Extremum seeking for unknown scalar maps in cascade with a class of parabolic partial differential equations

Oliveira, Tiago Roux; Feiling, Jan; Koga, Shumon; Krstić, Miroslav

doi:10.1002/acs.3117

Cited by 11 publications

(4 citation statements)

References 37 publications

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“…10 To solve the problem of unknown scalar maps in cascade with parabolic PDEs, a novel ESC method is proposed for unknown scalar maps in cascade with a class of parabolic PDEs. 11 Feiling et al use a gradient-based approach to update control inputs for static maps with execution dynamics governed by diffusion PDEs. 12 The theory of ESC has undergone significant development over the years, with important contributions in areas such as stability analysis, convergence rate, and the application of ESC to systems described by PDEs.…”

Section: Introductionmentioning

confidence: 99%

“…Then the mltivariable extremum seeking for partial differential equations (PDE) dynamic systems method is developed to extend the standard ESC scheme to multivariable PDE systems with nonlinear dynamics 10 . To solve the problem of unknown scalar maps in cascade with parabolic PDEs, a novel ESC method is proposed for unknown scalar maps in cascade with a class of parabolic PDEs 11 . Feiling et al use a gradient‐based approach to update control inputs for static maps with execution dynamics governed by diffusion PDEs 12 .…”

Section: Introductionmentioning

confidence: 99%

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Path planning for fast swarm source seeking in unknown environments

Chen,

Yuan,

Zhu

et al. 2023

Adaptive Control & Signal

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SummaryThis article proposes a novel path planning method for source seeking by UAV swarm using extremum seeking control mechanism and combined artificial potential functions, without the knowledge of position information. In particular, the swarm source seeking problem is reformulated as a minimum seeking of a combined artificial potential function that considers the potentials of obstacles, source, and collision avoidance between UAVs. The explicit form of the combined artificial potential function is unknown and its value can be measured by the sensors mounted on UAVs. The fast extremum seeking mechanism based on the normalized extremum seeking method is exploited to find the gradient of the combined artificial potential function and the target is located without using its position information. Finally, extensive simulations of source seeking for single UAV and swarm are presented to illustrate the effectiveness of the proposed path planning method.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Path planning for fast swarm source seeking in unknown environments

Chen,

Yuan,

Zhu

et al. 2023

Adaptive Control & Signal

View full text Add to dashboard Cite

show abstract

“…e state feedback and output feedback for fixed-time stabilization of a linear parabolic distributed parameter system with spacedependent reactivity is studied in [35]. A generalization of the scalar gradient extremum seeking algorithm, which maximizes static maps in the presence of parabolic PDEs, is presented in [36]. e stabilizability of linear partial integrodifferential equations with local term at left end was studied in [37][38][39].…”

Section: Introductionmentioning

confidence: 99%

Results on Boundary Control for Parabolic Systems Using Backstepping Method

Mathiyalagan

Renugadevi

Nidhi

2022

Mathematical Problems in Engineering

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This paper focuses on the stabilization problem for the linear parabolic system using the backstepping method. The exponentially stability results for considered parabolic system are derived in two cases with Dirichlet and Neumann local terms. Also, the boundary conditions for the problem is assumed to be mixed or Robin-type boundary conditions. The main aim is to achieve the stability of the considered system using the backstepping method with help of Volterra integral transformation. The explicit solutions of kernel functions in integral transformation is obtained by using Laplace transform and designed a boundary control law to the closed-loop system. Finally, the effectiveness and applicability of the derived results are validated through a single-species pattern generation model.

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“…The applications of this type of data‐driven optimal controllers are numerous and range from repetitive robotics tasks to particle accelerators control. In Reference 8, a new gradient‐based ESC is introduced for static maps in the presence of infinite‐dimensional dynamics described by parabolic partial differential equations (PDEs), where the PDE dynamics contains reaction–advection–diffusion. Generalization to a scalar Newton‐based ES algorithm is proposed, which allows to remove the dependence of the convergence rate on the unknown Hessian of the higher derivative of the cost function, which characterizes the standard gradient‐based ESC.…”

Section: Introductionmentioning

confidence: 99%

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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Extremum seeking for unknown scalar maps in cascade with a class of parabolic partial differential equations

Cited by 11 publications

References 37 publications

Path planning for fast swarm source seeking in unknown environments

Path planning for fast swarm source seeking in unknown environments

Results on Boundary Control for Parabolic Systems Using Backstepping Method

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

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