Multivariable Newton-based extremum seeking

Ghaffari, Azad; Krstić, Miroslav; Nešić, Dragan

doi:10.1016/j.automatica.2012.05.059

Cited by 255 publications

(158 citation statements)

References 25 publications

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“…2 shows (70) and its first derivative. We use low-pass and washout filters with corner frequencies (ω h and ω l ) to improve the controller performance (see [11,Figure 4]). We present simulations of the predictor (30), where c = 20, z is given by (9) with h (j) as in (7) and γ in (6).…”

Section: Simulation Resultsmentioning

confidence: 99%

“…In recent years, there have been a lot of publications on ES in theory [22], [23], [24], [14], [15], [16], [17], [19] as well as applications [20], [21]. In [7] and [11] Newton-based ES in absence of delay was deeply studied. A highlight of these works is the approach used to estimate the Hessian's inverse of the nonlinear map, which is generated by means of Riccati filter.…”

Section: Introductionmentioning

confidence: 99%

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Newton-based extremum seeking for higher derivatives of unknown Maps with Delays

Rušiti

Oliveira

Mills

et al. 2016

2016 IEEE 55th Conference on Decision and Control (CDC)

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Abstract-We present a Newton-based extremum seeking algorithm for maximizing higher derivatives of unknown maps in the presence of time delays. Different from previous works about extremum seeking for higher derivatives, arbitrarily long input-output delays are allowed. We incorporate a predictor feedback with a perturbation-based estimate for the Hessian's inverse using a differential Riccati equation. As a bonus, the convergence rate of the real-time optimizer can be made user-assignable, rather than being dependent on the unknown Hessian of the higher-derivative map. Furthermore, exponential stability and convergence to a small neighborhood of the unknown extremum point can be obtained for locally quadratic derivatives by using backstepping transformation and averaging theory in infinite dimensions. We also give a numerical example in order to highlight the effectiveness of the proposed predictorbased extremum seeking for time-delay compensation.

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Section: Simulation Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Newton-based extremum seeking for higher derivatives of unknown Maps with Delays

Rušiti

Oliveira

Mills

et al. 2016

2016 IEEE 55th Conference on Decision and Control (CDC)

View full text Add to dashboard Cite

show abstract

“…It requires the simultaneous estimation of h ′ (u) and h ′′ (u). Later this work was extended to include higher order derivatives (Nesić, Tan, Manzie, Mohammadi, & Moase, 2012; and multivariable ES (Ghaffari, Krstić, & Nesić, 2012).…”

Section: Introductionmentioning

confidence: 99%

Fast extremum seeking on Hammerstein plants: A model-based approach

2015

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“…The reader is referred to [10] for a detailed convergence proof and design method of the Newton-based ES. To summarize the dynamical system shown in Fig.…”

Section: ×1mentioning

confidence: 99%

“…However, the convergence of the gradient-based ES schemes depended on an unknown Hessian matrix, which resulted in different convergence speeds for multi-input optimization problems. Therefore, in [10] a Newton-based ES was introduced for a general MIMO system, where an estimate of the inverse of the Hessian is dynamically obtained. This allowed for the convergence rate to be user assigned and independent of the Hessian.…”

Section: Introductionmentioning

confidence: 99%

Real time optimization of solar powered direct contact membrane distillation based on multivariable extremum seeking

Karam

Laleg‐Kirati

2015

2015 IEEE Conference on Control Applications (CCA)

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Abstract-This paper presents a real time optimization scheme for a solar powered direct contact membrane distillation (DCMD) water desalination system. The sun and weather conditions vary and are inconsistent throughout the day. Therefore, the solar powered DCMD feed inlet temperature is never constant, which influences the distilled water flux. The problem of DCMD process optimization has not been studied enough. In this work, the response of the process under various feed inlet temperatures is investigated, which demonstrates the need for an optimal controller. To address this issue, we propose a multivariable Newton-based extremum seeking controller which optimizes the inlet feed and permeate mass flow rates as the feed inlet temperature varies. Results are presented and discussed for a realistic temperature profile. I. INTRODUCTIONMembrane distillation (MD) is a thermal separation technique driven by a vapor pressure difference across a hydrophobic membrane. In this process, a hot feed stream is passed along one side of a porous hydrophobic membrane. Water vapor is then transferred through the membrane to the other cooler (permeate) side. The vapor then condenses at the membrane-permeate interface and clean water is produced.MD has emerged as a sustainable water desalination technique, which offers several advantages over conventional desalination methods. In contrast to reverse osmosis, MD operates at a lower water pressure, hence is less susceptible to scaling and membrane fouling. Moreover, MD water desalination can be integrated with renewable and waste energy sources, since the feed water is not heated up to boiling temperature [1]. All of these features reduce the capital and operational cost of the MD process. Over the years, new MD configurations and membrane material were the main area of research [2]. However, very limited work has been done in terms of process control and optimization [3], [4].As it is well known, the objective is always to operate any process at optimal settings, which reduces the operational costs and guaranties the performance and stability of the system. This is true for the solar-powered MD water desalination, where the objective is to maximize the water production and reduce the energy consumption at the same time through the manipulation of the feed and permeate inlet mass flow rates.In terms of process optimization, the work in [4] developed a neural network model, which was used to calculate optimal

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Multivariable Newton-based extremum seeking

Cited by 255 publications

References 25 publications

Newton-based extremum seeking for higher derivatives of unknown Maps with Delays

Newton-based extremum seeking for higher derivatives of unknown Maps with Delays

Fast extremum seeking on Hammerstein plants: A model-based approach

Real time optimization of solar powered direct contact membrane distillation based on multivariable extremum seeking

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