WIN $150 GIFT VOUCHERS: ALADDIN'S GOLD

Close Notification

Your cart does not contain any items

Introduction to Geometric Control by Yuri Sachkov at Abbey's Bookshop,
Introduction to Geometric Control
— —
Yuri Sachkov

Introduction to Geometric Control

Yuri Sachkov

$152.95   $122.40

Paperback

Not in-store but you can order this
How long will it take?
English
Springer International Publishing AG
12 August 2022
Cybernetics & systems theory; Differential & Riemannian geometry; Optimisation; Automatic control engineering
Series: Springer Optimization and Its Applications
This text is an enhanced, English version of the Russian edition, published in early 2021 and is appropriate for an introductory course in geometric control theory. The concise presentation provides an accessible treatment of the subject for advanced undergraduate and graduate students in theoretical and applied mathematics, as well as to experts in classic control theory for whom geometric methods may be introduced. Theory is accompanied by characteristic examples such as stopping a train, motion of mobile robot, Euler elasticae, Dido's problem, and rolling of the sphere on the plane. Quick foundations to some recent topics of interest like control on Lie groups and sub-Riemannian geometry are included. Prerequisites include only a basic knowledge of calculus, linear algebra, and ODEs; preliminary knowledge of control theory is not assumed. The applications problems-oriented approach discusses core subjects and encourages the reader to solve related challenges independently. Highly-motivated readers can acquire working knowledge of geometric control techniques and progress to studying control problems and more comprehensive books on their own. Selected sections provide exercises to assist in deeper understanding of the material.

Controllability and optimal control problems are considered for nonlinear nonholonomic systems on smooth manifolds, in particular, on Lie groups. For the controllability problem, the following questions are considered: controllability of linear systems, local controllability of nonlinear systems, Nagano–Sussmann Orbit theorem, Rashevskii–Chow theorem, Krener's theorem. For the optimal control problem, Filippov's theorem is stated, invariant formulation of Pontryagin maximum principle on manifolds is given, second-order optimality conditions are discussed, and the sub-Riemannian problem is studied in detail. Pontryagin maximum principle is proved for sub-Riemannian problems, solution to the sub-Riemannian problems on the Heisenberggroup, the group of motions of the plane, and the Engel group is described.
By:  
Imprint:   Springer International Publishing AG
Country of Publication:   Switzerland
Edition:   1st ed. 2022
Volume:   192
Dimensions:   Height: 235mm,  Width: 155mm, 
Weight:   285g
ISBN:   9783031020728
ISBN 10:   3031020723
Series:   Springer Optimization and Its Applications
Pages:   162
Publication Date:  
Audience:   Professional and scholarly ,  Undergraduate
Format:   Paperback
Publisher's Status:   Active
1. Introduction.- 2. Controllability problem.- 3. Optimal control problem.- 4. Solution to optimal control problems.- 5. Conclusion.- A. Elliptic integrals, functions and equation of pendulum.- Bibliography and further reading.- Index.

Yuri Sachkov is the Chief of Control Processes Research Center at Program Systems Institute, Russian Academy of Sciences, in Pereslavl-Zalessky, Russia. His research interests include optimal control theory, sub-Riemannian, sub-Finsler and sub-Lorentzian geometry, and their applications to mechanics, robotics, and vision. Prof. Sachkov is a world renown expert in geometric control theory and has authored more than 80 research papers in leading international and Russian journals. Sachkov has also authored two well-known books: (with A.A. Agrachev) Control Theory from the Geometric Viewpoint, Springer (c) 2004, and Controllability and symmetries of invariant systems on Lie groups and homogeneous spaces (in Russian), Moscow, Fizmatlit, 2007. He is a managing editor of Journal of Dynamical and Control Systems, Springer.

See Also

Introduction to Geometric Control

An Introduction to Differential...

Jacques Lafontaine

Paperback

$130.95  $105.07

Not in-store but you can order this

ADD +
Introduction to Geometric Control

Meromorphic Dynamics

Volume 2: Elliptic Functions with...

Janina Kotus (Warsaw University...

Hardback

$251.95 

Not in-store but you can order this

ADD +
Introduction to Geometric Control

The Physical and Mathematical Foundations...

A Critical Analysis

Antonio Romano

Paperback

$130.95  $105.07

Not in-store but you can order this

ADD +
Introduction to Geometric Control

Frontiers of Fractal Analysis

Recent Advances and Challenges

Santo Banerjee (Politecnico di Torino,...

Paperback

$120 

Not in-store but you can order this

ADD +
Introduction to Geometric Control

Introduction to Differential Geometry...

Dipankar De (University of Calcutta,...

Hardback

$373.95 

Not in-store but you can order this

ADD +
Introduction to Geometric Control

From Calculus to Cohomology

De Rham Cohomology and Characteristic...

Ib H. Madsen (Aarhus Universitet,...

Paperback

$87.95 

Not in-store but you can order this

ADD +