Extremum-Seeking Control and Applications

A Numerical Optimization-Based Approach

verfasst von: Chunlei Zhang, Raúl Ordóñez

Verlag: Springer London

Buchreihe : Advances in Industrial Control

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

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.

Inhaltsverzeichnis

Frontmatter

Theory

Frontmatter

Chapter 1. Introduction

Abstract

The motivation of extremum seeking control is first presented, followed by a brief history of extremum seeking control and a literature overview of the last decades. The overview is separated in two parts: theory and applications. This distinction helps highlight the many problems of practical significance where extremum seeking control is a relevant design methodology; and at the same time, it provides the reader with a deeper understanding of the several available “flavors” of extremum seeking.

Chunlei Zhang, Raúl Ordóñez

Chapter 2. Numerical Optimization

Abstract

Numerical optimization is introduced as the mathematical foundation for this book, focusing on two basic unconstrained optimization algorithms: line search and trust-region methods. Line search optimization methods are relatively simple and commonly used gradient descent based methods. Their strength lies in their simplicity and ease of implementation, but their convergence properties degrade as the nonlinearity and complexity of the function to be optimized increases. Trust-region, or “restricted step” methods are presented as an often more practical alternative to line search that involved the construction of an approximation, or “model,” of the function to be minimized, together with a dynamic estimate of the region where this model is sufficiently valid. There are a large number of optimization methods, and the interested reader is referred to the bibliographical citations presented in this chapter. In this book we restrict our attention mainly to line search and trust-region methods, since we will use them in the context of their application to extremum seeking control and stability proofs thereof.

Chunlei Zhang, Raúl Ordóñez

Chapter 3. Design of Extremum Seeking Control

Abstract

A general nonlinear system is used to present the extremum seeking control problem. The analog optimization based extremum seeking control is first presented, where gradient based, sliding mode based and perturbation based schemes are discussed. We extend the applicability of perturbation based extremum seeking control to slightly and moderately unstable systems via the use of a phase lead compensator. Finally, numerical optimization based extremum seeking control is briefly introduced, to be later expanded upon in Chaps. 4 and 5. This chapter gives the reader an overview of the different “flavors” of extremum seeking control available in the literature.

Chunlei Zhang, Raúl Ordóñez

Chapter 4. Finite Time State Regulator Design

Abstract

In this chapter, the numerical optimization based extremum seeking control (NOESC) idea introduced in Chap. 3 is expanded upon and studied at length. Specifically, we consider the problem of incorporating two numerical optimization approaches, line search and trust region methods, into the set up of an extremum seeking control scheme. The convergence of the extremum seeking control scheme can be guaranteed if the optimization algorithm is globally convergent and the closed-loop system is outfitted with appropriate state regulation. We also analyze the robustness of line search methods and trust region methods, which allows us to relax the design requirement for the state regulator. In this manner, the robustness analysis provides further flexibility in designing extremum seeking controllers. Numerical examples are given to illustrate the analysis results.

Chunlei Zhang, Raúl Ordóñez

Chapter 5. Asymptotic State Regulator Design

Abstract

Extremum seeking is realized via a state regulator that drives the state along a convergent set point sequence generated by a numerical optimization algorithm. In this chapter, we propose an asymptotic state regulator design for state feedback linearizable systems, where we trade off finite time state regulation to obtain flexibility in designing a robust extremum seeking controller. Existing techniques such as nonlinear damping and nonlinear adaptive control are then used to deal with input disturbance and unmodeled plant dynamics. Simulation examples illustrate the effectiveness of the basic and robust extremum seeking schemes, and design guidelines are provided for engineering applications. We also show that the NOESC scheme allows a large design flexibility for general nonlinear systems and performance functions, where the key is having the ability to design a robust regulator.

Chunlei Zhang, Raúl Ordóñez

Applications

Frontmatter

Chapter 6. Antilock Braking Systems

Abstract

Extremum seeking control is used in the Antilock Braking Systems (ABS) problem. First, a single wheel model is presented, and then different designs of extremum seeking control are compared. These include perturbation based (PESC), sliding mode based (SMESC) and numerical optimization based (NOESC) approaches.

Chunlei Zhang, Raúl Ordóñez

Chapter 7. Impedance Matching in Semiconductor Plasma Processing Chamber

Abstract

In this chapter we study the problem of impedance matching, within the context of its industrial application. Impedance matching is performed in order to maximize power transfer in a circuit and minimize reflection from the load. The process can be computationally complex, especially when the circuit is large and contains interconnected subsystems. In this chapter we examine the application of extremum seeking control to solve the impedance matching problem in a semiconductor plasma processing chamber system. In particular, we present two tuning algorithms applied to a radio frequency (RF) matching network design for a capacitive coupled plasma (CCP) chamber: one has the objective of improving the productivity by providing a tuning algorithm to give the user an optimized preset for each particular recipe; another one is a real time auto-tuning algorithm. We show experimental results for these two algorithms obtained by one of the authors (Zhang) at Applied Materials.

Chunlei Zhang, Raúl Ordóñez

Chapter 8. Swarm Tracking

Abstract

In this chapter we study the swarm tracking problem, that is, the problem of finding a coordinated control scheme for a group of mobile agents that make them achieve and maintain a certain desired behavior; in particular, we concentrate on the problem of maintaining a given geometrical formation. At the same time, the agents need to seek a mobile source of a scalar signal or track a moving target. By using artificial potential functions to encode the agent-target, agent-agent, and/or agent-obstacle interaction, we are able to use extremum seeking techniques for controller design of each agent, which could be decentralized and in some instances does not require knowledge of target position and agent positions. The effectiveness of three different extremum seeking control designs is analytically established and compared via corresponding simulation results. Finally, an application of the swarming theory is presented, where localization of radar leakage points via a mobile sensor network is studied, and simulation results are provided.

Chunlei Zhang, Raúl Ordóñez

Backmatter

Titel: Extremum-Seeking Control and Applications
verfasst von: Chunlei Zhang
Raúl Ordóñez
Verlag: Springer London
Electronic ISBN: 978-1-4471-2224-1
Print ISBN: 978-1-4471-2223-4
DOI: https://doi.org/10.1007/978-1-4471-2224-1