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Applications of artificial neural networks for nonlinear data
\"This book is a collection of research on the contemporary nature of artificial neural networks and their specific implementations within data analysis\"-- Provided by publisher.
Book
Nonlinear system identification : NARMAX methods in the time, frequency, and spatio-temporal domains
Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains describes a comprehensive framework for the identification and analysis of nonlinear dynamic systems in the time, frequency, and spatio-temporal domains. This book is written with an emphasis on making the algorithms accessible so that they can be applied and used in practice.
Includes coverage of:
* The NARMAX (nonlinear autoregressive moving average with exogenous inputs) model
* The orthogonal least squares algorithm that allows models to be built term by term where the error reduction ratio reveals the percentage contribution of each model term
* Statistical and qualitative model validation methods that can be applied to any model class
* Generalised frequency response functions which provide significant insight into nonlinear behaviours
* A completely new class of filters that can move, split, spread, and focus energy
* The response spectrum map and the study of sub harmonic and severely nonlinear systems
* Algorithms that can track rapid time variation in both linear and nonlinear systems
* The important class of spatio-temporal systems that evolve over both space and time
* Many case study examples from modelling space weather, through identification of a model of the visual processing system of fruit flies, to tracking causality in EEG data are all included
to demonstrate how easily the methods can be applied in practice and to show the insight that the algorithms reveal even for complex systems
NARMAX algorithms provide a fundamentally different approach to nonlinear system identification and signal processing for nonlinear systems. NARMAX methods provide models that are transparent, which can easily be analysed, and which can be used to solve real problems.
This book is intended for graduates, postgraduates and researchers in the sciences and engineering, and also for users from other fields who have collected data and who wish to identify models to help to understand the dynamics of their systems.
eBook
Integral Barrier Lyapunov function-based adaptive control for switched nonlinear systems
This paper presents an adaptive control method for a class of uncertain strict-feedback switched nonlinear systems. First, we consider the constraint characteristics in the switched nonlinear systems to ensure that all states in switched systems do not violate the constraint ranges. Second, we design the controller based on the backstepping technique, while integral Barrier Lyapunov functions (iBLFs) are adopted to solve the full state constraint problems in each step in order to realize the direct constraints on state variables. Furthermore, we introduce the Lyapunov stability theory to demonstrate that the adaptive controller achieves the desired control goals. Finally, we perform a numerical simulation, which further verifies the significance and feasibility of the presented control scheme.
Journal Article
Migrating photon avalanche in different emitters at the nanoscale enables 46th-order optical nonlinearity
A photon avalanche (PA) effect that occurs in lanthanide-doped solids gives rise to a giant nonlinear response in the luminescence intensity to the excitation light intensity. As a result, much weaker lasers are needed to evoke such PAs than for other nonlinear optical processes. Photon avalanches are mostly restricted to bulk materials and conventionally rely on sophisticated excitation schemes, specific for each individual system. Here we show a universal strategy, based on a migrating photon avalanche (MPA) mechanism, to generate huge optical nonlinearities from various lanthanide emitters located in multilayer core/shell nanostructrues. The core of the MPA nanoparticle, composed of Yb3+ and Pr3+ ions, activates avalanche looping cycles, where PAs are synchronously achieved for both Yb3+ and Pr3+ ions under 852 nm laser excitation. These nanocrystals exhibit a 26th-order nonlinearity and a clear pumping threshold of 60 kW cm−2. In addition, we demonstrate that the avalanching Yb3+ ions can migrate their optical nonlinear response to other emitters (for example, Ho3+ and Tm3+) located in the outer shell layer, resulting in an even higher-order nonlinearity (up to the 46th for Tm3+) due to further cascading multiplicative effects. Our strategy therefore provides a facile route to achieve giant optical nonlinearity in different emitters. Finally, we also demonstrate applicability of MPA emitters to bioimaging, achieving a lateral resolution of ~62 nm using one low-power 852 nm continuous-wave laser beam.A general mechanism, migrating photon avalanche, can generate large optical nonlinearity from various lanthanides emitters at the nanoscale.
Journal Article
Nonlinear control for temperature and humidity of a 30m3$30 ext{ m}^3$ climate chamber determining VOCs
Abstract This paper studies the tracking control problem for a climate chamber control system used for determining volatile organic compounds. A new nonlinear controller, for the first time, is designed for the temperature and humidity control of a 30m3$30 ext{ m}^3$ climate chamber. For one thing, based on the backstepping technology, an improved control method is proposed with the help of the implicit function theorem instead of employing system linearization. In this way, simplification of the controlled system can be avoidable so that the control accuracy is promoted. For another, without approximations by fuzzy logics or neural networks, the number of complex computations are reduced a lot so that the control rate is improved considerably. In the end, simulation is conducted by Matlab to validate the effectiveness and superiority of the proposed control method.
Journal Article
Event-triggered predefined-time control for full-state constrained nonlinear systems: A novel command filtering error compensation method
In this paper, a command filter-based adaptive fuzzy predefined-time event-triggered tracking control problem is investigated for uncertain nonlinear systems with time-varying full-state constraints. By designing a sliding mode differentiator, the inherent computational complexity problem within the predefined-time backstepping framework is solved. Different from the existing command filter-based finite-time and fixed-time control strategies that the convergence time of the filtering error is adjusted through the system initial value or numerous parameters, a novel command filtering error compensation method is presented, which tunes one control parameter to make the filtering error converge in the predefined time, thereby reducing the complexity of design and analysis of processing the filtering error. Then, an improved event-triggered mechanism (ETM) that builds upon the switching threshold strategy, in which an inverse cotangent function is designed to replace the residual term of the ETM, is proposed to gradually release the controller’s dependence on the residual term with increasing time. Furthermore, a tan-type nonlinear mapping technique is applied to tackle the time-varying full-state constraints problem. By the predefined-time stability theory, all signals in the uncertain nonlinear systems exhibit predefined-time stability. Finally, the feasibility of the proposed algorithm is substantiated through two simulation results.
Journal Article
Improved prescribed performance constraint control for a strict feedback non-linear dynamic system
An improved prescribed performance control using a backstepping technique and adaptive fuzzy is proposed for a strict feedback nonlinear dynamic system. A new virtual variable was defined to generate the virtual control that forces the tracking errors to fall within prescribed boundaries, and an adaptive fuzzy system was used to obtain required approximation performances. A strict feedback controller and adaptive laws for estimating the unknown non-linear function were designed to avoid a singularity problem and calculation of the explosive number of terms generated by the error transformations of conventional error constraint method and the recursive steps of traditional backstepping control. Lyapunov stability analysis confirmed the boundedness and convergence of the closed-loop system. The prescribed error constraint performance of the proposed control scheme was validated by applying it to control the position of a second-order non-linear system and a robot manipulator.
Journal Article
On the theory of Weak Turbulence for the Nonlinear Schrödinger Equation
We study the Cauchy problem for a kinetic equation arising in the weak turbulence theory for the cubic nonlinear Schrödinger
equation. We define suitable concepts of weak and mild solutions and prove local and global well posedness results. Several qualitative
properties of the solutions, including long time asymptotics, blow up results and condensation in finite time are obtained. We also
prove the existence of a family of solutions that exhibit pulsating behavior.
eBook