Real Time Optimization By Extremum Seeking Control

An up-close look at the theory behind and application of extremum seeking Originally developed as a method of adaptive control for hard-to-model systems, extremum seeking solves some of the same problems as today's neural network techniques, but in a more rigorous and practical way. Following the resurgence in popularity of extremum-seeking control in aerospace and automotive engineering, Real-Time Optimization by Extremum-Seeking Control presents the theoretical foundations and selected applications of this method of real-time optimization. Written by authorities in the field and pioneers in adaptive nonlinear control systems, this book presents both significant theoretic value and important practical potential. Filled with in-depth insight and expert advice, Real-Time Optimization by Extremum-Seeking Control: * Develops optimization theory from the points of dynamic feedback and adaptation * Builds a solid bridge between the classical optimization theory and modern feedback and adaptation techniques * Provides a collection of useful tools for problems in this complex area * Presents numerous applications of this powerful methodology * Demonstrates the immense potential of this methodology for future theory development and applications Real-Time Optimization by Extremum-Seeking Control is an important resource for both students and professionals in all areas of engineering-electrical, mechanical, aerospace, chemical, biomedical-and is also a valuable reference for practicing control engineers.

Extremum-seeking control tracks a varying maximum or minimum in a performance function such as output or cost. It attempts to determine the optimal performance of a control system as it operates, thereby reducing downtime and the need for system analysis. Extremum-seeking Control and Applications is divided into two parts. In the first, the authors review existing analog-optimization-based extremum-seeking control including gradient-, perturbation- and sliding-mode-based control designs. They then propose a novel numerical-optimization-based extremum-seeking control based on optimization algorithms and state regulation. This control design is developed for simple linear time-invariant systems and then extended for a class of feedback linearizable nonlinear systems. The two main optimization algorithms – line search and trust region methods – are analyzed for robustness. Finite-time and asymptotic state regulators are put forward for linear and nonlinear systems respectively. Further design flexibility is achieved using the robustness results of the optimization algorithms and the asymptotic state regulator by which existing nonlinear adaptive control techniques can be introduced for robust design. The approach used is easier to implement and tends to be more robust than those that use perturbation-based extremum-seeking control. The second part of the book deals with a variety of applications of extremum-seeking control: a comparative study of extremum-seeking control schemes in antilock braking system design; source seeking, formation control, collision and obstacle avoidance for groups of autonomous agents; mobile radar networks; and impedance matching. MATLAB®/Simulink® code which can be downloaded from www.springer.com/ISBN helps readers to reproduce the results presented in the text and gives them a head start for implementing the algorithms in their own applications. Extremum-seeking Control and Applications will interest academics and graduate students working in control, and industrial practitioners from a variety of backgrounds: systems, automotive, aerospace, communications, semiconductor and chemical engineering.

This book is a printed edition of the Special Issue "Real-Time Optimization" that was published in Processes

Extremum Seeking through Delays and PDEs, the first book on the topic, expands the scope of applicability of the extremum seeking method, from static and finite-dimensional systems to infinite-dimensional systems. Readers will find numerous algorithms for model-free real-time optimization are developed and their convergence guaranteed, extensions from single-player optimization to noncooperative games, under delays and PDEs, are provided, the delays and PDEs are compensated in the control designs using the PDE backstepping approach, and stability is ensured using infinite-dimensional versions of averaging theory, and accessible and powerful tools for analysis. This book is intended for control engineers in all disciplines (electrical, mechanical, aerospace, chemical), mathematicians, physicists, biologists, and economists. It is appropriate for graduate students, researchers, and industrial users.

With this brief, the authors present algorithms for model-free stabilization of unstable dynamic systems. An extremum-seeking algorithm assigns the role of a cost function to the dynamic system’s control Lyapunov function (clf) aiming at its minimization. The minimization of the clf drives the clf to zero and achieves asymptotic stabilization. This approach does not rely on, or require knowledge of, the system model. Instead, it employs periodic perturbation signals, along with the clf. The same effect is achieved as by using clf-based feedback laws that profit from modeling knowledge, but in a time-average sense. Rather than use integrals of the systems vector field, we employ Lie-bracket-based (i.e., derivative-based) averaging. The brief contains numerous examples and applications, including examples with unknown control directions and experiments with charged particle accelerators. It is intended for theoretical control engineers and mathematicians, and practitioners working in various industrial areas and in robotics.

This book offers a comprehensive review of renewable energy sources and optimization strategies in hybrid power systems (HPSs). It analyses the main issues and challenges in the renewable (REW) HPS field, particularly those using fuel cell (FC) systems as their main source of energy. It then offers innovative solutions to these issues, comparing them to solutions currently found in the literature. The book discusses optimization algorithms and energy management strategies. The focus is chiefly on FC net power maximization and fuel economy strategies based on global optimization. The last two chapters discuss energy harvesting from photovoltaic systems and how to mitigate energy variability in REW FC HPS. The main content is supplemented by numerous examples and simulations. Academics, students and practitioners in relevant industrial branches interested in REW HPS finds it of considerable interest, as a reference book or for building their own HPSs based on the examples provided.

Powerful optimization algorithms are key ingredients in science and engineering applications. In this thesis, we develop a novel class of discrete-time, derivative-free optimization algorithms relying on gradient approximations based on non-commutative maps–inspired by Lie bracket approximation ideas in control systems. Those maps are defined by function evaluations and applied in such a way that gradient descent steps are approximated, and semi-global convergence guarantees can be given. We supplement our theoretical findings with numerical results. Therein, we provide several algorithm parameter studies and tuning rules, as well as the results of applying our algorithm to challenging benchmarking problems.