Nonlinear Systems

In this paper we propose digital control methods for steering real analytic controllable systems between arbitrary state configurations. The main idea is to achieve a multirate sampled procedure to perform motions in all the directions of controllability under piecewise constant controls. When it is applied to nonholonomic control systems without drift, the procedure simplifies. In particular, it results in exact steering on chained systems recently introduced in the motion planning literature. A classical example is reported.

A numerical algorithm for computing necessary conditions for performance specifications is developed for nonlinear uncertain systems. The algorithm is similar in nature and behavior to the power algorithm for the p lower bound, and doesn't rely on a descent method. The algorithm is applied to a practical example.

We consider the tracking problem of unknown, robustly stabilizable, multi-input multi-output (MIMO), affine in the control, nonlinear systems with guaranteed prescribed performance. By prescribed performance we mean that the tracking error converges to a predefined arbitrarily small residual set, with convergence rate no less than a prespecified value, exhibiting maximum overshoot as well as undershoot less than some sufficiently small preassigned constants. Utilizing an output error transformation, we obtain a transformed system whose robust stabilization is proven necessary and sufficient to achieve prescribed performance guarantees for the output tracking error of the original system, provided that initially the transformed system is well defined. Consequently, a switching robust control Lyapunov function (RCLF)-based adaptive, state feedback controller is designed, to solve the stated problem. The proposed controller is continuous and successfully overcomes the problem of computing the control law when the approximation model becomes uncontrollable. Simulations illustrate the approach.

This work presents system identification using neural network approaches for modelling a laboratory based twin rotor multi-input multi-output system (TRMS). Here we focus on a memetic algorithm based approach for training the multilayer perceptron neural network (NN) applied to nonlinear system identification. In the proposed system identification scheme, we have exploited three global search methods namely genetic algorithm (GA), Particle Swarm Optimization (PSO) and differential evolution (DE) which have been hybridized with the gradient descent method i.e. the back propagation (BP) algorithm to overcome the slow convergence of the evolving neural networks (EANN). The local search BP algorithm is used as an operator for GA, PSO and DE. These algorithms have been tested on a laboratory based TRMS for nonlinear system identification to prove their efficacy.

This paper demonstrates the ability of Genetic Algorithms (GAs) in the identification of dynamical nonlinear systems. The dynamics of the nonlinear systems have been described by first, second and third order terms. GAs were used suc-cessfully to identify the coefficient of these terms. A com-parison between least-square estimation (LSE) and genetic algorithms estimation (GAE) procedures is provided. The comparison was employed based on two factors, number of observations and estimation accuracy. Genetic algorithms show better performance in both noise free and noisy cases.

This work deals with the state estimation and diagnosis of nonlinear systems with application to power systems. Dynamic modeling is performed using an index 1 property and decoupling techniques. New methods of state estimation, based on Extended Kalman Filter including a sliding window of measurements, are proposed to improve the robustness and accuracy. A new convergence study based on Lyapunov function and conditioning of the observability matrix is proposed to ensure the convergence of the observers. A combination of extended Kalman filter with moving horizon and the version with unknown input is considered to ensure the monitoring task. Performances of the proposed approaches were evaluated by numerical simulations of IEEE power system test.

This paper presents a control methodology that enables nonlinear model-based control of pulse width modulated (PWM) pneumatic servo actuators. An averaging approach is developed to describe the equivalent continuous-time dynamics of a PWM controlled nonlinear system, which renders the system, originally discontinuous and possibly nonaffine in the input, into an equivalent system that is both continuous and affine in control input (i.e., transforms the system to nonlinear control canonical form). This approach is applied to a pneumatic actuator controlled by a pair of three-way solenoid actuated valves. The pneumatic actuation system is transformed into its averaged equivalent control canonical form, and a sliding mode controller is developed based on the resulting model. The controller is implemented on an experimental system, and the effectiveness of the proposed approach validated by experimental trajectory tracking.

This work proposes a methodology of identifying linear parameter varying (LPV) models for nonlinear systems. First, linear local models in some operating points, by applying standard identifications procedures for linear systems in time domain, are obtained. Next, a LPV model with linear fractional dependence (LFR) with respect to measured variables is fitted with the condition of containing all the linear models identified in previous step (differential inclusion). The fit is carried out using nonlinear least squares algorithms. Finally, this identification methodology will then be applied to a nonlinear turbocharged diesel engine.

Abstract—In this paper a nonlinear observer which synthe-sizes sliding mode techniques and neural state space models is proposed and is applied for robust fault diagnosis in a class of nonlinear systems. The sliding mode term is utilized to eliminate the effect of system uncertainties, ...

Many condensed matter experiments explore the finite temperature dynamics of systems near quantum critical points. Often, there are no well-defined quasiparticle excitations, and so quantum kinetic equations do not describe the transport properties completely. The theory shows that the transport co-efficients are not proportional to a mean free scattering time (as is the case in the Boltzmann theory of quasiparticles), but are completely determined by the absolute temperature and by equilibrium thermodynamic observables. Recently, explicit solutions of this quantum critical dynamics have become possible via the AdS/CFT duality discovered in string theory. This shows that the quantum critical theory provides a holographic description of the quantum theory of black holes in a negatively curved anti-de Sitter space, and relates its transport co-efficients to properties of the Hawking radiation from the black hole. We review how insights from this connection have led to new results for experimental systems: (i) the vicinity of the superfluid-insulator transition in the presence of an applied magnetic field, and its possible application to measurements of the Nernst effect in the cuprates, (ii) the magnetohydrodynamics of the plasma of Dirac electrons in graphene and the prediction of a hydrodynamic cyclotron resonance. this state, but there is a well-developed theory of the transport properties of the TL liquid. Historically, this theory evolved over several decades of research on quantum many body systems in one dimension. Key in the historical development were exact solutions of model Hamiltonians via the Bethe Ansatz. Insights gained from the structure of excitations in the Bethe Ansatz solutions led to a more general understanding of the low energy excitations of a generic Hamiltonian, and a universal low energy theory of the TL liquid. Thus while the exact solutions were restricted to artificial models, they played a key role in the development of the general theory. Of course, after the fact, with the general theory of the TL liquid before us, we can justify it in its own terms, and largely dispense with reference to the Bethe Ansatz solutions.

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In this research, a comparative study of two recurrent neural networks, nonlinear autoregressive with exogenous input (NARX) neural network and nonlinear autoregressive moving average (NARMA-L2), and a feedforward neural network (FFNN) is performed for their ability to provide adaptive control of nonlinear systems. Three dynamical nonlinear systems of different complexity are considered. The aim of this work is to make the output of the plant follow the desired reference trajectory. The problem becomes more challenging when the dynamics of the plants are assumed to be unknown, and to tackle this problem, a multilayer neural network-based approximate model is set up which will work in parallel to the plant and the control scheme. The network parameters are updated using the dynamic backpropagation (BP) algorithm.

A general formulation is presented for finite-horizon optimal control of a class of discrete-time, nonautonomous, uncertain, nonlinear stochastic systems. Full state information is assumed to be available in controller derivation and optimization is carried out for a variety of performance criteria within a common dissipative framework. This framework, for example, includes performance criteria such as H 2 , H I , and various kinds of passivity properties appropriately generalized to such stochastic systems. It is shown that the results obtained in this paper include some previous ones in the literature as special cases.

This paper compares four observers (virtual sensors) of vehicle sideslip angle and lateral forces. The first is linear and uses a linear vehicle model. The remaining observers use an extended nonlinear model. The three nonlinear observers are: extended Luenberger observer, extended Kalman filter and sliding-mode observer. Modeling, model simplification, and observers are described, and an observability analysis is performed for the entire vehicle trajectory. The paper also deals with three different sets of sensors to see the impact of observers results. Comparison is first done by simulation on a valid vehicle simulator, and then observers are used on experimental data. Our study shows that observers are more accurate than simple models as regards unmeasurable variables such as sideslip angle and transversal forces. It also shows that speed of center of gravity is not an indispensable variable here.

Fuzzy logic controllers (FLC) have gained popularity in the past few decades with successful implementation in many areas, including electrical machines' drive control. Many colleges are now offering fuzzy logic courses due to successful applications of FLCs in nonlinear systems. However, teaching students a fuzzy logic controlled drive system in a laboratory, or training technical staff, is time consuming and may be an expensive task. This paper presents an educational tool for fuzzy logic controlled brushless direct current motor (BDCM), which is a part of a virtual electrical machinery laboratory project. The tool has flexible structure and graphical interface. Motor and controller parameters of the drive system can be changed easily under different operating conditions. Index Terms-Brushless direct current motor (BDCM), educational tool, fuzzy logic controller (FLC).

It is demonstrated how the computer, used in a heuristic mode, has greatly augmented our understanding of the mathematics of nonlinear dynamical process. Examples are given of recent work in soliton mathematics (mainly), but also nonlinear iterative mappings and loworder nonlinear ordinary differential equation systems. The role of good graphics in enhancing the discovery and retention of new mathematical properties of equations is illustrated. Several examples are given of the present frontier of research in two space dimensional nonlinear evolutionary problems.

Considers control design using an adaptive backstepping algorithm for a class of nonlinear continuous uncertain processes with disturbances which can be converted to a parametric semi-strict feedback form. Sliding mode control using a combined adaptive backstepping sliding mode control algorithm is also studied. The algorithm follows a systematic procedure for the design of adaptive control laws for the output of observable minimum phase nonlinear systems with matched and unmatched uncertainty. An existing sufficient condition for sliding is not needed by the new algorithm

This paper deals with the control laws
reconguration of nonlinear systems, by using a
Fuzzy-Model-based Predictive Control (FMPC). It
should be noted that the studied systems are writ-
ten in the quasi-linear parametric varying (quasi-
LPV) form. This FMPC strategy is developed to
preserve closed-loop stability in the nominal and
actuator faulty case. Fault accommodation by per-
turbations rejection is presented. This step is done
by interpolation-based control to cover the entire
area of operation. To allow the process to maintain
current performances closed to desired performances,
a dynamic optimizer is used. Our contribution comes
from the combination of several aspects: fuzzy model,
quadratic programming and faults decoupling princi-
ple. The linearization around a family of equilibrium
points is also studied. The operating points are appro-
priately congured by a set of variables called premise.

This is a one page reference sheet for several common numerical methods.  It lists and/or describes several methods for root finding, linear & non-linear systems of equations, quadrature, and solving differential equations. It also  includes certain Mat-lab built in functions. As it is only one page, some numerical methods are only mentioned in order to provide a starting point for further research. A special thanks goes to my professor for the Mat-lab Programming & Numerical Methods class in Howard County Community College, Professor Mark Edelen, who was an excellent teacher for this class. He also looked over an earlier version of this paper and proofread it.

: The goal of this project was to put the intuitive idea of gain-scheduling on a rigorous foundation for a class of nonlinear, distributed-parameter systems. This involved a study of the existence and characterization of the ideal, infinite-dimensional, feedback control. Since in most applications the feedback function cannot be computed in closed form it was necessary to study the convergence of approximate feedback functions, based on increasingly higher order finite-dimensional approximations of the system, to the ideal function. Finally, the results were applied to Burgers' Equation, which can be viewed as a low-order approximation to a wide variety of physical phenomena, including viscous compressible flow.

A new dissipative method to design observers for a large class of nonlinear systems has been introduced recently by the author. It generalizes and includes several wellknown observer design methods in the literature. In this paper a procedure to design Proportional-Integral Observers based on the dissipativity theory is presented. Properties of these observers are discussed.

The ongoing and primary goal of the research is the pursuit of understanding of nonlinear processes in natural phenomena arising in optics and fluids. A considerable share of our attention is devoted to nonlinear optics, a relatively young subject, extremely rich in scientific and technological potential. While the studies focus on scientific questions connected with laser diode arrays, beam instabilities and the behavior of light beams at interfaces between nonlinear dielectrics, the technological ramifications and future opportunities are in many cases obvious. Optics also serves as a useful paradigm for gaining an increased understanding in other fields. For example, turbulence in optics, the study of the complex space-time filaments, patterns and defects which appear in feedback cavities and counterpropagating beams may be more analytically tractable than in other branches of continuous mechanics. There is little doubt that nonlinear optics is a subject in which interest is increasing.

Declaration None of the material contained in this thesis has previously been submitted for a degree in the University of Durham or any other university. None of the material contained in this thesis is based on joint research. The content of this thesis consists of the author's original individual contribution with appropriate recognition of any references being indicated throughout. iv Copyright The copyright of this thesis rests with the author. No quotation from it should be published without prior written consent and information derived from it should be acknowledged. v Dedication To my honourable teacher, supervisor Mehmet Asutay, my dear parents Durdu and Çetin Özkan, my brother Durmuş Özkan, my beloved wife Esra and cute daughter Gülbahar and son Tahir İbrahim. They are the sculptures of this author. Whatever I have well in me, either directly or indirectly, is because of them and, if the rest means something, the rest belongs to me alone. vi Acknowledgements My supervisor, Mehmet Asutay's adorable help is beyond all the praise. I applaud him from the faces of these pages. I learned many things from him but his personality is the most important and undoubtedly the hardest thing I could learn and imitate. Nevertheless, I could have not gotten the opportunity of meeting him in the first place… This has been possible by the Turkish Government. This project received funding from the Ministry of Interior of the Republic of Turkey and without their support even the imagination of it was not possible for the author with his financial circumstances. My colleagues Kutluer Karademir and Haluk B. Gulec's help also deserves praise as well as other colleagues who put up with the absence of my soul in the workplace. I owe a great deal to their invaluable and continuous support. My father, my mother and my brother they will have a big relief after this study completely finishes. Thank you for your never-failing-support. My beloved wife, Esra, without her encouragement, patience and smiles, this thesis would not be possible. Gulbahar and Tahir, when you come to the age of understanding these sentences you should know that my love for you was part of my patience. I wish you all; the happiest life ever lived in the universe.

This paper presents a Lyapunov-based switching controller design method for non-linear systems using Takagi-Sugeno fuzzy models. The basic idea of the proposed approach is to represent the fuzzy model as a set of uncertain linear systems. The controller is obtained by solving the corresponding set of Algebraic Ricatti Equations (AREs). A simulation example is given to illustrate the effectiveness of this approach.

A total of 49 extended abstracts are included in this volume of papers presented at the 15th International Workshop on Water Waves and Floating Bodies, held 17 February - 1 March, 2000, Caesarea, Israel. Also see http://www.eng.tau.ac.il/-miloh/iwwwfb. The objective of the Workshop is to provide a forum for informal discussions of fundamental research, of mutual interest to both engineers and scientists, in the broad area of wave interactions with fixed, floating or submerged bodies.

The various techniques available for the analysis of nonlinear systems subjected to random excitations are briefly introduced and an overview of the progress which has been made in this area of research is presented. The discussion is mainly focused on the basis, scope and limitations of the solution techniques and not on specific applications.

The Extended Kalman Filter (EKF) has become a standard technique used in a number of nonlinear estimation and machine learning applications. These include estimating the state of a nonlinear dynamic system, estimating parameters for nonlinear system identification (e.g., learning the weights of a neural network), and dual estimation (e.g., the Expectation Maximization (EM) algorithm) where both states and parameters are estimated simultaneously.

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This paper presents a hierarchical flight control system for unmanned aerial vehicles. The proposed system executes high-level mission objectives by progressively substantiating them into machine-level commands. The acquired information from various sensors is propagated back to the higher layers for reactive decision making. Each vehicle is connected via standardized wireless communication protocol for scalable multi-agent coordination. The proposed system has been successfully implemented on a number of small helicopters and validated in various applications. Results from waypoint navigation, a probabilistic pursuit-evasion game and vision-based target tracking demonstrate the potential of the proposed approach toward intelligent flying robots. r

In this paper, sliding-mode control is applied on multi-input/multi-output (MIMO) nonlinear systems. A novel approach is proposed, which allows chattering reduction on control input while keeping high tracking performance of the controller in steady-state regime. This approach consists of designing a nonlinear reaching law by using an exponential function that dynamically adapts to the variations of the controlled system. Experimental study was focused on a MIMO modular robot arm. Experimental results are presented to show the effectiveness of the proposed approach, regarding particularly the chattering reduction on control input in steady-state regime.

An universal controller is constructed, formulated in input-output terms only, which causes the output of any uncertain smooth single-input-single-output (SISO) minimum-phase dynamic system with known relative degree to vanish in finite time. That allows exact tracking of arbitrary real-time smooth signals. Only one parameter is to be adjusted. The approach being based on higher-order finite-time-convergence sliding modes, the control can be made arbitrarily smooth, providing for the arbitrarily-high tracking-accuracy order with respect to the sampling step.

Declaration None of the material contained in this thesis has previously been submitted for a degree in the University of Durham or any other university. None of the material contained in this thesis is based on joint research. The content of this thesis consists of the author's original individual contribution with appropriate recognition of any references being indicated throughout. iv Copyright The copyright of this thesis rests with the author. No quotation from it should be published without prior written consent and information derived from it should be acknowledged. v Dedication To my honourable teacher, supervisor Mehmet Asutay, my dear parents Durdu and Çetin Özkan, my brother Durmuş Özkan, my beloved wife Esra and cute daughter Gülbahar and son Tahir İbrahim. They are the sculptures of this author. Whatever I have well in me, either directly or indirectly, is because of them and, if the rest means something, the rest belongs to me alone. vi Acknowledgements My supervisor, Mehmet Asutay's adorable help is beyond all the praise. I applaud him from the faces of these pages. I learned many things from him but his personality is the most important and undoubtedly the hardest thing I could learn and imitate. Nevertheless, I could have not gotten the opportunity of meeting him in the first place… This has been possible by the Turkish Government. This project received funding from the Ministry of Interior of the Republic of Turkey and without their support even the imagination of it was not possible for the author with his financial circumstances. My colleagues Kutluer Karademir and Haluk B. Gulec's help also deserves praise as well as other colleagues who put up with the absence of my soul in the workplace. I owe a great deal to their invaluable and continuous support. My father, my mother and my brother they will have a big relief after this study completely finishes. Thank you for your never-failing-support. My beloved wife, Esra, without her encouragement, patience and smiles, this thesis would not be possible. Gulbahar and Tahir, when you come to the age of understanding these sentences you should know that my love for you was part of my patience. I wish you all; the happiest life ever lived in the universe.

Lie algebra is an area of mathematics that is largely used by electrical engineer students, mainly at post-graduation level in the control area. The purpose of this paper is to illustrate the use of Lie algebra to control nonlinear systems, essentially in the framework of mobile robot control. The study of path following control of a mobile robot using an input-output feedback linearization controller is performed. The effectiveness of the nonlinear controller is illustrated with simulation examples.

We consider the design of a robust continuous sliding mode controller for the output regulation of a class of minimum-phase nonlinear systems. Previous work has shown how to do this by incorporating a linear servocompensator in the sliding mode design, but the transient performance is degraded when compared to ideal sliding mode control. Extending previous ideas from the design of 'conditional integrators' for the case of asymptotically constant references and disturbances, we design the servocompensator as a conditional one that provides servocompensation only inside the boundary layer; achieving asymptotic output regulation, but with improved transient performance. We give both regional as well as semi-global results for error convergence, and show that the controller can be tuned to recover the performance of an ideal sliding mode control.