An experimental application of extremum seeking control to cultures of the microalgae <i>Scenedesmus obliquus</i> in a continuous photobioreactor

Letchindjio, Christian G. Feudjio; Dewasme, Laurent; Wouwer, Alain Vande

doi:10.1002/acs.3196

Cited by 7 publications

(4 citation statements)

References 26 publications

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“…In addition, ES based constrained optimization was proposed in [5]. An experimental application of ES method has been presented for the control of microalgae Scenedesmus obliquus culture in a photobioreactor [6] .…”

Section: Introductionmentioning

confidence: 99%

A Novel Extremum Seeking Hyperparameter Design for Joint State and Parameter Estimation of Nonlinear Systems

Beyhan

2023

AIS

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This paper introduces a novel hyperparameter design based on extremum seeking (ES) method to enhance the convergence speed of Extended-Kalman Filter (EKF). ES method produces a real-time optimization output based on the second-order gradient of performance function so that the estimation performance of EKF is simultaneously optimized. In addition to the convergence speed, the proposed hyperparameter reduces the effect of initial covariance matrices, and improves the accuracy of estimation for the fast changes without any knowledge about system dynamics. In numerical applications, EKF with and without the proposed hyperparameter were first used to estimate the unknown parameters of a linear time-varying system. Second, on a real-time collected data, they were applied for the joint estimation of velocity and payload mass of a real-time nonlinear servo-system where the performance improvement is provided almost 30%. Performance measurements are given in terms of the root-mean squared-error (RMSE) of estimation.

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Section: Introductionmentioning

confidence: 99%

A Novel Extremum Seeking Hyperparameter Design for Joint State and Parameter Estimation of Nonlinear Systems

Beyhan

2023

AIS

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“…[31][32][33][34] Among these algorithms, a key term separation gradient iterative algorithm was derived to identify a fractional-order nonlinear system, 30 a recursive gradient algorithm was proposed to estimate the nonlinear parameters using multifrequency sine signals, 35 a maximum likelihood gradient iterative algorithm was developed for identifying the parameters of bilinear systems, 36 a gradient-based recursive least squares estimator was applied in the model-free extremum seeking control. 37 However, the estimate for the NRM given by the traditional SG algorithm is biased because the output y(k) in the information vector is correlated to the noise v(k) (see Equation (6) for detail). Similar to References 18 and 19, a bias compensation method is adopted to obtain an unbiased estimate for the NRM.…”

Section: Introductionmentioning

confidence: 99%

“…There are many gradient‐based algorithms, such as information gradient algorithms and accelerated gradient algorithms 31‐34 . Among these algorithms, a key term separation gradient iterative algorithm was derived to identify a fractional‐order nonlinear system, 30 a recursive gradient algorithm was proposed to estimate the nonlinear parameters using multifrequency sine signals, 35 a maximum likelihood gradient iterative algorithm was developed for identifying the parameters of bilinear systems, 36 a gradient‐based recursive least squares estimator was applied in the model‐free extremum seeking control 37 …”

Section: Introductionmentioning

confidence: 99%

Bias compensated stochastic gradient algorithm for identification of an ARX‐type nonlinear rational model and its application in modeling of the dynamic of the cellular toxicity

Jing

Kiely

Luxton

2022

Intl J Robust & Nonlinear

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Nonlinear rational model (NRM) is a generalized nonlinear model, the NAR-MAX model and Volterra model can be regarded as its special cases. In this article, the parameter identification of a class of nonlinear rational models is studied. Due to the coupling of the model output and the information vector, the parameter identification of the NRM is very challenging. To reduce the complexity of the identification, the stochastic gradient algorithm is used. However, the estimate given by traditional stochastic gradient algorithm is biased. To obtain unbiased estimation, the bias is calculated by using the observations and the previous estimate and then compensated to the biased estimate. A variable factor considering the estimation error is introduced to speed up the algorithm. Theoretical analysis shows that the proposed algorithm can obtain an unbiased estimate and has the complexity of O(n). The proposed algorithm is validated by a numerical example and is applied in modeling the dynamics of the cellular toxicity using the tetra-ethyl ammonium chloride. Results show that the proposed algorithm can obtain an accurate estimate for the nonlinear rational model with less computation.

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“…On the application side, Reference 14 reports exciting results on the application of ESC to the problem of cultivation of microalgae in photobioreactors (PBRs). The authors explore the use of model‐free ESC to optimally regulate the productivity of a continuous PBR.…”

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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An experimental application of extremum seeking control to cultures of the microalgae Scenedesmus obliquus in a continuous photobioreactor

Cited by 7 publications

References 26 publications

A Novel Extremum Seeking Hyperparameter Design for Joint State and Parameter Estimation of Nonlinear Systems

A Novel Extremum Seeking Hyperparameter Design for Joint State and Parameter Estimation of Nonlinear Systems

Bias compensated stochastic gradient algorithm for identification of an ARX‐type nonlinear rational model and its application in modeling of the dynamic of the cellular toxicity

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

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