1,789 research outputs found
Adaptive Quantizers for Estimation
In this paper, adaptive estimation based on noisy quantized observations is
studied. A low complexity adaptive algorithm using a quantizer with adjustable
input gain and offset is presented. Three possible scalar models for the
parameter to be estimated are considered: constant, Wiener process and Wiener
process with deterministic drift. After showing that the algorithm is
asymptotically unbiased for estimating a constant, it is shown, in the three
cases, that the asymptotic mean squared error depends on the Fisher information
for the quantized measurements. It is also shown that the loss of performance
due to quantization depends approximately on the ratio of the Fisher
information for quantized and continuous measurements. At the end of the paper
the theoretical results are validated through simulation under two different
classes of noise, generalized Gaussian noise and Student's-t noise
Ill-posedness of time-dependent inverse problems in Lebesgue-Bochner spaces
We consider time-dependent inverse problems in a mathematical setting using
Lebesgue-Bochner spaces. Such problems arise when one aims to recover
parameters from given observations where the parameters or the data depend on
time. There are various important applications being subject of current
research that belong to this class of problems. Typically inverse problems are
ill-posed in the sense that already small noise in the data causes tremendous
errors in the solution. In this article we present two different concepts of
ill-posedness: temporally (pointwise) ill-posedness and uniform ill-posedness
with respect to the Lebesgue-Bochner setting. We investigate the two concepts
by means of a typical setting consisting of a time-depending observation
operator composed by a compact operator. Furthermore we develop regularization
methods that are adapted to the respective class of ill-posedness.Comment: 21 pages, no figure
Digital repetitive control under varying frequency conditions
Premi extraordinari doctorat curs 2011-2012, à mbit d’Enginyeria IndustrialThe tracking/rejection of periodic signals constitutes a wide field of research in the control theory and applications area and
Repetitive Control has proven to be an efficient way to face this topic; however, in some applications the period of the signal to
be tracked/rejected changes in time or is uncertain, which causes and important performance degradation in the standard
repetitive controller. This thesis presents some contributions to the open topic of repetitive control working under varying
frequency conditions. These contributions can be organized as follows:
One approach that overcomes the problem of working under time varying frequency conditions is the adaptation of the
controller sampling period, nevertheless, the system framework changes from Linear Time Invariant to Linear Time-Varying
and the closed-loop stability can be compromised. This work presents two different methodologies aimed at analysing the
system stability under these conditions. The first one uses a Linear Matrix Inequality (LMI) gridding approach which provides
necessary conditions to accomplish a sufficient condition for the closed-loop Bounded Input Bounded Output stability of the
system. The second one applies robust control techniques in order to analyse the stability and yields sufficient stability
conditions. Both methodologies yield a frequency variation interval for which the system stability can be assured. Although
several approaches exist for the stability analysis of general time-varying sampling period controllers few of them allow an
integrated controller design which assures closed-loop stability under such conditions. In this thesis two design
methodologies are presented, which assure stability of the repetitive control system working under varying sampling period
for a given frequency variation interval: a mu-synthesis technique and a pre-compensation strategy.
On a second branch, High Order Repetitive Control (HORC) is mainly used to improve the repetitive control performance
robustness under disturbance/reference signals with varying or uncertain frequency. Unlike standard repetitive control, the
HORC involves a weighted sum of several signal periods. With a proper selection of the associated weights, this high order
function offers a characteristic frequency response in which the high gain peaks located at harmonic frequencies are
extended to a wider region around the harmonics. Furthermore, the use of an odd-harmonic internal model will make the
system more appropriate for applications where signals have only odd-harmonic components, as in power electronics
systems. Thus an Odd-harmonic High Order Repetitive Controller suitable for applications involving odd-harmonic type
signals with varying/uncertain frequency is presented. The open loop stability of internal models used in HORC and the one
presented here is analysed. Additionally, as a consequence of this analysis, an Anti-Windup (AW) scheme for repetitive
control is proposed. This AW proposal is based on the idea of having a small steady state tracking error and fast recovery
once the system goes out of saturation.
The experimental validation of these proposals has been performed in two different applications: the Roto-magnet plant and
the active power filter application. The Roto-magnet plant is an experimental didactic plant used as a tool for analysing and
understanding the nature of the periodic disturbances, as well as to study the different control techniques used to tackle this
problem. This plant has been adopted as experimental test bench for rotational machines. On the other hand, shunt active
power filters have been widely used as a way to overcome power quality problems caused by nonlinear and reactive loads.
These power electronics devices are designed with the goal of obtaining a power factor close to 1 and achieving current
harmonics and reactive power compensation.Award-winningPostprint (published version
Contraction analysis of nonlinear systems and its application
The thesis addresses various issues concerning the convergence properties of switched systems and differential algebraic equation (DAE) systems. Specifically, we focus on contraction analysis problem, as well as tackling problems related to stabilization and synchronization. We consider the contraction analysis of switched systems and DAE systems. To address this, a transformation is employed to convert the contraction analysis problem into a stabilization analysis problem. This transformation involves the introduction of virtual systems, which exhibit a strong connection with the Jacobian matrix of the vector field. Analyzing these systems poses a significant challenge due to the distinctive structure of their Jacobian matrices. Regarding the switched systems, a time-dependent switching law is established to guarantee uniform global exponential stability (UGES). As for the DAE system, we begin by embedding it into an ODE system. Subsequently, the UGES property is ensured by analyzing its matrix measure. As our first application, we utilize our approach to stabilize time-invariant switched systems and time-invariant DAE systems, respectively. This involves designing control laws to achieve system contractivity, thereby ensuring that the trajectory set encompasses the equilibrium point. In oursecond application, we propose the design of a time-varying observer by treating the system’s output as an algebraic equation of the DAE system. In our study on synchronization problems, we investigate two types of synchronization issues: the trajectory tracking of switched oscillators and the pinning state synchronization. In the case of switched oscillators, we devise a time-dependent switching law to ensure that these oscillators effectively follow the trajectory of a time-varying system. As for the pinning synchronization problem, we define solvable conditions and, building upon these conditions, we utilize contraction theory to design dynamic controllers that guarantee synchronization is achieved among the agents
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