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Modern Tokamaks have evolved from the initial axisymmetric circular plasma shape to an elongated axisymmetric plasma shape that improves the energy confinement time and the triple product, which is a generally used figure of merit for the…

This paper presents a novel extremum seeking control (ESC) approach for the vibrational stabilization of a class of mechanical systems (e.g., systems characterized by equations of motion resulting from Newton second law or Euler-Lagrange…

Optimization and Control · Mathematics 2025-05-28 Ahmed A. Elgohary , Sameh A. Eisa

In [22] a form of extremum seeking for control (ESC) was developed for the stabilization of uncertain nonlinear systems. In ESC the extremum seeker itself controls the systems through feedback rather than fine tuning a controller. The ESC…

Dynamical Systems · Mathematics 2016-08-17 Alexander Scheinker , David Scheinker

In this paper, we introduce a model-free, real-time, dynamic optimization and control method for a class of rigid body dynamics. Our method is based on a recent extremum seeking control for vibrational stabilization (ESC-VS) approach that…

Optimization and Control · Mathematics 2026-04-21 Rohan Palanikumar , Ahmed A. Elgohary , Simone Martini , Sameh A. Eisa

In this paper the finite-time stabilization problem is solved for a linear time-varying system with unknown control direction by exploiting a modified version of the classical extremum seeking algorithm. We propose to use a suitable…

Optimization and Control · Mathematics 2021-03-12 Adriano Mele , Gianmaria De Tommasi , Alfredo Pironti

Extremum seeking control (ESC) are optimization algorithms in continuous time, with model-based ESCs using true derivative information of the cost function and model-free ESCs utilizing perturbation-based estimates instead. Stability…

Optimization and Control · Mathematics 2025-07-22 Patrick McNamee , Zahra Nili Ahmadabadi , Mirslav Krstić

The Tokamak device is the most promising candidate for producing sustainable electric power by nuclear fusion. It is a torus-shaped device that confines plasma by a strong magnetic field. The development, design and control of the design…

Plasma Physics · Physics 2022-11-17 M. Holst , V. Kungurtsev , S. Mukherjee

This paper introduces extremum seeking (ES) algorithms designed to achieve perfect tracking of arbitrary time-varying extremum. In contrast to classical ES approaches that employ constant frequencies and controller gains, our algorithms…

Optimization and Control · Mathematics 2024-02-23 Cemal Tugrul Yilmaz , Mamadou Diagne , Miroslav Krstic

The vertical motion of a tokamak plasma is analytically modelled during its non-linear phase by a free-moving current-carrying rod inductively coupled to a set of fixed conducting wires or a cylindrical conducting shell. The solutions…

Plasma Physics · Physics 2018-05-08 David Pfefferlé , Amitava Bhattacharjee

This paper presents an extremum seeking control (ESC) method for cooling tower fans to minimize overall power consumption of a chilled water plant system. Simulation studies across different climate locations demonstrate energy savings of…

Systems and Control · Electrical Eng. & Systems 2026-05-18 Min Gyung Yu , Alex Vlachokostas , Karthik Devaprasad , Matt Cornachione , Stephanie Johnson , Tim A. Yoder , Timothy I. Salsbury

We propose a novel extremum seeking control (ESC) method that operates in a lifted Koopman state space to minimize the filtered RMS energy in the dominant subspace. The lifted representation provides linear embeddings of nonlinear dynamics,…

Systems and Control · Electrical Eng. & Systems 2026-05-15 Timothy I. Salsbury , Min Gyung Yu , Sayak Mukherjee

This paper studies the extremum seeking control (ESC) problem for a class of constrained nonlinear systems. Specifically, we focus on a family of constraints allowing to reformulate the original nonlinear system in the so-called…

Optimization and Control · Mathematics 2021-03-24 Shuai Yuan , Filippo Fabiani , Simone Baldi

This paper addresses the multivariable gradient-based extremum seeking control (ESC) subject to saturation. Two distinct saturation scenarios are investigated here: saturation acting on the input of the function to be optimized, which is…

In this paper, we study the problem of extremum seeking control for mechanical systems in dissipation-free environments. This includes attitude control of satellites in space and displacement control of rigid bodies in ideal fluids. The…

Optimization and Control · Mathematics 2022-11-30 Raik Suttner , Miroslav Krstic

This paper addresses the design and analysis of an extremum-seeking (ES) controller for scalar static maps in the context of infinite-dimensional dynamics governed by complex-valued partial differential equations (PDEs) of Schrodinger type.…

Optimization and Control · Mathematics 2025-11-18 Paulo Henrique Foganholo Biazetto , Gustavo Artur de Andrade , Tiago Roux Oliveira , Miroslav Krstic

Negative triangularity (NT) tokamak configurations may be more susceptible to magneto-hydrodynamic instability, posing challenges for recent reactor designs centered around their favorable properties, such as improved confinement and…

Plasma Physics · Physics 2024-01-30 S. Guizzo , A. O. Nelson , C. Hansen , F. Logak , C. Paz-Soldan

In this paper, we study gradient-based classical extremum seeking (ES) for uncertain n-dimensional (nD) static quadratic maps in the presence of known large constant distinct input delays and large output constant delay with a small…

Systems and Control · Electrical Eng. & Systems 2023-10-17 Xuefei Yang , Emilia Fridman

Reliable position and shape control in tokamak plasmas requires accurate real-time regulation of several strongly coupled shape parameters. The control vectors that disentangle these couplings, referred to as \textit{virtual circuits}…

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. We propose novel adaptation laws for…

Systems and Control · Electrical Eng. & Systems 2021-01-06 Diganta Bhattacharjee , Kamesh Subbarao

This paper presents the design of an extremum seeking controller based on sliding modes and cyclic search for real-time optimization of non-linear multivariable dynamic systems. These systems have arbitrary relative degree, compensated by…

Optimization and Control · Mathematics 2024-07-31 Nerito Oliveira Aminde , Tiago Roux Oliveira , Liu Hsu
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