Optimization In Control Applications

This book contains refereed papers which were presented at the 34th Workshop of the International School of Mathematics "G. Stampacchia,” the International Workshop on Optimization and Control with Applications. The book contains 28 papers that are grouped according to four broad topics: duality and optimality conditions, optimization algorithms, optimal control, and variational inequality and equilibrium problems. The specific topics covered in the individual chapters include optimal control, unconstrained and constrained optimization, complementarity and variational inequalities, equilibrium problems, semi-definite programs, semi-infinite programs, matrix functions and equations, nonsmooth optimization, generalized convexity and generalized monotinicity, and their applications. Audience This book is suitable for researchers, practitioners, and postgraduate students in optimization, operations research, and optimal control.

This volume gives the latest advances in optimization and optimal control which are the main part of applied mathematics. It covers various topics of optimization, optimal control and operations research.

Mathematical optimization is the selection of the best element in a set with respect to a given criterion. Optimization has become one of the most-used tools in modern control theory for computing the control law, adjusting the controller parameters (tuning), model fitting, and finding suitable conditions in order to fulfill a given closed-loop property, among others. In the simplest case, optimization consists of maximizing or minimizing a function by systematically choosing input values from a valid input set and computing the function value. Nevertheless, real-world control systems need to comply with several conditions and constraints that have to be taken into account in the problem formulation-these represent challenges in the application of the optimization algorithms. The aim of this Special Issue is to offer the state-of-the-art of the most advanced optimization techniques (online and offline) and their applications in control engineering.

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.

Stochastic optimization problems arise in decision-making problems under uncertainty, and find various applications in economics and finance. On the other hand, problems in finance have recently led to new developments in the theory of stochastic control. This volume provides a systematic treatment of stochastic optimization problems applied to finance by presenting the different existing methods: dynamic programming, viscosity solutions, backward stochastic differential equations, and martingale duality methods. The theory is discussed in the context of recent developments in this field, with complete and detailed proofs, and is illustrated by means of concrete examples from the world of finance: portfolio allocation, option hedging, real options, optimal investment, etc. This book is directed towards graduate students and researchers in mathematical finance, and will also benefit applied mathematicians interested in financial applications and practitioners wishing to know more about the use of stochastic optimization methods in finance.

This book offers a comprehensive presentation of optimization and polyoptimization methods. The examples included are taken from various domains: mechanics, electrical engineering, economy, informatics, and automatic control, making the book especially attractive. With the motto “from general abstraction to practical examples,” it presents the theory and applications of optimization step by step, from the function of one variable and functions of many variables with constraints, to infinite dimensional problems (calculus of variations), a continuation of which are optimization methods of dynamical systems, that is, dynamic programming and the maximum principle, and finishing with polyoptimization methods. It includes numerous practical examples, e.g., optimization of hierarchical systems, optimization of time-delay systems, rocket stabilization modeled by balancing a stick on a finger, a simplified version of the journey to the moon, optimization of hybrid systems and of the electrical long transmission line, analytical determination of extremal errors in dynamical systems of the rth order, multicriteria optimization with safety margins (the skeleton method), and ending with a dynamic model of bicycle. The book is aimed at readers who wish to study modern optimization methods, from problem formulation and proofs to practical applications illustrated by inspiring concrete examples.

Applications of Nonlinear Programming to Optimization and Control.

Applications of Nonlinear Programming to Optimization and Control is a collection of papers presented at the Fourth International Federation of Automatic Control Workshop by the same title, held in San Francisco, California on June 20-21, 1983. This workshop aims to exchange information on the applications of optimization and nonlinear programming techniques to real-life control problems, to investigate ideas that arise from these exchanges, and to look for advances in nonlinear programming that are useful in solving control problems. This book is divided into 16 chapters. It covers a wide range of related topics, starting with computer-aided-design of practical control systems, continuing through advanced work on quasi-Newton methods and gradient restoration algorithms. Other chapters provide specific examples, which apply these methods to representative problems. The remaining chapters present examples, including trajectory optimization, optimal design of a structure for a satellite, identification of hovercraft characteristics, determination of optimal electricity generation, and optimal automatic transmission for road vehicles. This book is of value to computer scientists and mathematicians.