## What is/are Extremum Seeking?

Extremum Seeking - Through these studies, the RGP-based adaptation approach is shown to be effective and is shown to exhibit favorable convergence times when compared with a mature adaptive control technique, extremum seeking (ES).^{[1]}We propose two perturbation-based extremum seeking control (ESC) schemes for general single input single output nonlinear dynamical systems, having structures similar to that of the classical ESC scheme.

^{[2]}The execution stage quickly stabilizes optimal mode-locking using various algorithmic innovations including (i) extremum seeking control, (ii) deep reinforcement learning and (iii) deep model predictive control.

^{[3]}Extremum seeking control (ESC) and its slope seeking generalization are applied in a highfidelity flow simulation framework for reduction of acoustic noise generated by a NACA0012 airfoil.

^{[4]}Quadrotor Controller, PID, Automatic Tuning PID, extremum seeking, ES.

^{[5]}This article addresses the problem of extremum seeking of a continuous-time dynamical system with a single input and a single output.

^{[6]}In this paper, we generalize our previous results of Newton-based extremum seeking of higher derivatives via predictors with averaging-based estimates for uncertain delays.

^{[7]}The main contribution of the paper is the formulation of the problem using the penalty method and the development of an extremum seeking algorithm based on a modified synchronous detection method for computing a stochastic gradient descent procedure.

^{[8]}A suitable normalization technique is introduced to improve the robustness properties of the conventional perturbation-based extremum seeking (ES).

^{[9]}In practical application, for sensors in some complex environment, due to the lack of the ability to perceive the location of the source or its own position, we use the nonmodel gradient estimation of extremum seeking algorithm.

^{[10]}This letter proposes a design of extremum seeking controllers that guarantees precise convergence of the control system to the unknown optimizer of a measured unknown cost function.

^{[11]}This paper focuses on extremum seeking (ES) controllers with adversarial attacks in the form of deception signals.

^{[12]}In this study, to overcome limitations of model-based strategies, a model-free control strategy based on extremum seeking control (ESC) without reliance on building models was proposed for real-time control of thermal environment.

^{[13]}In this paper the Newton-based extremum seeking for an unknown static map which is coupled with a diffusion partial differential equation (PDE) is presented.

^{[14]}Extremum Seeking is a black box optimization/-control technique that utilizes perturbations to system inputs in order to optimize outputs.

^{[15]}We introduce a concept in extremum seeking, namely biased extremum seeking, which adaptively finds a set point corresponding to a prescribed bias of the value that optimizes an unknown static map.

^{[16]}In recent years, an approach to extremum seeking control made it possible to design control vector fields that lead to asymptotic stability of the minimum point provided that the minimum value of the function is known a priori.

^{[17]}In this paper, an extremum seeking control scheme to the recently developed wind turbine MOWEA (Modulare Windenergieanlagen GmbH) is proposed and successfully applied.

^{[18]}We present an extremum seeking-based robust observer design for thermal-fluid systems, pursuing an application to efficient energy management in buildings.

^{[19]}Our model-free approach is based on the use of Extremum Seeking Control (ESC) as the real-time optimizer.

^{[20]}The application of extremum seeking control (ESC) algorithm to antilock braking systems (ABSs) is attractive for maximizing the longitudinal frictional force.

^{[21]}Our approach consists of a two level scheme: in the lower level we use an extremum seeking controller to track a single particle by first seeking it then orbiting around it.

^{[22]}The aim of this paper is to discuss the optimal tuning of the PID controller using extremum seeking (ES).

^{[23]}Next, an extremum seeking control algorithm is applied to an existing SEC test rig to control the cycle averaged formation of different autoignition modes by optimizing the fuel supply.

^{[24]}As second main contribution, we design a data-driven variant of the former algorithm where each agent estimates their individual pseudo-gradient via zero-order information, namely, measurements of their individual cost function values, as typical of extremum seeking control.

^{[25]}This letter focuses on extremum seeking (ES) controllers with adversarial attacks in the form of deception signals.

^{[26]}The PI gain of the voltage controller is automatically adjusted by the extremum seeking algorithm to dynamically respond to the changes of the network.

^{[27]}While the classical objective of extremum seeking control is to drive a process performance index to its optimum, this paper also considers slope seeking, which allows driving the performance index to a desired level (which is thus sub-optimal).

^{[28]}The approach relies on the extremum seeking algorithm and on averaging theory to bring to zero the motion of the plasma along the unstable mode, hence achieving the stabilization of its vertical dynamic.

^{[29]}In particular, we propose a family of extremum seeking dynamics that can be universally modeled as singularly perturbed hybrid dynamical systems with restarting mechanisms.

^{[30]}The prime objective of using the PR-P controller is to utilize inherited properties of the signal produced by the controller’s resonant path and integrate it to update best estimated perturbation that represents the working principle of extremum seeking control (ESC) to use in P&O algorithm that characterizes the overall system learning-based real time adaptive (RTA).

^{[31]}We therefore formulate a constrained optimization problem and utilize an extremum seeking approach to maximize the desired production rate while limiting the burden on the cellular organism.

^{[32]}The upper level scheduler solves a chance-constrained optimal power flow (OPF) problem to plan the operation of the DERs based on forecasts, and the lower level distributed DER controllers leverage the extremum seeking approach to deliver the planned power at the feeder head.

^{[33]}This paper presents experimental results of a lab-scale implementation of an extremum seeking control strategy for maximizing the biomass productivity of cultures of the micro-algae Dunaliella tertiolecta in a flat-panel photobioreactor operated in continuous mode.

^{[34]}Conventional perturbation-based extremum seeking control (ESC) employs a slow time-dependent periodic signal to find an optimum of an unknown plant.

^{[35]}In order to control the ignition delay, this strategy adapts the amount of CNG injected into the prechamber with a linear controller or an extremum seeking algorithm depending on the air-to-fuel ratio of the main chamber.

^{[36]}For nonlinear system as photovoltaic system, extremum seeking control algorithm can reach good control effect.

^{[37]}In this sense, the unified criterion is a tool for the formulation of the extremum seeking problem as well.

^{[38]}We address a Newton-based extremum seeking algorithm for maximizing higher derivatives of unknown maps in the presence of known time delays.

^{[39]}The proposed method uses the concept of model predictive control (MPC) in conjunction with extremum seeking optimization to track the true MPP and can operate without a priori knowledge of the PV panel parameters or ambient condition.

^{[40]}As far as we know, extremum seeking based on climbing control is usually implemented by multiple vehicles or agents because of the large range of measurement and easy acquisition of gradient estimation.

^{[41]}In this paper, we present novel multi-variable Newton-based extremum seeking systems, based on Lie bracket approximation methods.

^{[42]}We design a Newton-like phasor-based Extremum Seeking Control (ESC) aimed at multi-variable nonlinear control systems.

^{[43]}First, a novel speed optimization scheme combining the extremum seeking (ES) algorithm with the self-tuning fuzzy logic system is proposed.

^{[44]}In this work, we describe an implementation of an Extremum Seeking Controller that performs identification and tracking of thermoclines at its point of highest temperature gradient in a completely autonomous way.

^{[45]}Indeed, the classical model-free approaches (such as Gradient Ascent or Extremum Seeking algorithms) have intrinsic limitations.

^{[46]}The maximum concentration of methane gas is achieved by extremum seeking control based on periodic perturbation signals.

^{[47]}A Lie bracket averaging technique is used to design the extremum seeking regulation mechanism.

^{[48]}Besides, variable of optimization methods and control strategies, especially the extremum seeking control, are referred.

^{[49]}In order to the extremum seeking in the outer loop it is enough to form a typical integral controller with information about the gradient.

^{[50]}

## maximum power point

This paper introduces an Extremum Seeking Control Maximum Power Point Tracking (ESC-MPPT) applied to solar photovoltaic (SPV) water pumping system with fast- tracking ability.^{[1]}The sliding mode extremum seeking control (SMESC) could track the maximum power point (MPP) of wind energy conversion system (WECS) without wind speed or wind turbine parameters.

^{[2]}In this study, we tried to combine maximum power point trackers (MPPT) and «Extremum Seeking» in a single multi-parameter extremum seekeng system for orienting solar panels and draw attention to the problem of a deeper study of nonlinear adaptive control using appropriate methods for their analysis.

^{[3]}The sliding mode extremum seeking control (SMESC) could track the maximum power point (MPP) of wind energy conversion system (WECS) without wind speed or wind turbine parameters.

^{[4]}

## steady state oscillation

Subsequently, an extremum seeking algorithm without steady-state oscillation (ESA-SSO) is introduced to tune the design parameters of the ADRC-based ship course tracking control law so as to obtain the better performance of ship course tracking control.^{[1]}Additionally, in contrast to the most classical extremum seeking algorithms, this algorithm can converge to Nash equilibria without steady state oscillation and faster, because the amplitude of excitation sinusoidal signal in the conventional extremum seeking is adjusted to converge to zero, so the deleterious effects of steady state oscillation will be eliminated.

^{[2]}Concentrated on the problem of steady-state oscillation of the traditional extremum seeking algorithm (ESA) that it is not beneficial to the speed optimization of unmanned sailboat, a novel speed optimization scheme with feedforward of unmanned sailboat via extremum seeking without steady-state oscillation (ESWSO) is proposed.

^{[3]}

## real time optimization

In particular, the extremum seeking controller is applied as a model-free real-time optimization strategy for such purpose.^{[1]}It is then proposed a combination of the modelbased tracking strategy with the Extremum Seeking Control real-time optimization technique – which by itself is accurate but slow – and both accurate and fast maximum power point tracking capabilities are observed, while still maintaining a simple control project.

^{[2]}It is then proposed a combination of the modelbased tracking strategy with the Extremum Seeking Control real-time optimization technique – which by itself is accurate but slow – and both accurate and fast maximum power point tracking capabilities are observed, while still maintaining a simple control project.

^{[3]}

## recursive least square

The proposed method is based on recursive least square-based extremum seeking control.^{[1]}Then for enhanced performance, two rotational inertia online estimators (RIOE), extremum seeking (ES) and recursive least-square (RLS), are attempted and evaluated in simulation.

^{[2]}The proposed method is based on recursive least square based extremum seeking control.

^{[3]}

## Mode Extremum Seeking

In this paper, a novel sliding mode extremum seeking control (SMESC) scheme is proposed to improve the performance of the classic SMESC.^{[1]}In this paper, a novel sliding mode extremum seeking control (SMESC) scheme is proposed to improve the performance of the classic SMESC.

^{[2]}To alleviate the problem, the proposed controller combines the merits of a multi-level DC link inverter with a multivariable sliding-mode extremum seeking tuned PI controller to achieve fast and precise trajectory tracking.

^{[3]}The sliding mode extremum seeking control (SMESC) could track the maximum power point (MPP) of wind energy conversion system (WECS) without wind speed or wind turbine parameters.

^{[4]}The sliding mode extremum seeking control (SMESC) could track the maximum power point (MPP) of wind energy conversion system (WECS) without wind speed or wind turbine parameters.

^{[5]}

## Global Extremum Seeking

Also, two optimization loops based on the Global Extremum Seeking algorithm are used to find the global optimum of the optimization function by real-time control of both fueling rates.^{[1]}The Energy Management Strategy uses a Load Following control loop of requested load demand on DC bus and an optimization control loop to improve the fuel economy based on the Global Extremum Seeking algorithm applied to the air flow rate.

^{[2]}The fuel economy strategy uses the fuel and air flow rates to efficiently operate the proton-exchange membrane (PEM) fuel cell (FC) system based on the load-following control and the global extremum seeking (GES) algorithm.

^{[3]}

## Stochastic Extremum Seeking

Based on the method of stochastic extremum seeking, we propose a distributed stochastic source seeking algorithm with switching topology.^{[1]}We consider the problem of using the velocity actuated vehicle as search agent, and only use the noisy measurements of a scalar signal field to design a discrete-time stochastic extremum seeking controller to tune the vehicle towards the source of the signal field.

^{[2]}This paper presents a Gradient-based stochastic extremum seeking method for unknown mappings with known time delays.

^{[3]}

## Driven Extremum Seeking

We finally add an adaptation layer to our framework, where we tune the closure models in real-time, using data-driven extremum seeking controllers.^{[1]}Moreover, the uncertain parameters estimate used in the designed observer are optimized through iterations of a data-driven extremum seeking (ES) algorithm.

^{[2]}For verification of the implementation, the model-free, gradient-based and data-driven Extremum Seeking Control (ESC) optimization scheme is employed.

^{[3]}

## Adaptive Extremum Seeking

In this letter, an adaptive extremum seeking control (AESC) based estimation scheme is proposed to estimate the resonant frequency of the LCL filter online.^{[1]}Unlike existing adaptive extremum seeking approaches that presume the satisfaction of a persistence of excitation condition on the agents of the network, we propose a novel approach that leverages the presence of cooperation and information-rich data sets in the system.

^{[2]}

## Robust Extremum Seeking

This conference paper suggests an interesting application of a Robust Extremum Seeking Algorithm for dynamic plants with uncertainties and perturbations.^{[1]}This paper suggests a novel continuous-time robust extremum seeking algorithm for an unknown convex function constrained by a dynamical plant with uncertainties.

^{[2]}

## Free Extremum Seeking

This paper proposes a model-free extremum seeking control (ESC) approach to optimize the productivity of continuous cultures of microalgae, considering the dilution rate and the light intensity as manipulated variables, and the biomass concentration as single measurement.^{[1]}This paper proposes a model-free extremum seeking control (ESC) algorithm for a three-level (3-L) inverter to reduce torque ripples and improve the drive efficiency.

^{[2]}

## Gradient Extremum Seeking

To calculate optimal parameters of the PI controllers, an ‘Extremum Seeking’ (ES) algorithm was used, more precisely, its version that assumes that gradient can be calculated [hence the name ‘Gradient Extremum Seeking’ (GES)].^{[1]}Gradient extremum seeking for compensating wave actuator dynamics in cascade with static scalar maps is addressed in the present paper.

^{[2]}

## extremum seeking control

We propose two perturbation-based extremum seeking control (ESC) schemes for general single input single output nonlinear dynamical systems, having structures similar to that of the classical ESC scheme.^{[1]}We propose the use of Bayesian Optimization (BO) to warm-start a state-of-the-art extremum seeking control (ESC) algorithm and then accelerate the ESC on-line with Adam, a well-studied adaptive moment-based optimization method used to solve high-dimensional non-convex optimization problems such as training deep neural networks.

^{[2]}The execution stage quickly stabilizes optimal mode-locking using various algorithmic innovations including (i) extremum seeking control, (ii) deep reinforcement learning and (iii) deep model predictive control.

^{[3]}Extremum seeking control (ESC) and its slope seeking generalization are applied in a highfidelity flow simulation framework for reduction of acoustic noise generated by a NACA0012 airfoil.

^{[4]}In this letter, an adaptive extremum seeking control (AESC) based estimation scheme is proposed to estimate the resonant frequency of the LCL filter online.

^{[5]}The proposed method is based on recursive least square-based extremum seeking control.

^{[6]}This paper proposes a model-free extremum seeking control (ESC) approach to optimize the productivity of continuous cultures of microalgae, considering the dilution rate and the light intensity as manipulated variables, and the biomass concentration as single measurement.

^{[7]}Then, based on the information provided by the derived simplified model, a model-guided extremum seeking control (MGESC) scheme with backtracking line search is developed, which can automatically estimate the best value of step-size at each search iteration to improve the performance of the control system for target tracking.

^{[8]}In this study, to overcome limitations of model-based strategies, a model-free control strategy based on extremum seeking control (ESC) without reliance on building models was proposed for real-time control of thermal environment.

^{[9]}Moreover, the optimized extremum seeking control (ESC) is employed to reduce energy consumption under environmental disturbances.

^{[10]}In this paper, a novel sliding mode extremum seeking control (SMESC) scheme is proposed to improve the performance of the classic SMESC.

^{[11]}In recent years, an approach to extremum seeking control made it possible to design control vector fields that lead to asymptotic stability of the minimum point provided that the minimum value of the function is known a priori.

^{[12]}In this paper, an extremum seeking control scheme to the recently developed wind turbine MOWEA (Modulare Windenergieanlagen GmbH) is proposed and successfully applied.

^{[13]}Our model-free approach is based on the use of Extremum Seeking Control (ESC) as the real-time optimizer.

^{[14]}Then, leveraging extremum seeking control loops, it minimizes this artificial potential to navigate smoothly to the source location.

^{[15]}The application of extremum seeking control (ESC) algorithm to antilock braking systems (ABSs) is attractive for maximizing the longitudinal frictional force.

^{[16]}Next, an extremum seeking control algorithm is applied to an existing SEC test rig to control the cycle averaged formation of different autoignition modes by optimizing the fuel supply.

^{[17]}As second main contribution, we design a data-driven variant of the former algorithm where each agent estimates their individual pseudo-gradient via zero-order information, namely, measurements of their individual cost function values, as typical of extremum seeking control.

^{[18]}While the classical objective of extremum seeking control is to drive a process performance index to its optimum, this paper also considers slope seeking, which allows driving the performance index to a desired level (which is thus sub-optimal).

^{[19]}The prime objective of using the PR-P controller is to utilize inherited properties of the signal produced by the controller’s resonant path and integrate it to update best estimated perturbation that represents the working principle of extremum seeking control (ESC) to use in P&O algorithm that characterizes the overall system learning-based real time adaptive (RTA).

^{[20]}The proposed method is based on recursive least square based extremum seeking control.

^{[21]}This paper introduces an Extremum Seeking Control Maximum Power Point Tracking (ESC-MPPT) applied to solar photovoltaic (SPV) water pumping system with fast- tracking ability.

^{[22]}This paper presents experimental results of a lab-scale implementation of an extremum seeking control strategy for maximizing the biomass productivity of cultures of the micro-algae Dunaliella tertiolecta in a flat-panel photobioreactor operated in continuous mode.

^{[23]}This paper demonstrate the feasibility and illustrates some challenges of applying extremum seeking control to online optimization of the drilling process.

^{[24]}Conventional perturbation-based extremum seeking control (ESC) employs a slow time-dependent periodic signal to find an optimum of an unknown plant.

^{[25]}For nonlinear system as photovoltaic system, extremum seeking control algorithm can reach good control effect.

^{[26]}We design a Newton-like phasor-based Extremum Seeking Control (ESC) aimed at multi-variable nonlinear control systems.

^{[27]}It is then proposed a combination of the modelbased tracking strategy with the Extremum Seeking Control real-time optimization technique – which by itself is accurate but slow – and both accurate and fast maximum power point tracking capabilities are observed, while still maintaining a simple control project.

^{[28]}This paper presents a new extremum seeking control (ESC) that is able to handle a class of unknown actuator hysteresis in the form of the Bouc-Wen Model with unknown parameters.

^{[29]}The maximum concentration of methane gas is achieved by extremum seeking control based on periodic perturbation signals.

^{[30]}In this paper, we propose an extension for the phasor extremum seeking control approach to solve constrained optimization problems.

^{[31]}Besides, variable of optimization methods and control strategies, especially the extremum seeking control, are referred.

^{[32]}Traditional methods for extremum seeking control (ESC) disregard possible prior knowledge of the system model.

^{[33]}This brief presents the results of a comprehensive field-test evaluation of extremum seeking control (ESC) for Region 2.

^{[34]}In this article, the extremum seeking control of a two-dimensional mobile robot with external disturbances is discussed by applying dynamic angular velocity turning method.

^{[35]}More specifically, an Extremum Seeking Control (ESC) scheme, which can search for the unknown or slowly varying optimum input with respect to a certain performance index, is adopted.

^{[36]}The technique incorporates a mechanism for adjusting the amplitude of the extremum seeking control dither signal.

^{[37]}In this paper, a novel sliding mode extremum seeking control (SMESC) scheme is proposed to improve the performance of the classic SMESC.

^{[38]}The proposed strategy is based on Extremum Seeking control and (a) does not require any model of the power consumption of the system, (b) can be executed on-line, and (c) guarantees adaptation to unknown disturbances.

^{[39]}We propose an extremum seeking control (ESC) framework as a model-free optimal control strategy for internal heat exchanger (IHXC) based VI-ASHP, minimizing the total power consumption in real time.

^{[40]}For verification of the implementation, the model-free, gradient-based and data-driven Extremum Seeking Control (ESC) optimization scheme is employed.

^{[41]}In this paper, an extremum seeking control (ESC) algorithm is implemented in real-time to compute the optimal cadence and torque trajectory (i.

^{[42]}Extremum seeking control aims at determining and keeping the output of a nonlinear map on its unknown extremum point.

^{[43]}It is then proposed a combination of the modelbased tracking strategy with the Extremum Seeking Control real-time optimization technique – which by itself is accurate but slow – and both accurate and fast maximum power point tracking capabilities are observed, while still maintaining a simple control project.

^{[44]}This paper proposes a model-free extremum seeking control (ESC) algorithm for a three-level (3-L) inverter to reduce torque ripples and improve the drive efficiency.

^{[45]}In this paper, we propose a detection threshold control method using extremum seeking control in realistic environments.

^{[46]}In particular, by using an Extremum Seeking Control (ESC) scheme, we determine the dryer operating temperature that ensures a final (desired) residual moisture content in textile materials.

^{[47]}In this paper, extremum seeking control and source seeking control is reviewed.

^{[48]}Compared to known extremum seeking control laws by means of Lie bracket approximations, the proposed approach has the advantage that the velocity remains bounded in the high-frequency limit.

^{[49]}The sliding mode extremum seeking control (SMESC) could track the maximum power point (MPP) of wind energy conversion system (WECS) without wind speed or wind turbine parameters.

^{[50]}

## extremum seeking algorithm

To assure that the states of the network are close to the average state, the problem of deviation minimization is solved in addition, using a novel extremum seeking algorithm.^{[1]}The main contribution of the paper is the formulation of the problem using the penalty method and the development of an extremum seeking algorithm based on a modified synchronous detection method for computing a stochastic gradient descent procedure.

^{[2]}In practical application, for sensors in some complex environment, due to the lack of the ability to perceive the location of the source or its own position, we use the nonmodel gradient estimation of extremum seeking algorithm.

^{[3]}We verified the accuracy and efficiency of the proposed algorithm by training single-layer neural networks with nonlinear activation function and compared its performance with Particle Swarm Optimizer (PSO), a well-studied extremum seeking algorithm, and the original BAS algorithm.

^{[4]}The PI gain of the voltage controller is automatically adjusted by the extremum seeking algorithm to dynamically respond to the changes of the network.

^{[5]}Subsequently, an extremum seeking algorithm without steady-state oscillation (ESA-SSO) is introduced to tune the design parameters of the ADRC-based ship course tracking control law so as to obtain the better performance of ship course tracking control.

^{[6]}The approach relies on the extremum seeking algorithm and on averaging theory to bring to zero the motion of the plasma along the unstable mode, hence achieving the stabilization of its vertical dynamic.

^{[7]}Additionally, in contrast to the most classical extremum seeking algorithms, this algorithm can converge to Nash equilibria without steady state oscillation and faster, because the amplitude of excitation sinusoidal signal in the conventional extremum seeking is adjusted to converge to zero, so the deleterious effects of steady state oscillation will be eliminated.

^{[8]}In order to control the ignition delay, this strategy adapts the amount of CNG injected into the prechamber with a linear controller or an extremum seeking algorithm depending on the air-to-fuel ratio of the main chamber.

^{[9]}In this work, discrete-time extremum seeking algorithms for unconstrained optimization problems are developed.

^{[10]}We address a Newton-based extremum seeking algorithm for maximizing higher derivatives of unknown maps in the presence of known time delays.

^{[11]}Also, two optimization loops based on the Global Extremum Seeking algorithm are used to find the global optimum of the optimization function by real-time control of both fueling rates.

^{[12]}Indeed, the classical model-free approaches (such as Gradient Ascent or Extremum Seeking algorithms) have intrinsic limitations.

^{[13]}Based on the improved extremum seeking algorithm and the 2-D formation deployment algorithm, a multi-robot hybrid seeking algorithm with formation deployment is proposed.

^{[14]}The Energy Management Strategy uses a Load Following control loop of requested load demand on DC bus and an optimization control loop to improve the fuel economy based on the Global Extremum Seeking algorithm applied to the air flow rate.

^{[15]}Because the dither’s frequency dictates the searching speed of the optimum in the perturbed extremum seeking algorithm, this parameter has been selected from multiple parameters involved in the optimization problem to improve the fuel economy based on sensitivity analysis.

^{[16]}Specifically, the simplified Newton-based CEE (SNE) is modified from the Newton extremum seeking algorithm.

^{[17]}This conference paper suggests an interesting application of a Robust Extremum Seeking Algorithm for dynamic plants with uncertainties and perturbations.

^{[18]}The proposed market is modeled as a non-cooperative, multiplayer game, and a Nash equilibrium solution is obtained using an extremum seeking algorithm.

^{[19]}In the proposed approach, the grid frequency is obtained by minimizing the error signal using a frequency-locked loop mechanism that consists of a resonant adaptive filter and a perturbation-based extremum seeking algorithm.

^{[20]}Concentrated on the problem of steady-state oscillation of the traditional extremum seeking algorithm (ESA) that it is not beneficial to the speed optimization of unmanned sailboat, a novel speed optimization scheme with feedforward of unmanned sailboat via extremum seeking without steady-state oscillation (ESWSO) is proposed.

^{[21]}The extremum seeking algorithm is developed for identifying the parameters of batteries on the basis of an electrical circuit model incorporating hysteresis effect.

^{[22]}This paper suggests a novel continuous-time robust extremum seeking algorithm for an unknown convex function constrained by a dynamical plant with uncertainties.

^{[23]}We present a generalization of the scalar Newton-based extremum seeking algorithm, which maximizes the map’s higher derivatives in the presence of dynamics described by Reaction-Advection-Diffusion (RAD) equations.

^{[24]}

## extremum seeking controller

This paper introduces a new class of non-smooth extremum seeking controllers (ESCs) with convergence bounds given by class- $\mathcal{K}\mathcal{L}$ functions that have a uniformly bounded settling time.^{[1]}We finally add an adaptation layer to our framework, where we tune the closure models in real-time, using data-driven extremum seeking controllers.

^{[2]}This letter proposes a design of extremum seeking controllers that guarantees precise convergence of the control system to the unknown optimizer of a measured unknown cost function.

^{[3]}Our approach consists of a two level scheme: in the lower level we use an extremum seeking controller to track a single particle by first seeking it then orbiting around it.

^{[4]}In particular, the extremum seeking controller is applied as a model-free real-time optimization strategy for such purpose.

^{[5]}In this work, we describe an implementation of an Extremum Seeking Controller that performs identification and tracking of thermoclines at its point of highest temperature gradient in a completely autonomous way.

^{[6]}We consider the problem of using the velocity actuated vehicle as search agent, and only use the noisy measurements of a scalar signal field to design a discrete-time stochastic extremum seeking controller to tune the vehicle towards the source of the signal field.

^{[7]}In this paper, a multivariate extremum seeking controller is used to manipulate, respectively, the luminance of multilighting equipment, in order to track the minimal LC efficiently.

^{[8]}

## extremum seeking approach

We therefore formulate a constrained optimization problem and utilize an extremum seeking approach to maximize the desired production rate while limiting the burden on the cellular organism.^{[1]}The upper level scheduler solves a chance-constrained optimal power flow (OPF) problem to plan the operation of the DERs based on forecasts, and the lower level distributed DER controllers leverage the extremum seeking approach to deliver the planned power at the feeder head.

^{[2]}Unlike existing adaptive extremum seeking approaches that presume the satisfaction of a persistence of excitation condition on the agents of the network, we propose a novel approach that leverages the presence of cooperation and information-rich data sets in the system.

^{[3]}

## extremum seeking problem

In this sense, the unified criterion is a tool for the formulation of the extremum seeking problem as well.^{[1]}The paper deals with the extremum seeking problem for a class of cost functions depending only on a part of state variables of a control system.

^{[2]}

## extremum seeking system

In this paper, we present novel multi-variable Newton-based extremum seeking systems, based on Lie bracket approximation methods.^{[1]}The stability property of the resulting constrained extremum seeking system is proved, and its effectiveness is shown in simulation.

^{[2]}

## extremum seeking scheme

Furthermore, an advanced extremum seeking scheme along with backtracking line search is exploited, which can automatically identify the best parameter value before each extremum search to improve the controllability based on this model for the target trajectory in slow-scan axis control.^{[1]}In this paper we apply a dynamic extremum seeking scheme to estimate the marginal GOR online using transient measurements, which is based on identifying a local linear dynamic model around the current operating point instead of a local linear static model.

^{[2]}