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On state representations of time-varying nonlinear systems

SILVA, Paulo Sergio Pereira da; BATISTA, Simone
Fonte: PERGAMON-ELSEVIER SCIENCE LTD Publicador: PERGAMON-ELSEVIER SCIENCE LTD
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
65.94%
This work considers a nonlinear time-varying system described by a state representation, with input u and state x. A given set of functions v, which is not necessarily the original input u of the system, is the (new) input candidate. The main result provides necessary and sufficient conditions for the existence of a local classical state space representation with input v. These conditions rely on integrability tests that are based on a derived flag. As a byproduct, one obtains a sufficient condition of differential flatness of nonlinear systems. (C) 2009 Elsevier Ltd. All rights reserved.; Conselho National de Desenvolvimento Cientifico e Tecnologico CNPq, Brazil

A new approach for modeling and control of nonlinear systems via norm-bounded linear differential inclusions; Uma nova abordagem para modelagem e controle de sistemas não-lineares via inclusões diferenciais lineares limitadas por norma

Kuiava, Roman; Ramos, Rodrigo Andrade; Pota, Hemanshu R.
Fonte: Sociedade Brasileira de Automática Publicador: Sociedade Brasileira de Automática
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
66.02%
A systematic approach to model nonlinear systems using norm-bounded linear differential inclusions (NLDIs) is proposed in this paper. The resulting NLDI model is suitable for the application of linear control design techniques and, therefore, it is possible to fulfill certain specifications for the underlying nonlinear system, within an operating region of interest in the state-space, using a linear controller designed for this NLDI model. Hence, a procedure to design a dynamic output feedback controller for the NLDI model is also proposed in this paper. One of the main contributions of the proposed modeling and control approach is the use of the mean-value theorem to represent the nonlinear system by a linear parameter-varying model, which is then mapped into a polytopic linear differential inclusion (PLDI) within the region of interest. To avoid the combinatorial problem that is inherent of polytopic models for medium- and large-sized systems, the PLDI is transformed into an NLDI, and the whole process is carried out ensuring that all trajectories of the underlying nonlinear system are also trajectories of the resulting NLDI within the operating region of interest. Furthermore, it is also possible to choose a particular structure for the NLDI parameters to reduce the conservatism in the representation of the nonlinear system by the NLDI model...

Formas triangulares para sistemas não-lineares com duas entradas e controle de sistemas sem arrasto em SU(n) com aplicações em mecânica quântica.; Triangular forms for nonlinear systems with two inputs and control of driftless systems on SU(n) with applications in quantum mechanics.

Silveira, Hector Bessa
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 19/02/2010 PT
Relevância na Pesquisa
65.98%
A presente tese aborda dois problemas distintos e independentes: triangularização de sistemas não-lineares com duas entradas e controle de sistemas sem arrasto que evoluem no grupo especial unitário SU(n). Em relação ao primeiro, estabeleceu-se, através da generalização de resultados bem conhecidos, condições geométricas para que um sistema com duas entradas seja descrito por uma forma triangular específica após uma mudança de coordenadas e uma realimentação de estado estática regular. Para o segundo problema, desenvolveu-se uma estratégia de controle que força o estado do sistema a rastrear assintoticamente uma trajetória de referência periódica que passa por um estado objetivo arbitrário. O método de controle proposto utiliza os resultados de convergência de tipo- Lyapunov que foram estabelecidos pela presente pesquisa e que tiveram como inspiração uma versão periódica do princípio da invariância de LaSalle. Apresentou-se, ainda, os resultados de simulação obtidos com a aplicação da técnica de controle desenvolvida a um sistema quântico consistindo de duas partículas de spin-1/2, com o objetivo de gerar a porta lógica quântica C-NOT.; This thesis treats two distinct and independent problems: triangularization of nonlinear systems with two inputs and control of driftless systems which evolve on the special unitary group SU(n). Concerning the first...

Propostas de metodologias para controle inteligente de sistemas não lineares com incertezas parametricas e funcionais; Advances on methodologies for intelligent control of nonlinear systems with parametric and functional uncertainties

Erick Vile Grinits
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 24/08/2008 PT
Relevância na Pesquisa
65.99%
Esta tese apresenta contribuições para o controle inteligente de sistemas não lineares com incertezas paramétricas e funcionais. São desenvolvidas duas abordagens. Em primeiro lugar, é proposta uma modificação ao backstepping adaptativo clássico, fundamentada em Extensão do Princípio de Invariância de La Salle que contempla o caso em que a derivada da função de Lyapunov ao longo das soluções do sistema é permitida ser definida positiva em regiões limitadas do espaço de estados, que favorece o pleno uso de técnicas de otimização baseadas em computação evolutiva com vistas à melhoria de desempenho da solução em termos de redução expressiva de esforço de controle e conformação da resposta transitória conforme critérios de tempo de estabilização, magnitude de sobre-sinal, etc. Em segundo lugar, é proposta uma metodologia de controle adaptativo neural, estruturada na técnica de backstepping, aplicável a sistemas não lineares com incertezas com múltiplas entradas e múltiplas saídas compostos de subsistemas interconectados cujas matrizes de entrada apresentam funções não lineares e cujas interconexões entre subsistemas também apresentam não linearidades. A estratégia apresentada propõe-se a sanar várias das dificuldades encontradas em metodologias análogas...

Identificação de sistemas não-lineares usando modelos de Volterra baseados em funções ortonormais de Kautz e generalizadas; Identification of nonlinear systems using volterra models based on Kautz functions and generalized orthonormal functions

Alex da Rosa
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 12/03/2009 PT
Relevância na Pesquisa
66.01%
Este trabalho enfoca a modelagem de sistemas não-lineares usando modelos de Volterra com funções de base ortonormal (Orthonormal Basis Functions - OBF). Os modelos de Volterra representam uma generalização do modelo de resposta ao impulso para a descrição de sistemas não-lineares e, em geral, exigem um elevado número de termos para representar os kernels de Volterra. Esta desvantagem pode ser superada representando-se os kernels usando um conjunto de funções ortonormais. O modelo resultante, conhecido como modelo OBF-Volterra, pode ser truncado em um n´umero menor de termos se as funções da base forem projetadas adequadamente. O problema central é como selecionar os polos livres que completamente parametrizam estas funções, particularmente as funções de Kautz e as funções ortonormais generalizadas (Generalized Orthonormal Basis Functions - GOBF). Uma das abordagens adotadas para resolver este problema envolve a minimização de um limitante superior para o erro resultante do truncamento da expansao do kernel. Cada kernel multidimensional é decomposto em um conjunto de bases de Kautz independentes, em que cada base é parametrizada por um par individual de pólos complexos conjugados com a intenção de representar a dinamica dominante do kernel ao longo de uma dimensão particular. Obtem-se uma solução analítica para um dos parâmetros de Kautz...

A filled function method for nonlinear systems of equalities and inequalities

Wan,Zhongping; Yuan,Liuyang; Chen,Jiawei
Fonte: Sociedade Brasileira de Matemática Aplicada e Computacional Publicador: Sociedade Brasileira de Matemática Aplicada e Computacional
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/01/2012 EN
Relevância na Pesquisa
65.94%
In this paper a filled function method is suggested for solving nonlinear systems of equalities and inequalities. Firstly, the original problem is reformulated into an equivalent constrained global optimization problem. Subsequently, a new filled function with one parameter is constructed based on the special characteristics of the reformulated optimization problem. Some properties of the filled function are studied and discussed. Finally, an algorithm based on the proposed filled function for solving nonlinear systems of equalities and inequalities is presented. The objective function value can be reduced by half in each iteration of our filled function algorithm. The implementation of the algorithm on several test problems is reported with numerical results. Mathematical subject classification: 65K05, 90C30.

On the estimation of robust stability regions for nonlinear systems with saturation

Coutinho,Daniel F.; Pagano,Daniel J.; Trofino,Alexandre
Fonte: Sociedade Brasileira de Automática Publicador: Sociedade Brasileira de Automática
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/09/2004 EN
Relevância na Pesquisa
65.94%
This paper addresses the problem of determining robust stability regions for a class of nonlinear systems with time-invariant uncertainties subject to actuator saturation. The unforced nonlinear system is represented by differential-algebraic equations where the system matrices are allowed to be rational functions of the state and uncertain parameters, and the saturation nonlinearity is modelled by a sector bound condition. For this class of systems, local stability conditions in terms of linear matrix inequalities are derived based on polynomial Lyapunov functions in which the Lyapunov matrix is a quadratic function of the state and uncertain parameters. To estimate a robust stability region is considered the largest level surface of the Lyapunov function belonging to a given polytopic region of state. A numerical example is used to demonstrate the approach.

State feedback fuzzy-model-based control for Markovian jump nonlinear systems

Arrifano,Natache S. D.; Oliveira,Vilma A.
Fonte: Sociedade Brasileira de Automática Publicador: Sociedade Brasileira de Automática
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/09/2004 EN
Relevância na Pesquisa
65.96%
This paper deals with the fuzzy-model-based control design for a class of Markovian jump nonlinear systems. A fuzzy system modeling is proposed to represent the dynamics of this class of systems. The structure of the fuzzy system is composed of two levels, a crisp level which describes the Markovian jumps and a fuzzy level which describes the system nonlinearities. A sufficient condition on the existence of a stochastically stabilizing controller using a Lyapunov function approach is presented. The fuzzy-model-based control design is formulated in terms of a set of linear matrix inequalities. Simulation results for a single-machine infinite-bus power system which is modeled as a Markovian jump nonlinear system in the infinite-bus voltage are presented to illustrate the applicability of the technique.

A new approach for modeling and control of nonlinear systems via norm-bounded linear differential inclusions

Kuiava,Roman; Ramos,Rodrigo A.; Pota,Hemanshu R.
Fonte: Sociedade Brasileira de Automática Publicador: Sociedade Brasileira de Automática
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/08/2012 EN
Relevância na Pesquisa
66.02%
A systematic approach to model nonlinear systems using norm-bounded linear differential inclusions (NLDIs) is proposed in this paper. The resulting NLDI model is suitable for the application of linear control design techniques and, therefore, it is possible to fulfill certain specifications for the underlying nonlinear system, within an operating region of interest in the state-space, using a linear controller designed for this NLDI model. Hence, a procedure to design a dynamic output feedback controller for the NLDI model is also proposed in this paper. One of the main contributions of the proposed modeling and control approach is the use of the mean-value theorem to represent the nonlinear system by a linear parameter-varying model, which is then mapped into a polytopic linear differential inclusion (PLDI) within the region of interest. To avoid the combinatorial problem that is inherent of polytopic models for medium- and large-sized systems, the PLDI is transformed into an NLDI, and the whole process is carried out ensuring that all trajectories of the underlying nonlinear system are also trajectories of the resulting NLDI within the operating region of interest. Furthermore, it is also possible to choose a particular structure for the NLDI parameters to reduce the conservatism in the representation of the nonlinear system by the NLDI model...

A theory of nonlinear systems

Bose, Amar G
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: iii, 113 leaves
ENG
Relevância na Pesquisa
66.05%
Introduction: A physically realizable nonlinear system, like a linear one, is a system whose present output is a function of the past of its input. We may regard the system as a computer that operates on the past of one time function to yield the present value of another time function. Mathematically we say that the system performs a transformation on the past of its input to yield its present output. When this transformation is linear (the case of linear systems) we can take advantage of the familiar convolution integral to obtain the present output from the past of the input and the system is said to be characterized by its response to an impulse. That is, the response of a linear system to an impulse is sufficient to determine its response to any input. When the transformation is nonlinear we no longer have a simple relation like the convolution integral relating the output to the past of the input and the system can no longer be characterized by its response to an impulse since superposition does not apply. Wiener has shown, however, that we can characterize a nonlinear system by a set of coefficients and that these coefficients can be determined from a knowledge of the response of the system to shot noise excitation. Thus, shot noise occupies the same position as a probe for investigating nonlinear systems that the impulse occupies as a probe for investigating linear systems. The first section of this thesis is devoted to the Wiener theory of nonlinear system characterization. Emphasis is placed on important concepts of this theory that are used in succeeding chapters to develop a theory for determining optimum nonlinear systems.; by Amar Gopal Bose.; Thesis (Sc. D.)--Massachusetts Institute of Technology...

Global robust tracking control of non-affine nonlinear systems with application to yaw control of uav helicopter

Xu, D.; Jiang, B.; Shi, P.
Fonte: Springer Publicador: Springer
Tipo: Artigo de Revista Científica
Publicado em //2013 EN
Relevância na Pesquisa
65.99%
In this paper, a novel robust nonlinear tracking control scheme is proposed for the yaw channel of an unmanned-aerial-vehicle helicopter that is non-affine in the control input. By a novel dynamic modeling technique, the non-affine nonlinear systems are approximated to facilitate the desired control design. In the controller design procedure, the terminal sliding model control method is introduced to deal with the unknown uncertainties/disturbances. Moreover, filter and disturbance estimator are combined to further reduce the chattering. A systematic procedure is developed and related theoretical and practical issues are discussed. The proposed nonlinear tracking control scheme can guarantee the asymptotic output tracking of the closed-loop control systems in spite of unknown uncertainties/disturbances. Finally, the simulation results on the dynamic model of a real helicopter-on-arm are provided to demonstrate the effectiveness of the proposed new control techniques.; De-Zhi Xu, Bin Jiang, and Peng Shi

Robust H∞ filtering for nonlinear systems with interval time-varying delays; Robust H-infinity filtering for nonlinear systems with interval time-varying delays

Deng, Z.; Shi, P.; Yang, H.; Xia, Y.
Fonte: ICIC International Publicador: ICIC International
Tipo: Artigo de Revista Científica
Publicado em //2010 EN
Relevância na Pesquisa
65.96%
In this paper, robust H∞ filtering problem for a class of linear fractional uncertain continuous-time nonlinear systems with interval time-varying delays is investigated. The delay factor is assumed to be time-varying and belongs to a given interval, which means that the lower and upper bounds of the interval time-varying delays are available. Furthermore, the derivative of the time-varying delay function can be larger than one. Based on Lyapunov-Krasovskii functional, a new sufficient condition for the solvability of this problem is presented in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, an expression of a desired H∞ filter is given. A numerical example is given to illustrate the effectiveness of the developed techniques.; Zhihong Deng, Peng Shi, Hongjiu Yang and Yuanqing Xia

Uma abordagem fuzzy para a estabilização de uma classe de sistemas não-lineares com saltos Markovianos; A fuzzy stabilization approach for a class of Markovian jump nonlinear systems

Arrifano, Natache do Socorro Dias
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 30/04/2004 PT
Relevância na Pesquisa
65.98%
Neste trabalho é apresentada uma abordagem fuzzy para a estabilização de uma classe de sistemas não-lineares com parâmetros descritos por saltos Markovianos. Uma nova modelagem fuzzy de sistemas é formulada para representar esta classe de sistemas na vizinhança de pontos de operação escolhidos. A estrutura deste sistema fuzzy é composta de dois níveis, um para descrição dos saltos Markovianos e outro para descrição das não-linearidades no estado do sistema. Condições suficientes para a estabilização estocástica do sistema fuzzy considerado são derivadas usando uma função de Lyapunov acoplada. O projeto de controle fuzzy é então formulado a partir de um conjunto de desigualdades matriciais lineares. Em adição, um exemplo de aplicação, envolvendo a representação da operação de um sistema elétrico de potência em esquema de co-geração por um sistema com saltos Markovianos, é construído para validação dos resultados.; This work deals with the fuzzy-model-based control design for a class of Markovian jump nonlinear systems. A new fuzzy system modeling is proposed to approximate the dynamics of this class of systems. The structure of the new fuzzy system is composed of two levels, a crisp level which describes the Markovian jumps and a fuzzy level which describes the system nonlinearities. A sufficient condition on the existence of a stochastically stabilizing controller using a Lyapunov function approach is presented. The fuzzy-model-based control design is formulated in terms of a set of linear matrix inequalities. In addition...

Back-propagation neural networks in adaptive control of unknown nonlinear systems

Cakarcan, Alpay
Fonte: Monterey, California. Naval Postgraduate School Publicador: Monterey, California. Naval Postgraduate School
Tipo: Tese de Doutorado
EN_US
Relevância na Pesquisa
66.03%
The objective of this thesis research is to develop a Back-Propagation Neural Network (BNN) to control certain classes of unknown nonlinear systems and explore the network's capabilities. The structure of the Direct Model Reference Adaptive Controller (DMRAC) for Linear Time Invariant (LTI) systems with unknown parameters is first analyzed and then is extended to nonlinear systems by using BNN, Nonminimum phase systems, both linear and nonlinear, have also be considered. The analysis of the experiments shows that the BNN DMRAC gives satisfactory results for the representative nonlinear systems considered, while the conventional least-squares estimator DMRAC fails. Based on the analysis and experimental findings, some general conditions are shown to be required to ensure that this technique is satisfactory. These conditions are presented and discussed. It has been found that further research needs to be done for the nonminimum phase case in order to guarantee stability and tracking. Also, to establish this as a more general and significant control technique, further research is required to develop more specific rules and guidelines for the BNN design and training.; Lieutenant Junior Grade, Turkish Navy

State Estimation and Parameter Identification of Continuous-time Nonlinear Systems

DHALIWAL, SAMANDEEP SINGH
Fonte: Quens University Publicador: Quens University
Tipo: Tese de Doutorado
EN; EN
Relevância na Pesquisa
66%
The problem of parameter and state estimation of a class of nonlinear systems is addressed. An adaptive identifier and observer are used to estimate the parameters and the state variables simultaneously. The proposed method is derived using a new formulation. Uncertainty sets are defined for the parameters and a set of auxiliary variables for the state variables. An algorithm is developed to update these sets using the available information. The algorithm proposed guarantees the convergence of parameters and the state variables to their true value. In addition to its application in difficult estimation problems, the algorithm has also been adapted to handle fault detection problems. The technique of estimation is applied to two broad classes of systems. The first involves a class of continuous time nonlinear systems subject to bounded unknown exogenous disturbance with constant parameters. Using the proposed set-based adaptive estimation, the parameters are updated only when an improvement in the precision of the parameter estimates can be guaranteed. The formulation provides robustness to parameter estimation error and bounded disturbance. The parameter uncertainty set and the uncertainty associated with an auxiliary variable is updated such that the set is guaranteed to contain the unknown true values. The second class of system considered is a class of nonlinear systems with timevarying parameters. Using a generalization of the set-based adaptive estimation technique proposed...

Evaluation of signal-to-noise and distortion ratio degradation in nonlinear systems

Lavrador, P.M.; Carvalho, N. Borges de; Pedro, J.C.
Fonte: Universidade de Aveiro Publicador: Universidade de Aveiro
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
66.04%
This paper presents a new figure-of-merit to evaluate signal-to-noise and distortion (S1NAD) ratio degradation in nonlinear systems, herein referred to as the noise and distortion figure (NDF). In order to obtain a mathematical formula for this NDF, the best linear approximation calculation is presented for memoryless and dynamic nonlinear systems, which can be modeled by a finite Volterra series. To the best of the authors' knowledge, this is the first time such an attempt of calculating the NDF for a nonlinear and dynamic system is made. NDF results are discussed in both types of systems by means of numerical simulations of systems up to the third order.

Quadratic Stability of a Class of Switched Nonlinear Systems

Zhao, Jun; Dimirovski, Georgi
Fonte: Institute of Electrical and Electronics Engineers (IEEE Inc) Publicador: Institute of Electrical and Electronics Engineers (IEEE Inc)
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
66.02%
Quadratic stability of a class of switched nonlinear systems is studied in this note. We first transform quadratic stability problem into an equivalent nonlinear programming problem. Then, we derive a necessary and sufficient condition for quadratic stabi

A Hybrid Impulsive and Switching Control Strategy for Synchronization of NonLinear Systems and Application to Chua's Chaotic Circuit

Guan, Zhi-Hong; Hill, David; Yao, Jing
Fonte: World Scientific Publishing Company Publicador: World Scientific Publishing Company
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
65.94%
In this paper, a new hybrid impulsive and switching control strategy for synchronization of nonlinear systems is developed. Using switched Lyapunov functions, several new criteria for global exponential stability of hybrid impulsive and switching nonlinea

Systematical Design and Stability Analysis of Global Control for a Class of Nonlinear Systems.

Zhang, G H; Wang, Youyi; Hill, David
Fonte: Institute of Electrical and Electronics Engineers (IEEE Inc) Publicador: Institute of Electrical and Electronics Engineers (IEEE Inc)
Tipo: Conference paper
Relevância na Pesquisa
66.01%
This paper presents the systematical global control approach to further improves the feasibility of nonlinear systems control. A class of nonlinear system is represented by global system models and global controller can be obtained by utilizing the proposed design procedure. The main idea of global control is first to decompose the nonlinear systems into partial subspaces, where the partial controllers are respectively designed. Then the global control law is then constructed by combining all the control actions through the partial membership functions. Moreover, the global stability conditions of nonlinear systems are simplified as the stabilization of partial models in terms of Lyapunov functions. The design methodology is illustrated by application to the cart and pole system.

Worst case power generating capabilities of nonlinear systems

Dower, Peter M; James, Matthew
Fonte: Springer Publicador: Springer
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
66.02%
In this paper we analyze the worst case power generating capabilities of a class of nonlinear systems which exhibit a power gain property. This class of systems includes systems which exhibit persistent excitation in the absence of inputs. Examples include limit cycle systems and chaotic systems. In order to capture the power generating capability of a nonlinear system, we define a worst case average cost per unit time performance index. This performance index, called the available power, is in effect the most power that can be generated by a system via the application of any input. The main result of the paper is that the input which achieves this worst case performance is typically a persistent input whose power is given explicitly by a function of the derivative of the available power with respect to the power gain of the system. A natural corollary of this result is that the available power may be recast as an optimization over power inputs.