A Primer on Pontryagin's Principle in Optimal Control

2015-03-03 Mathematics

Author : I. Michael Ross
Release : 2015-03-03
Genre : Mathematics
Kind : eBook
Book Rating : 116/5 ( reviews)

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Book Synopsis A Primer on Pontryagin's Principle in Optimal Control by : I. Michael Ross

Download or read book A Primer on Pontryagin's Principle in Optimal Control written by I. Michael Ross. This book was released on 2015-03-03. Available in PDF, EPUB and Kindle. Book excerpt: EDITORIAL REVIEW: This book provides a guided tour in introducing optimal control theory from a practitioner's point of view. As in the first edition, Ross takes the contrarian view that it is not necessary to prove Pontryagin's Principle before using it. Using the same philosophy, the second edition expands the ideas over four chapters: In Chapter 1, basic principles related to problem formulation via a structured approach are introduced: What is a state variable? What is a control variable? What is state space? And so on. In Chapter 2, Pontryagin's Principle is introduced using intuitive ideas from everyday life: Like the process of "measuring" a sandwich and how it relates to costates. A vast number of illustrations are used to explain the concepts without going into the minutia of obscure mathematics. Mnemonics are introduced to help a beginner remember the collection of conditions that constitute Pontryagin's Principle. In Chapter 3, several examples are worked out in detail to illustrate a step-by-step process in applying Pontryagin's Principle. Included in this example is Kalman's linear-quadratic optimal control problem. In Chapter 4, a large number of problems from applied mathematics to management science are solved to illustrate how Pontryagin's Principle is used across the disciplines. Included in this chapter are test problems and solutions. The style of the book is easygoing and engaging. The classical calculus of variations is an unnecessary prerequisite for understanding optimal control theory. Ross uses original references to weave an entertaining historical account of various events. Students, particularly beginners, will embark on a minimum-time trajectory to applying Pontryagin's Principle.

Pontryagin's Maximum (minimum) Principle

1984 Mathematical optimization

Author : Bronwyn Nowitzke
Release : 1984
Genre : Mathematical optimization
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Pontryagin's Maximum (minimum) Principle by : Bronwyn Nowitzke

Download or read book Pontryagin's Maximum (minimum) Principle written by Bronwyn Nowitzke. This book was released on 1984. Available in PDF, EPUB and Kindle. Book excerpt:

Automotive Model Predictive Control

2010-03-11 Technology & Engineering

Author : Luigi Del Re
Release : 2010-03-11
Genre : Technology & Engineering
Kind : eBook
Book Rating : 712/5 ( reviews)

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Book Synopsis Automotive Model Predictive Control by : Luigi Del Re

Download or read book Automotive Model Predictive Control written by Luigi Del Re. This book was released on 2010-03-11. Available in PDF, EPUB and Kindle. Book excerpt: Automotive control has developed over the decades from an auxiliary te- nology to a key element without which the actual performances, emission, safety and consumption targets could not be met. Accordingly, automotive control has been increasing its authority and responsibility – at the price of complexity and di?cult tuning. The progressive evolution has been mainly ledby speci?capplicationsandshorttermtargets,withthe consequencethat automotive control is to a very large extent more heuristic than systematic. Product requirements are still increasing and new challenges are coming from potentially huge markets like India and China, and against this ba- ground there is wide consensus both in the industry and academia that the current state is not satisfactory. Model-based control could be an approach to improve performance while reducing development and tuning times and possibly costs. Model predictive control is a kind of model-based control design approach which has experienced a growing success since the middle of the 1980s for “slow” complex plants, in particular of the chemical and process industry. In the last decades, severaldevelopments haveallowedusing these methods also for “fast”systemsandthis hassupporteda growinginterestinitsusealsofor automotive applications, with several promising results reported. Still there is no consensus on whether model predictive control with its high requi- ments on model quality and on computational power is a sensible choice for automotive control.

Optimal Control of a Double Integrator

2016-07-26 Technology & Engineering

Author : Arturo Locatelli
Release : 2016-07-26
Genre : Technology & Engineering
Kind : eBook
Book Rating : 263/5 ( reviews)

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Book Synopsis Optimal Control of a Double Integrator by : Arturo Locatelli

Download or read book Optimal Control of a Double Integrator written by Arturo Locatelli. This book was released on 2016-07-26. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introductory yet rigorous treatment of Pontryagin’s Maximum Principle and its application to optimal control problems when simple and complex constraints act on state and control variables, the two classes of variable in such problems. The achievements resulting from first-order variational methods are illustrated with reference to a large number of problems that, almost universally, relate to a particular second-order, linear and time-invariant dynamical system, referred to as the double integrator. The book is ideal for students who have some knowledge of the basics of system and control theory and possess the calculus background typically taught in undergraduate curricula in engineering. Optimal control theory, of which the Maximum Principle must be considered a cornerstone, has been very popular ever since the late 1950s. However, the possibly excessive initial enthusiasm engendered by its perceived capability to solve any kind of problem gave way to its equally unjustified rejection when it came to be considered as a purely abstract concept with no real utility. In recent years it has been recognized that the truth lies somewhere between these two extremes, and optimal control has found its (appropriate yet limited) place within any curriculum in which system and control theory plays a significant role.

Feedback Systems

2021-02-02 Technology & Engineering

Author : Karl Johan Åström
Release : 2021-02-02
Genre : Technology & Engineering
Kind : eBook
Book Rating : 47X/5 ( reviews)

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Book Synopsis Feedback Systems by : Karl Johan Åström

Download or read book Feedback Systems written by Karl Johan Åström. This book was released on 2021-02-02. Available in PDF, EPUB and Kindle. Book excerpt: The essential introduction to the principles and applications of feedback systems—now fully revised and expanded This textbook covers the mathematics needed to model, analyze, and design feedback systems. Now more user-friendly than ever, this revised and expanded edition of Feedback Systems is a one-volume resource for students and researchers in mathematics and engineering. It has applications across a range of disciplines that utilize feedback in physical, biological, information, and economic systems. Karl Åström and Richard Murray use techniques from physics, computer science, and operations research to introduce control-oriented modeling. They begin with state space tools for analysis and design, including stability of solutions, Lyapunov functions, reachability, state feedback observability, and estimators. The matrix exponential plays a central role in the analysis of linear control systems, allowing a concise development of many of the key concepts for this class of models. Åström and Murray then develop and explain tools in the frequency domain, including transfer functions, Nyquist analysis, PID control, frequency domain design, and robustness. Features a new chapter on design principles and tools, illustrating the types of problems that can be solved using feedback Includes a new chapter on fundamental limits and new material on the Routh-Hurwitz criterion and root locus plots Provides exercises at the end of every chapter Comes with an electronic solutions manual An ideal textbook for undergraduate and graduate students Indispensable for researchers seeking a self-contained resource on control theory

Popular eBooks

A Primer on Pontryagin's Principle in Optimal Control

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Automotive Model Predictive Control

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