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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
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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 and published by . This book was released on 2010 with total page 96 pages. 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.
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 and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 454 pages. 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.
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 and published by Birkhäuser. This book was released on 2024-09-01 with total page 0 pages. 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.
Book Synopsis Optimal Impulsive Control by : Aram Arutyunov
Download or read book Optimal Impulsive Control written by Aram Arutyunov and published by Springer. This book was released on 2018-12-17 with total page 174 pages. 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.
Book Synopsis Dynamic Programming for Impulse Feedback and Fast Controls by : Alexander B. Kurzhanski
Download or read book Dynamic Programming for Impulse Feedback and Fast Controls written by Alexander B. Kurzhanski and published by Springer. This book was released on 2019-03-29 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamic Programming for Impulse Feedback and Fast Controls offers a description of feedback control in the class of impulsive inputs. This book deals with the problem of closed-loop impulse control based on generalization of dynamic programming techniques in the form of variational inequalities of the Hamilton–Jacobi–Bellman type. It provides exercises and examples in relation to software, such as techniques for regularization of ill-posed problems. It also gives an introduction to applications such as hybrid dynamics, control in arbitrary small time, and discontinuous trajectories. This book walks the readers through: the design and description of feedback solutions for impulse controls; the explanation of impulses of higher order that are derivatives of delta functions; the description of their physically realizable approximations - the fast controls and their approximations; the treatment of uncertainty in impulse control and the applications of impulse feedback. Of interest to both academics and graduate students in the field of control theory and applications, the book also protects users from common errors , such as inappropriate solution attempts, by indicating Hamiltonian techniques for hybrid systems with resets.
Book Synopsis Continuous Time Dynamical Systems by : B. M. Mohan
Download or read book Continuous Time Dynamical Systems written by B. M. Mohan and published by CRC Press. This book was released on 2017-11-22 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book presents the developments in problems of state estimation and optimal control of continuous-time dynamical systems using orthogonal functions since 1975. It deals with both full and reduced-order state estimation and problems of linear time-invariant systems. It also addresses optimal control problems of varieties of continuous-time systems such as linear and nonlinear systems, time-invariant and time-varying systems, as well as delay-free and time-delay systems. Content focuses on development of recursive algorithms for studying state estimation and optimal control problems"--
Book Synopsis Optimal Control for Control Actions with Mixed Impulse Functions and Bounded Piecewise Continuous Functions by : Jiecai Luo
Download or read book Optimal Control for Control Actions with Mixed Impulse Functions and Bounded Piecewise Continuous Functions written by Jiecai Luo and published by . This book was released on 2000 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Measure-driven Impulsive Systems by :
Download or read book Measure-driven Impulsive Systems written by and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation studies various standard facets of nonlinear control problems in the impulsive setting, using a framework of measure-driven systems. Containing a Borel measure in their dynamics, these systems model significant time scale discrepancies; the measure may weight actions at instants, producing trajectories that mix discrete and continuous dynamics on the "fast" and "slow" time scales, respectively. A central feature of our work is the careful use of a time reparametrization to transform these systems into standard, non-impulsive ones, so that the wealth of recent results in nonlinear control may be applied. Closed-loop stabilization of impulsive control systems containing a measure in the dynamics is addressed. It is proved that, as for regular affine systems, an almost everywhere continuous stabilizing impulsive feedback control law exists for such impulsive systems. An example illustrating the loop closing features is also presented. Necessary conditions for optimal control have recently been developed in the non-convex case by Clarke and Vinter, among others. We extend these results to generalized differential inclusions where a signed, vector-valued measure appears. In particular, we offer a set of stratified necessary conditions in optimal control of measure-driven systems, as well as a set of standard (global) conditions under weak regularity hypotheses on the differential inclusion maps. An auxiliary result essential to our proof extends existing free end-time necessary conditions results to Clarke's stratified framework. We work in the context of pseudo-Lipschitz multifunctions, which provide localized Lipschitz-like properties in the absence of convexity. We take a well-evolved solution concept framework in new directions, introducing a workable system of state-dependent measures and measure-based constraints, such as a forced impulse schedule, a restriction to purely discrete impulse dynamics or a state-dependent impulse restriction, and prov.
Book Synopsis Some New Methods for Optimal Control of Constrained Dynamical Systems by : John Edward Hurtado
Download or read book Some New Methods for Optimal Control of Constrained Dynamical Systems written by John Edward Hurtado and published by . This book was released on 1995 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Optimal Adaptive Control and Differential Games by Reinforcement Learning Principles by : Draguna L. Vrabie
Download or read book Optimal Adaptive Control and Differential Games by Reinforcement Learning Principles written by Draguna L. Vrabie and published by IET. This book was released on 2013 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book reviews developments in the following fields: optimal adaptive control; online differential games; reinforcement learning principles; and dynamic feedback control systems.
Book Synopsis Time Optimal Control of Discrete Systems Using State Variable Feedback by : James Michael Miletich
Download or read book Time Optimal Control of Discrete Systems Using State Variable Feedback written by James Michael Miletich and published by . This book was released on 1969 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Optimal Control of Discrete Systems by : Vladimir Grigorʹevich Bolti︠a︡nskiĭ
Download or read book Optimal Control of Discrete Systems written by Vladimir Grigorʹevich Bolti︠a︡nskiĭ and published by . This book was released on 1978 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Discrete Event Dynamic Systems by : Joseph Benedict Logsdon
Download or read book Discrete Event Dynamic Systems written by Joseph Benedict Logsdon and published by . This book was released on 1995 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Discrete-Time Inverse Optimal Control for Nonlinear Systems by : Edgar N. Sanchez
Download or read book Discrete-Time Inverse Optimal Control for Nonlinear Systems written by Edgar N. Sanchez and published by CRC Press. This book was released on 2017-03-29 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book presents a novel inverse optimal control approach for stabilization and trajectory tracking of discrete-time nonlinear systems, avoiding the need to solve the associated Hamilton-Jacobi-Bellman equation, and minimizing a cost functional, resulting in efficient controllers. Additionally, the book proposes the use of recurrent neural networks as a tool to model discrete-time nonlinear systems; such models combined with the inverse optimal control constitute a powerful tool to deal with uncertainties such as unmodeled dynamics and disturbances. Different simulations illustrate the effectiveness of the synthesized controllers for stabilization and trajectory tracking of discrete-time nonlinear systems"--
Book Synopsis Formal Methods for Discrete-Time Dynamical Systems by : Calin Belta
Download or read book Formal Methods for Discrete-Time Dynamical Systems written by Calin Belta and published by Springer. This book was released on 2017-03-08 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book bridges fundamental gaps between control theory and formal methods. Although it focuses on discrete-time linear and piecewise affine systems, it also provides general frameworks for abstraction, analysis, and control of more general models. The book is self-contained, and while some mathematical knowledge is necessary, readers are not expected to have a background in formal methods or control theory. It rigorously defines concepts from formal methods, such as transition systems, temporal logics, model checking and synthesis. It then links these to the infinite state dynamical systems through abstractions that are intuitive and only require basic convex-analysis and control-theory terminology, which is provided in the appendix. Several examples and illustrations help readers understand and visualize the concepts introduced throughout the book.
Book Synopsis Quantum Optimal Control Theory by : Jan Werschnik
Download or read book Quantum Optimal Control Theory written by Jan Werschnik and published by . This book was released on 2006 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Optimal Control of Impulsive Systems Using Adaptive Critic Based Neural Networks by : Xiaohua Wang
Download or read book Optimal Control of Impulsive Systems Using Adaptive Critic Based Neural Networks written by Xiaohua Wang and published by . This book was released on 2008 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This dissertation presents systematic computational tools for the optimal control synthesis of fixed-time and variable-time impulsive systems. Necessary conditions for optimality have been derived for a fixed-time and a variable-time impulsive system using the calculus of variations method. Properties of the costates and the states relation are studied and presented in theorems for the optimal control of a linear fixed-time impulsive system. Optimal control of a variable-time impulsive problem is investigated. A single neural network adaptive critic (SNAC) method for an impulsive system is developed. Algorithms are presented for calculating the optimal impulsive solutions in finite and infinite horizon cases. Since the construction of the networks and the synthesis of the controllers are relatively free of problem-specific assumptions, the method presented here is suitable for a wide range of real life nonlinear impulsive systems. Linear and nonlinear examples of impulsive systems with continuous and impulsive dynamics are considered for the proposed method and algorithms. The given examples show that the proposed method provides the optimal solution for finite and infinite horizon cases"--Abstract, leaf iii.
