Sliding Mode Control of Uncertain Multivariable Nonlinear Systems With Unknown Control Direction via Switching and Monitoring Function

Oliveira, Tiago Roux; Peixoto, Alessandro Jacoud; Hsu, Liu

doi:10.1109/tac.2010.2041986

Cited by 91 publications

(59 citation statements)

References 22 publications

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“…This section will generalize the results of [10,12,13] to adaptive control, proposing a new monitoring function. The control signal is defined by (11) with adaptation law…”

Section: B-mrac With Monitoring Functionsmentioning

confidence: 91%

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Binary robust adaptive control with monitoring functions for systems under unknown high‐frequency‐gain sign, parametric uncertainties and unmodeled dynamics

Oliveira

Peixoto

Nunes

2015

Adaptive Control & Signal

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In this paper, we propose an adaptive output-feedback controller for uncertain linear systems without a priori knowledge of the plant high-frequency-gain sign. To deal with parametric uncertainties and unmodeled dynamics, we consider a robust adaptive strategy named binary model reference adaptive control, which has the good transient properties and robustness of sliding mode control with the important advantage of having a continuous control signal free of chattering. The effective way of tackling unknown high-frequencygain sign is employing monitoring functions. The developed adaptive control guarantees global exponential stability of the closed-loop error system with respect to a compact residual set. Moreover, in the absence of unmodeled dynamics, exact tracking of a reference signal can be achieved. Numerical simulations illustrate the efficacy of the proposed approach.

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“…This section will generalize the results of [10,12,13] to adaptive control, proposing a new monitoring function. The control signal is defined by (11) with adaptation law…”

Section: B-mrac With Monitoring Functionsmentioning

confidence: 91%

“…The signals w 1 and w 2 are obtained from I/O state variable filters defined in (7). The adaptation law is given by (12) and (13). Considering the state X D x T w T 1 w T 2 , the plant (24) and the filters (7) can be rewritten as…”

Section: B-mrac Robustness To Unmodeled Dynamicsmentioning

confidence: 99%

Binary robust adaptive control with monitoring functions for systems under unknown high‐frequency‐gain sign, parametric uncertainties and unmodeled dynamics

Oliveira

Peixoto

Nunes

2015

Adaptive Control & Signal

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“…Em (Oliveira et al, 2010), foi desenvolvida um método baseado nos trabalhos de (Sontag and Wang, 1997) e (Krichman et al, 2001) para a obtenção dos observadores da norma. Este métodoé capaz de contemplar de forma direta as equações diferenciais que formam o sistema de Lorenz.…”

Section: Observadores Da Normaunclassified

Estabilização global do sistema caótico de lorenz através do controle por modos deslizantes via observadores da norma

Rodrigues¹,

Oliveira²

2013

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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Abstract-In this paper, we have assumed that all parameters of the Lorenz system are unknown and only the output variable is available for feedback. Exploring ISS (Input-to-State Stability) properties of the system, an upper bound for the norm of the unmeasured state vector is developed from the system output. Such norm estimate provided by the norm observer is applied to obtain the output-feedback sliding mode control law. Based on Lyapunov's stability theory, it was possible to guarantee that the proposed controller is capable to globally stabilize the Lorenz system. Simulation results are also presented to show the robustness of the control strategy with respect to parametric uncertainties.Keywords-Chaotic Dynamics, Nonlinear Control, Global Stability, Output-feedback, Lorenz System Resumo-Neste artigo, assume-se que todos os parâmetros do sistema de Lorenz são desconhecidos e que apenas uma variável de saída está disponível para o projeto do controlador. Explorando a característica ISS (Input-to-State Stability) do sistema, desenvolve-se um limitante superior para a norma do vetor de estado através destaúnica saída medida. Esse limitante fornecido pelo observador da normaé utilizado na lei de controle por modos deslizantes via realimentação de saída. Baseado na teoria de estabilidade de Lyapunov, foi possível mostrar que o controlador propostoé capaz de estabilizar globalmente o sistema de Lorenz. Resultados de simulações são apresentados para mostrar também a robustez da estratégia de controle a incertezas paramétricas.Palavras-chave-Dinâmica Caótica, Controle Não-linear, Estabilidade Global, Realimentação de Saída, Sistema de Lorenz IntroduçãoSistemas caóticos têm sua existência conhecida desde o século XIX, no entanto sua importância para uma grande variedade de aplicações só começou a ser estudada nasúltimas décadas. Sistemas dinâmicos são chamados de caóticos se suaś orbitas são tipicamente não periódicas, limitadas dentro de uma região no espaço de estados e possuem alta sensibilidadeàs condições iniciais. A teoria caótica tem sido aplicada a vários campos de estudo como cardiologia (Cheng-Yu Yeh and Yau, 2012), circuitos eletrônicos (Guo and Liu, 2011), sincronização (Souza et al., 2008;Souza et al., 2012), comunicação segura (Cuomo and Oppenheim, 1993;Mozelli et al., 2007), conversão de energia (Hou, 2012), dinâmica dos fluidos (Lorenz, 1963) e economia (Goodwin, 1990).Depois do trabalho pioneiro de (Ott et al., 1990), o controle de sistemas caóticos tem sido estudado de forma intensiva. Em (Ott et al., 1990), o método OGY foi desenvolvido permitindo converter um atrator caótico em um grande número de trajetórias periódicas instáveis injetando pequenas perturbações variáveis no tempo em um dos parâmetros acessíveis do sistema.Em (Wang and Ge, 2001), uma técnica para eliminar os termos cruzados do sistema de Lorenz foi utilizada para desenvolver um controlador que estabiliza globalmente o sistema, no entanto o controlador necessita o conhecimento de todo o vetor de estado. Em (Araujo and Singh, 2002)...

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“…This control method has been studied extensively for over 50 years due to its invariance property to system uncertainties on the sliding surface [1]. Meanwhile, many applications of the SMC system have been presented [2][3][4][5][6]. Since the system uncertainties unavoidably exist in the practical systems, a switching control term that consists of a sign function is required to maintain the sliding variable on the sliding surface.…”

Section: Introductionmentioning

confidence: 99%

“…The nominal dynamics of control plants is required in the DSMC and CSMC schemes. Since the nominal dynamics may be unknown or perturbed Page 4 of 38 A c c e p t e d M a n u s c r i p t Accepted Paper (ASOC-D-13-01314R1) 3 in real applications, the DSMC and CSMC systems cannot be obtained.…”

Section: Introductionmentioning

confidence: 99%

Intelligent complementary sliding-mode control with dead-zone parameter modification

Hsu

Kuo

2014

Applied Soft Computing

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Sliding Mode Control of Uncertain Multivariable Nonlinear Systems With Unknown Control Direction via Switching and Monitoring Function

Cited by 91 publications

References 22 publications

Binary robust adaptive control with monitoring functions for systems under unknown high‐frequency‐gain sign, parametric uncertainties and unmodeled dynamics

Binary robust adaptive control with monitoring functions for systems under unknown high‐frequency‐gain sign, parametric uncertainties and unmodeled dynamics

Estabilização global do sistema caótico de lorenz através do controle por modos deslizantes via observadores da norma

Intelligent complementary sliding-mode control with dead-zone parameter modification

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