Distributed Wireless Networked H

A new approach to solving the distributed control problem for a class of discrete-time nonlinear systems via a wireless neural control network (WNCN) is presented in this paper. A unified Lurie-type model termed delayed standard neural network model (DSNNM) is used to describe these nonlinear systems. We assume that all neuron nodes in WNCN which have limited energy, storage space, and computing ability can be regarded as a subcontroller, then the whole WNCN is characterized by a mesh-like structure with partially connected neurons distributed over a wide geographical area, which can be considered as a fully distributed nonlinear output feedback dynamic controller. The unreliable wireless communication links within WNCN are modeled by fading channels. Based on the Lyapunov functional and the S-procedure, the WNCN is solved and configured for the DSNNM to absolutely stabilize the whole closed-loop system in the sense of mean square with a H∞ disturbance attenuation index using LMI approach. A numerical example shows the effectiveness of the proposed design approaches

Positive Filtering with l

This paper is concerned with the positive filtering problem for discrete-time positive systems under the l1-induced performance. We aim to propose a pair of positive filters with error-bounding features to estimate the output of positive systems. A novel characterization is first constructed so that the filtering error system is asymptotically stable with a prescribed l1-induced performance. Then, necessary and sufficient conditions for the existence of required filters are presented, and the obtained results are expressed as linear programming problems. Moreover, it is pointed out that the results can be easily checked by standard software. In addition, a numerical example is given to show the effectiveness of the proposed design procedures

Control of nonlinear systems using n-fuzzy models

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia de Automação e Sistemas, Florianópolis, 2015.A utilização de modelos fuzzy Takagi-Sugeno (T-S) tem sido extensivamente investigada no decorrer das últimas décadas, principalmente por propiciarem o desenvolvimento de metodologias de projeto de sistemas de controle não lineares que possuem caráter sistemático e solução numérica, fazendo-se uso de propriedades inerentes como a de aproximação universal e/ou de convexidade dos modelos. Nota-se, entretanto, que as técnicas de modelagem fuzzy T-S atuais, em geral, garantem a convexidade do modelo e/ou a sua precisão de representação somente para uma determinada região do espaço de estados. Desta forma, para estratégias de controle baseadas em propriedades de convexidade, a estabilidade do sistema de malha fechada formado pelo sistema não linear realimentado pela lei de controle fuzzy deve ser estudada no contexto de estabilidade local, sendo fundamental a determinação de regiões de estabilidade para o sistema de malha fechada. Esta importante característica dos modelos fuzzy T-S raramente é considerada na literatura, podendo implicar em perda de desempenho e até mesmo instabilidade do sistema em malha fechada. Outro problema inerente à utilização de modelos fuzzy T-S diz respeito ao aumento exponencial de complexidade do modelo com o número de não linearidades presentes no sistema, principalmente quando se busca descrever de forma exata a dinâmica do sistema a controlar, o que implica no aumento da complexidade numérica dos algoritmos para análise e projeto, assim como do aumento da complexidade de implementação de leis de controle. Neste contexto, esta tese busca evidenciar a importância da consideração da validade regional dos modelos fuzzy de tipo T-S para o desenvolvimento de ferramentas de análise e síntese de sistemas de controle não lineares, assim como considerar outras restrições físicas presentes no sistema de controle como limites nos atuadores, e discutir a problemática associada à complexidade dos modelos fuzzy T-S. Um método de modelagem baseado no uso de regras não lineares locais é desenvolvido permitindo, além de uma representação compacta e precisa da planta não linear original, o tratamento do problema de projeto de controladores dinâmicos por realimentação de saídas na presença de não linearidades dependentes de estados não mensuráveis do sistema. Utilizando-se funções de Lyapunov fuzzy (FLF), são desenvolvidas condições de estabilidade e estabilização para o sistema em malha fechada que podem ser verificadas em termos de factibilidade de um conjunto de desigualdades matriciais lineares. Os controladores propostos são baseados na realimentação de estados e do vetor de não linearidades de setor, ao qual são consideradas perturbações limitadas em energia ou amplitude, e na realimentação dinâmica de saídas, para sistemas não perturbados com atuadores saturantes ou para sistemas sujeitos a perturbações persistentes. Exemplos numéricos são apresentados ao longo do trabalho com o objetivo de ilustrar a eficiência dos métodos propostos. Ainda, objetivando auxiliar estudantes, engenheiros e pesquisadores na análise e projeto de controle de sistemas não lineares, apresenta-se o desenvolvimento de uma ferramenta computacional interativa para a modelagem e controle fuzzy. Aspectos práticos e um estudo da complexidade de implementação digital de controladores fuzzy também são discutidos através da simulação Hardware-in-the-Loop (HIL) com utilização de uma placa de desenvolvimento FPGA (do inglês Field Programmable Gate Array).Abstract : Takagi-Sugeno (T-S) fuzzy models have been extensively investigated over the last decade to develop the so-called fuzzy model based (FMB) control techniques, providing nonlinear control design methodologies with a systematic aspect and numerical solution. However, the actual T-S fuzzy modeling techniques, in general, only guarantee the convexity of the model and/or their accuracy of representation for a specific domain of the state space. Thus, for control strategies based on convexity properties, the stability of the closed-loop system composed of the nonlinear system and the fuzzy controller should be analyzed in a local context, being fundamental to determining stability regions for the closed-loop system. This inherent local characteristic is often not considered in most FMB control design results, which may lead to poor performance or even instability of the closed-loop system. In this sense, this thesis aims to consider the regional validity of the T-S fuzzy models for the development of nonlinear control systems analysis and design tools, to consider other physical constraints and to discuss the problems associated with the complexity of T-S fuzzy models. A modeling method based on the use of nonlinear local rules that provides a compact and accurate representation is presented, allowing also to handle with the dynamic output feedback control problem for systems with nonlinearities that may depend on unmeasurable states. Using fuzzy Lyapunov functions (FLF), closed-loop stability conditions are provided, which can be verified in terms of the feasibility of a set of linear matrix inequalities (LMIs). The proposed controllers are based on a state and sector nonlinearities feedback, for systems subject to disturbances bounded in energy or amplitude, and on a dynamic output feedback, for systems with saturating actuators. Numerical examples are presented throughout this document to illustrate the effectiveness of the proposed design methodologies. Further, aiming to assist students and engineers in the nonlinear control system design, an interactive computational tool is presented for fuzzy modeling and control. Practical aspects and a study of the digital implementation of fuzzy controllers are discussed using a Hardware-in-the-Loop (HIL) simulation with a Field Programmable Gate Array (FPGA) development board

Robust Event-Triggered Energy-to-Peak Filtering for Polytopic Uncertain Systems over Lossy Network with Quantized Measurements

The event-triggered energy-to-peak filtering for polytopic discrete-time linear systems is studied with the consideration of lossy network and quantization error. Because of the communication imperfections from the packet dropout of lossy link, the event-triggered condition used to determine the data release instant at the event generator (EG) can not be directly applied to update the filter input at the zero order holder (ZOH) when performing filter performance analysis and synthesis. In order to balance such nonuniform time series between the triggered instant of EG and the updated instant of ZOH, two event-triggered conditions are defined, respectively, whereafter a worst-case bound on the number of consecutive packet losses of the transmitted data from EG is given, which marginally guarantees the effectiveness of the filter that will be designed based on the event-triggered updating condition of ZOH. Then, the filter performance analysis conditions are obtained under the assumption that the maximum number of packet losses is allowable for the worst-case bound. In what follows, a two-stage LMI-based alternative optimization approach is proposed to separately design the filter, which reduces the conservatism of the traditional linearization method of filter analysis conditions. Subsequently a codesign algorithm is developed to determine the communication and filter parameters simultaneously. Finally, an illustrative example is provided to verify the validity of the obtained results

Robust Control

The need to be tolerant to changes in the control systems or in the operational environment of systems subject to unknown disturbances has generated new control methods that are able to deal with the non-parametrized disturbances of systems, without adapting itself to the system uncertainty but rather providing stability in the presence of errors bound in a model. With this approach in mind and with the intention to exemplify robust control applications, this book includes selected chapters that describe models of H-infinity loop, robust stability and uncertainty, among others. Each robust control method and model discussed in this book is illustrated by a relevant example that serves as an overview of the theoretical and practical method in robust control

Advanced Strategies for Robot Manipulators

Amongst the robotic systems, robot manipulators have proven themselves to be of increasing importance and are widely adopted to substitute for human in repetitive and/or hazardous tasks. Modern manipulators are designed complicatedly and need to do more precise, crucial and critical tasks. So, the simple traditional control methods cannot be efficient, and advanced control strategies with considering special constraints are needed to establish. In spite of the fact that groundbreaking researches have been carried out in this realm until now, there are still many novel aspects which have to be explored

Control and filtering of time-varying linear systems via parameter dependent Lyapunov functions

The main contribution of this dissertation is to propose conditions for linear filter and controller design, considering both robust and parameter dependent structures, for discrete time-varying systems. The controllers, or filters, are obtained through the solution of optimization problems, formulated in terms of bilinear matrix inequalities, using a method that alternates convex optimization problems described in terms of linear matrix inequalities. Both affine and multi-affine in different instants of time (path dependent) Lyapunov functions were used to obtain the design conditions, as well as extra variables introduced by the Finsler\u27s lemma. Design problems that take into account an H-infinity guaranteed cost were investigated, providing robustness with respect to unstructured uncertainties. Numerical simulations show the efficiency of the proposed methods in terms of H-infinity performance when compared with other strategies from the literature

Control of chaos in nonlinear circuits and systems

Nonlinear circuits and systems, such as electronic circuits (Chapter 5), power converters (Chapter 6), human brains (Chapter 7), phase lock loops (Chapter 8), sigma delta modulators (Chapter 9), etc, are found almost everywhere. Understanding nonlinear behaviours as well as control of these circuits and systems are important for real practical engineering applications. Control theories for linear circuits and systems are well developed and almost complete. However, different nonlinear circuits and systems could exhibit very different behaviours. Hence, it is difficult to unify a general control theory for general nonlinear circuits and systems. Up to now, control theories for nonlinear circuits and systems are still very limited. The objective of this book is to review the state of the art chaos control methods for some common nonlinear circuits and systems, such as those listed in the above, and stimulate further research and development in chaos control for nonlinear circuits and systems. This book consists of three parts. The first part of the book consists of reviews on general chaos control methods. In particular, a time-delayed approach written by H. Huang and G. Feng is reviewed in Chapter 1. A master slave synchronization problem for chaotic Lur’e systems is considered. A delay independent and delay dependent synchronization criteria are derived based on the H performance. The design of the time delayed feedback controller can be accomplished by means of the feasibility of linear matrix inequalities. In Chapter 2, a fuzzy model based approach written by H.K. Lam and F.H.F. Leung is reviewed. The synchronization of chaotic systems subject to parameter uncertainties is considered. A chaotic system is first represented by the fuzzy model. A switching controller is then employed to synchronize the systems. The stability conditions in terms of linear matrix inequalities are derived based on the Lyapunov stability theory. The tracking performance and parameter design of the controller are formulated as a generalized eigenvalue minimization problem which is solved numerically via some convex programming techniques. In Chapter 3, a sliding mode control approach written by Y. Feng and X. Yu is reviewed. Three kinds of sliding mode control methods, traditional sliding mode control, terminal sliding mode control and non-singular terminal sliding mode control, are employed for the control of a chaotic system to realize two different control objectives, namely to force the system states to converge to zero or to track desired trajectories. Observer based chaos synchronizations for chaotic systems with single nonlinearity and multi-nonlinearities are also presented. In Chapter 4, an optimal control approach written by C.Z. Wu, C.M. Liu, K.L. Teo and Q.X. Shao is reviewed. Systems with nonparametric regression with jump points are considered. The rough locations of all the possible jump points are identified using existing kernel methods. A smooth spline function is used to approximate each segment of the regression function. A time scaling transformation is derived so as to map the undecided jump points to fixed points. The approximation problem is formulated as an optimization problem and solved via existing optimization tools. The second part of the book consists of reviews on general chaos controls for continuous-time systems. In particular, chaos controls for Chua’s circuits written by L.A.B. Tôrres, L.A. Aguirre, R.M. Palhares and E.M.A.M. Mendes are discussed in Chapter 5. An inductorless Chua’s circuit realization is presented, as well as some practical issues, such as data analysis, mathematical modelling and dynamical characterization, are discussed. The tradeoff among the control objective, the control energy and the model complexity is derived. In Chapter 6, chaos controls for pulse width modulation current mode single phase H-bridge inverters written by B. Robert, M. Feki and H.H.C. Iu are discussed. A time delayed feedback controller is used in conjunction with the proportional controller in its simple form as well as in its extended form to stabilize the desired periodic orbit for larger values of the proportional controller gain. This method is very robust and easy to implement. In Chapter 7, chaos controls for epileptiform bursting in the brain written by M.W. Slutzky, P. Cvitanovic and D.J. Mogul are discussed. Chaos analysis and chaos control algorithms for manipulating the seizure like behaviour in a brain slice model are discussed. The techniques provide a nonlinear control pathway for terminating or potentially preventing epileptic seizures in the whole brain. The third part of the book consists of reviews on general chaos controls for discrete-time systems. In particular, chaos controls for phase lock loops written by A.M. Harb and B.A. Harb are discussed in Chapter 8. A nonlinear controller based on the theory of backstepping is designed so that the phase lock loops will not be out of lock. Also, the phase lock loops will not exhibit Hopf bifurcation and chaotic behaviours. In Chapter 9, chaos controls for sigma delta modulators written by B.W.K. Ling, C.Y.F. Ho and J.D. Reiss are discussed. A fuzzy impulsive control approach is employed for the control of the sigma delta modulators. The local stability criterion and the condition for the occurrence of limit cycle behaviours are derived. Based on the derived conditions, a fuzzy impulsive control law is formulated so that the occurrence of the limit cycle behaviours, the effect of the audio clicks and the distance between the state vectors and an invariant set are minimized supposing that the invariant set is nonempty. The state vectors can be bounded within any arbitrary nonempty region no matter what the input step size, the initial condition and the filter parameters are. The editors are much indebted to the editor of the World Scientific Series on Nonlinear Science, Prof. Leon Chua, and to Senior Editor Miss Lakshmi Narayan for their help and congenial processing of the edition