Multivariable extremum seeking control via cyclic search and monitoring function

Aminde, Nerito Oliveira; Oliveira, Tiago Roux; Hsu, Liu

doi:10.1002/acs.3151

Cited by 6 publications

(8 citation statements)

References 38 publications

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“…Em (Aminde et al, 2020), foi projetado o controle extremal multivariável via modos deslizantes, função de monitoração e busca cíclica para problemas do tipo da seção anterior, mas para mapeamentos estáticos. Aqui pretendese mostrar que os resultados obtidos em (Aminde et al, 2020) podem ser estendidos para mapeamentos dinâmicos.…”

Section: Análise Por Perturbação Singularunclassified

“…O esquema de controle extremal cíclico multivariável via função de monitoração está ilustrado na Figura 1, correspondente ao sistema ( 7)-( 9), sem dinâmicas não modeladas (η = 0). A lei de controle para plantas multivariáveis com ganho de alta frequência desconhecido e busca cíclica é definida conforme (Aminde et al, 2020):…”

Section: Projeto Do Controlador Via Fun ç ãO De Monitora ç ãO E Busca...unclassified

“…A função de monitoração foi introduzida e desenvolvida em (Yan et al, 2003;Oliveira et al, 2007Oliveira et al, , 2010 e pela primeira vez, foi aplicada ao problema de controle extremal escalar por modos deslizantes em (Aminde et al, 2013) e multivariável em (Aminde et al, 2020). Partindo-se do princípio de que a desigualdade (28) é garantida quando a direção de controle é correta, é natural usar ζ i como referência para se decidir quando o chaveamento de u i em (16) ocorre de u + i para u − i (ou vice-versa), isto é, o chaveamento ocorre apenas quando (28) é violada.…”

Section: Projeto Da Função De Monitoraçãounclassified

“…No entanto, os autores formularam hipóteses muito restritivas, com relação ao gradiente da função objetivo. Então, foi proposto o controle extremal multivariável por modos deslizantes usando função de monitoração e busca cíclica em (Aminde et al, 2020), onde foram relaxadas tais hipóteses além de garantir a convergência e estabilidade globais. Entretanto, os resultados foram alcançados para plantas com os mapeamentos estáticos.…”

Section: Introdu ç ãOunclassified

“…Neste artigo, são generalizados os resultados em (Aminde et al, 2020) para mapeamentos dinâmicos com grau relativo arbitrário, que por simplicidade, são considerados sistemas dinâmicos lineares estáveis em cascata com um mapeamento não-linear. A mitigação do grau relativo é alcançado através da técnica de escalonamento temporal.…”

Section: Introdu ç ãOunclassified

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Controle Extremal para Mapeamentos Dinâmicos Multivariáveis usando Função de Monitoração e Busca Cíclica

Aminde

Oliveira²,

Hsu

2021

Procedings Do XV Simpósio Brasileiro De Automação Inteligente

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Recently, a multivariable sliding-mode based extremum seeking controller via monitoring function was introduced for static maps. In this paper, a generalization is made, including linear dynamics with arbitrary relative degree. For this purpose, the techniques of time-scaling and singular perturbation are considered, preserving the previous results of stability and global convergence for a neighborhood of the desired extremum. Cyclic search allows the controller to search the directional extremum at each time, cyclically. Simulation results with a system of two inputs and a single output illustrate the properties of the proposed multivariable control strategy, in terms of speed of convergence and small residual errors. Resumo: Recentemente, foi introduzido um controlador extremal multivariável por modos deslizantes e função de monitoração para mapeamentos estáticos. No presente artigo, faz-se uma generalização que inclui dinâmicas lineares com grau relativo arbitrário. Para tal, usam-se as técnicas de escalonamento temporal e perturbação singular, que preservam o resultado de estabilidade e convergência global para uma vizinhança do extremo desejado. A busca cíclica permite que o controlador encontre um extremo direcional por vez, ciclicamente. Resultados de simulação com um sistema de duas entradas e uma única saída ilustram as propriedades da estratégia de controle multivariável proposta, em termos de taxa de convergência e de erros residuais pequenos.

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Section: Análise Por Perturbação Singularunclassified

Section: Projeto Do Controlador Via Fun ç ãO De Monitora ç ãO E Busca...unclassified

Section: Projeto Da Função De Monitoraçãounclassified

Section: Introdu ç ãOunclassified

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Controle Extremal para Mapeamentos Dinâmicos Multivariáveis usando Função de Monitoração e Busca Cíclica

Aminde

Oliveira²,

Hsu

2021

Procedings Do XV Simpósio Brasileiro De Automação Inteligente

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Editorial for the special issue on extremum seeking control: Theory and applications

Benosman

KrstićMiroslav

GuayMartin

et al. 2021

Adaptive Control & Signal

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Real-world systems have to operate in uncertain and changing environments, thus the necessity to design feedback controllers which can adapt to such uncertainties. Controllers which are designed to satisfy this goal are called adaptive controllers. We can classify adaptive control into three main subclasses, for example, Reference 1: Classical model-based adaptive control, which mainly uses models of the controlled system; learning-based adaptive control, which uses both model-based and data-driven techniques to design modular adaptive controllers; and data-driven adaptive control, which is based on the interaction of the controller with the system. In this special issue, we shall focus on a specific class of data-driven adaptive controllers, namely, extremum seekers.Recently, there have been a lot of efforts in this direction of control. One of the reasons behind this increasing interest is that, following the pioneering ESC analysis paper, 2 the field of ESC has reached a certain maturity, which has led to good analysis and understanding of the main properties of the available algorithms. The idea behind ESC is to design a closed-loop dynamical system, such that its flow converges to the optimum of a given static or dynamic cost function, for example, References 3-5. This type of optimization algorithms is also referred to as continuous optimization, for example, Reference 6. The advantages of such optimization approaches comparatively to classical optimization algorithms is the fact that extremum seekers do not require a closed-form expression of the cost function. Moreover, they do not require multiple evaluation of the cost function at each point to estimate the gradient (or higher order derivatives) of the cost function, since they include some internal states which converge to an estimate of the derivatives of the cost over time. Besides, their formulation as a closed-loop control problem allows us to use numerous tools from dynamical systems theory and control theory, for example, time-scale separation, averaging theory, Lyapunov stability theory, to perform rigorous analysis of their convergence and robustness properties w.r.t. initial conditions changes and other hyperparameters tuning.In this special issue, we have included 10 papers, which could be divided into two main types. The first type, more theoretical, presents new extremum seeking methods designed for different dynamical systems, from systems with delays, and multiagent systems, to distributed systems. The second type of papers deals with real-world applications of extremum seeking controllers to challenging systems, ranging from microalgae cultivation control to heating and ventilation systems. These papers are compiled in a special virtual issue of the journal at the journal homepage. To access all of the papers, please follow the following link (https://onlinelibrary.wiley.com/toc/10991115/2021/35/7).For instance, Reference 7 presents a novel ESC for batch-to-batch optimal control of unknown time-varying systems. The authors show that the ...

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Practical prescribed‐time tracking control of unknown nonlinear systems: A low‐complexity approach

Xie,

Zhang,

Jing

et al. 2024

Intl J Robust & Nonlinear

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This article is concerned with the trajectory tracking control problem for the nonlinear systems in the sense of the predefined settling time and accuracy. In contrast with the existing works, we focus on the cases where the system dynamics, its bounding functions, the unmatched disturbances, and the time‐varying parameters are totally unknown; the derivatives of the desired trajectory are not required to be available. They significantly challenge the identification and/or approximation‐based control solutions. To overcome this obstacle, a novel robust prescribed performance control approach via state feedback is put forward in this article. It not only ensures the natural satisfaction of the specific initial condition but also realizes a full‐time performance specification for trajectory tracking. Furthermore, for the case of unmeasured state variables, an output‐feedback control approach is further derived by adopting an input‐driven filter and conducting trivial changes on the design procedure. Moreover, both approaches exhibit significant simplicity, without the needs for parameter identification, function approximation, disturbance estimation, derivative calculation, or command filtering. Three simulation studies are conducted to clarify and verify the above theoretical findings.

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Multivariable extremum seeking control via cyclic search and monitoring function

Cited by 6 publications

References 38 publications

Controle Extremal para Mapeamentos Dinâmicos Multivariáveis usando Função de Monitoração e Busca Cíclica

Controle Extremal para Mapeamentos Dinâmicos Multivariáveis usando Função de Monitoração e Busca Cíclica

Editorial for the special issue on extremum seeking control: Theory and applications

Practical prescribed‐time tracking control of unknown nonlinear systems: A low‐complexity approach

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