Descript 
1 online resource (x, 314 pages) : illustrations, digital ; 24 cm 

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computer c rdamedia 

online resource cr rdacarrier 

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Note 
Part I. Introduction  Introductory Remarks  Historical Perspective  Outline of Contents  Part II. Problem Statement  Deterministic Systems  Stochastic Systems  General Problem  Part III. The Direct Method Approach: Generalities  General Approach  Gradient and Integration Methods  Representation Methods  Part IV. Gradient and Integration Methods in Control Problems  Computation of Gradients for ODE Problems  Computation of Gradients for PDE Problems  Integration Methods  Part V. Representation Methods  RitzGalerkin Expansion  KarhunenLoeve Expansion  Levy Processes  Bibliography  Index 

The primary focus of this book is on explicating the direct method approach. Historically, direct methods have not been fully exploited in control problems. The key is constructing convergent minimizing families. Integration methods (for example the gradient method) and representation methods (such as the RitzGalerkin and Finite Element methods) are examined in this text in an abstract (with concrete examples) functional analytic way. The aim is to consider direct methods from a unified general point of view and to provide a stimulus for future research. Explicitly, implicitly and by example, potential areas of research interest are indicated. The book is a suitable reference for graduate students, researchers, applied mathematicians, and control engineers. Some of the material is of independent mathematical interest. The work may be used as a text for a graduate course or seminar on direct methods in control. A degree of mathematical sophistication and some knowledge of control theory is required 
Host Item 
Springer eBooks

Subject 
Control theory


Systems Theory, Control


Control, Robotics, Mechatronics


Calculus of Variations and Optimal Control; Optimization


Approximations and Expansions


Probability Theory and Stochastic Processes


Computational Mathematics and Numerical Analysis

Alt Author 
SpringerLink (Online service)

