that are nonlinear with respect to the system parameters and decision variables. The model determines a figure of merit from which alternative concepts concerning transportation, assembly, and maintenance of satellite power stations are studied. A hybrid optimization model was developed to optimize the system's decision variables. The optimization model consists of a random search procedure and the optimal-steepest descent method. A FORTRAN computer program was developed to enable the user to optimize nonlinear functions using the model. Specifically, the computer program was used to optimize Satellite Power Station system components
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