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A Method to Accomplish the Optimal Control of Continuous Dynamical Systems with Impulse Controls Via Discrete Optimal Control and Utilizing Optimal Control Theory to Explore the Emergence of Synchrony

2010
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Release : 2010
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Book Synopsis A Method to Accomplish the Optimal Control of Continuous Dynamical Systems with Impulse Controls Via Discrete Optimal Control and Utilizing Optimal Control Theory to Explore the Emergence of Synchrony by : Rachel Natalie Graves

Download or read book A Method to Accomplish the Optimal Control of Continuous Dynamical Systems with Impulse Controls Via Discrete Optimal Control and Utilizing Optimal Control Theory to Explore the Emergence of Synchrony written by Rachel Natalie Graves. This book was released on 2010. Available in PDF, EPUB and Kindle. Book excerpt: This research concerns the development of new optimal control methodologies and applications. In the first chapter we consider systems of ordinary differential equations subject to a restricted number of impulse controls. Examples of such systems include tumor growth, in which case the impulsive control is the administration of medication, and ecological invasion, in which case the impulse control is the release of predator species. Impulse control problems are typically solved via related partial differential equations known as quasi-variational inequalities. We show that these types of impulse control problems can be formulated as a discrete optimal control problems. Furthermore, this formulation is advantageous because it simplifies numerical calculations. In the second chapter we consider how optimal control can be used to investigate the emergence of synchrony in networks of coupled oscillators. In particular, we apply optimal control to a network of Kuramoto oscillators with time-varying coupling in order to relate network synchrony to network connectivity. To the best of our knowledge this is the first such use of optimal control theory.

Impulsive Control in Continuous and Discrete-Continuous Systems

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 958/5 ( reviews)

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Book Synopsis Impulsive Control in Continuous and Discrete-Continuous Systems by : Boris M. Miller

Download or read book Impulsive Control in Continuous and Discrete-Continuous Systems written by Boris M. Miller. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: Impulsive Control in Continuous and Discrete-Continuous Systems is an up-to-date introduction to the theory of impulsive control in nonlinear systems. This is a new branch of the Optimal Control Theory, which is tightly connected to the Theory of Hybrid Systems. The text introduces the reader to the interesting area of optimal control problems with discontinuous solutions, discussing the application of a new and effective method of discontinuous time-transformation. With a large number of examples, illustrations, and applied problems arising in the area of observation control, this book is excellent as a textbook or reference for a senior or graduate-level course on the subject, as well as a reference for researchers in related fields.

Optimization of Dynamical Systems with Impulse Controls and Shocks

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Book Rating : 248/5 ( reviews)

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Book Synopsis Optimization of Dynamical Systems with Impulse Controls and Shocks by : Boris Miller

Download or read book Optimization of Dynamical Systems with Impulse Controls and Shocks written by Boris Miller. This book was released on . Available in PDF, EPUB and Kindle. Book excerpt:

Optimal Impulsive Control

2018-12-17 Technology & Engineering
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Release : 2018-12-17
Genre : Technology & Engineering
Kind : eBook
Book Rating : 609/5 ( reviews)

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Book Synopsis Optimal Impulsive Control by : Aram Arutyunov

Download or read book Optimal Impulsive Control written by Aram Arutyunov. This book was released on 2018-12-17. Available in PDF, EPUB and Kindle. Book excerpt: Optimal Impulsive Control explores the class of impulsive dynamic optimization problems—problems that stem from the fact that many conventional optimal control problems do not have a solution in the classical setting—which is highly relevant with regard to engineering applications. The absence of a classical solution naturally invokes the so-called extension, or relaxation, of a problem, and leads to the notion of generalized solution which encompasses the notions of generalized control and trajectory; in this book several extensions of optimal control problems are considered within the framework of optimal impulsive control theory. In this framework, the feasible arcs are permitted to have jumps, while the conventional absolutely continuous trajectories may fail to exist. The authors draw together various types of their own results, centered on the necessary conditions of optimality in the form of Pontryagin’s maximum principle and the existence theorems, which shape a substantial body of optimal impulsive control theory. At the same time, they present optimal impulsive control theory in a unified framework, introducing the different paradigmatic problems in increasing order of complexity. The rationale underlying the book involves addressing extensions increasing in complexity from the simplest case provided by linear control systems and ending with the most general case of a totally nonlinear differential control system with state constraints. The mathematical models presented in Optimal Impulsive Control being encountered in various engineering applications, this book will be of interest to both academic researchers and practising engineers.

Optimization of Dynamical Systems with Impulse Controls and Shocks

2024-09-01 Science
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Release : 2024-09-01
Genre : Science
Kind : eBook
Book Rating : 237/5 ( reviews)

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Book Synopsis Optimization of Dynamical Systems with Impulse Controls and Shocks by : Boris Miller

Download or read book Optimization of Dynamical Systems with Impulse Controls and Shocks written by Boris Miller. This book was released on 2024-09-01. Available in PDF, EPUB and Kindle. Book excerpt: This text explores the state-of-the-art in the rapidly developing theory of impulse control and introduces the theory of singular space-time transformations, a new method for studying shock mechanical systems. Two approaches in the theory of impulse control are presented: The first, more traditional approach defines the impulsive action as a discontinuity of phase coordinates depending on the current time, the state preceding the action, and its magnitude. The second requires the use of modern methods for describing dynamical systems - differential equations with measures. The impulse is treated as an idealization of a very short action of high magnitude, which produces an almost abrupt change of phase coordinates. The relation between these two approaches is also discussed, and several applications, both traditional and emerging, are considered. This text is intended for graduate students and researchers in control engineering and optimal control theory for dynamical systems. Readers are assumed to be familiar with the theory of ODEs, optimal control, and functional analysis, though an appendix is included that covers many of the necessary mathematical concepts.

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