598 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
Advanced control and optimisation of DC-DC converters with application to low carbon technologies
Prompted by a desire to minimise losses between power sources and loads, the aim of this Thesis is
to develop novel maximum power point tracking (MPPT) algorithms to allow for efficient power
conversion within low carbon technologies. Such technologies include: thermoelectric generators
(TEG), photovoltaic (PV) systems, fuel cells (FC) systems, wind turbines etc. MPPT can be
efficiently achieved using extremum seeking control (ESC) also known as perturbation based extremum
seeking control. The basic idea of an ESC is to search for an extrema in a closed loop fashion
requiring only a minimum of a priori knowledge of the plant or system or a cost function.
In recognition of problems that accompany ESC, such as limit cycles, convergence speed, and
inability to search for global maximum in the presence local maxima this Thesis proposes novel
schemes based on extensions of ESC. The first proposed scheme is a variance based switching
extremum seeking control (VBS-ESC), which reduces the amplitude of the limit cycle
oscillations. The second scheme proposed is a state dependent parameter extremum seeking control
(SDP-ESC), which allows the exponential decay of the perturbation signal. Both the VBS-ESC and the
SDP-ESC are universal adaptive control schemes that can be applied in the aforementioned systems.
Both are suitable for local maxima search. The global maximum search scheme proposed in this
Thesis is based on extensions of the SDP-ESC. Convergence to the global maximum is achieved by the
use of a searching window mechanism which is capable of scanning all available maxima within
operating range. The ability of the proposed scheme to converge to the global maximum is
demonstrated through various examples. Through both simulation and experimental studies the benefit
of the SDP-ESC has been consistently demonstrated
Condensates and Singularities in String Theory
We derive a class of solutions to the string sigma-model equations for the
closed bosonic string. The tachyon field is taken to form a constant condensate
and the beta-function equations at one-loop level are solved for the evolution
of the metric and the dilaton. The solutions represent critical string theories
in arbitrary dimensions. The spectrum of the subclass of models with a linearly
rising asymptotic dilaton is found using the Feigin-Fuks method. Certain
approximate solutions arising in string field theory are used to illustrate the
results explicitly. An argument based on conformal invariance leads to the
conjecture that that stringy corrections to at least some singular spacetimes
in general relativity result in non-singular metrics. We use the singularities
of the big-bang/crunch type appearing in our models to examine this conjecture.Comment: 20 pages, DAMTP-R92-40, IUHET 24
Physical parameters and basis transformations in the Two-Higgs-Doublet model
A direct connection between physical parameters of general Two-Higgs-Doublet
Model (2HDM) potentials after electroweak symmetry breaking (EWSB) and the
parameters that define the potentials before EWSB is established. These
physical parameters, such as the mass matrix of the neutral Higgs bosons, have
well defined transformation properties under basis transformations transposed
to the fields after EWSB. The relations are also explicitly written in a basis
covariant form. Violation of these relations may indicate models beyond 2HDMs.
In certain cases the whole potential can be defined in terms of the physical
parameters. The distinction between basis transformations and
reparametrizations is pointed out. Some physical implications are discussed.Comment: 11 pages. 1 figure. v2: references and comments adde
Unified analysis of terminal-time control in classical and quantum systems
Many phenomena in physics, chemistry, and biology involve seeking an optimal
control to maximize an objective for a classical or quantum system which is
open and interacting with its environment. The complexity of finding an optimal
control for maximizing an objective is strongly affected by the possible
existence of sub-optimal maxima. Within a unified framework under specified
conditions, control objectives for maximizing at a terminal time physical
observables of open classical and quantum systems are shown to be inherently
free of sub-optimal maxima. This attractive feature is of central importance
for enabling the discovery of controls in a seamless fashion in a wide range of
phenomena transcending the quantum and classical regimes.Comment: 10 page
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