Numerical Methods for Optimal Control Problems with State Constraints

Numerical Methods for Optimal Control Problems with State Constraints

Author: Radoslaw Pytlak

Publisher: Springer

Published: 2006-11-14

Total Pages: 224

ISBN-13: 3540486623

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While optimality conditions for optimal control problems with state constraints have been extensively investigated in the literature the results pertaining to numerical methods are relatively scarce. This book fills the gap by providing a family of new methods. Among others, a novel convergence analysis of optimal control algorithms is introduced. The analysis refers to the topology of relaxed controls only to a limited degree and makes little use of Lagrange multipliers corresponding to state constraints. This approach enables the author to provide global convergence analysis of first order and superlinearly convergent second order methods. Further, the implementation aspects of the methods developed in the book are presented and discussed. The results concerning ordinary differential equations are then extended to control problems described by differential-algebraic equations in a comprehensive way for the first time in the literature.


Foundations of Dynamic Economic Analysis

Foundations of Dynamic Economic Analysis

Author: Michael R. Caputo

Publisher: Cambridge University Press

Published: 2005-01-10

Total Pages: 632

ISBN-13: 1107717639

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Foundations of Dynamic Economic Analysis presents a modern and thorough exposition of the fundamental mathematical formalism used to study optimal control theory, i.e., continuous time dynamic economic processes, and to interpret dynamic economic behavior. The style of presentation, with its continual emphasis on the economic interpretation of mathematics and models, distinguishes it from several other excellent texts on the subject. This approach is aided dramatically by introducing the dynamic envelope theorem and the method of comparative dynamics early in the exposition. Accordingly, motivated and economically revealing proofs of the transversality conditions come about by use of the dynamic envelope theorem. Furthermore, such sequencing of the material naturally leads to the development of the primal-dual method of comparative dynamics and dynamic duality theory, two modern approaches used to tease out the empirical content of optimal control models. The stylistic approach ultimately draws attention to the empirical richness of optimal control theory, a feature missing in virtually all other textbooks of this type.


Constrained Optimal Control of Linear and Hybrid Systems

Constrained Optimal Control of Linear and Hybrid Systems

Author: Francesco Borrelli

Publisher: Springer

Published: 2003-09-04

Total Pages: 206

ISBN-13: 3540362258

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Many practical control problems are dominated by characteristics such as state, input and operational constraints, alternations between different operating regimes, and the interaction of continuous-time and discrete event systems. At present no methodology is available to design controllers in a systematic manner for such systems. This book introduces a new design theory for controllers for such constrained and switching dynamical systems and leads to algorithms that systematically solve control synthesis problems. The first part is a self-contained introduction to multiparametric programming, which is the main technique used to study and compute state feedback optimal control laws. The book's main objective is to derive properties of the state feedback solution, as well as to obtain algorithms to compute it efficiently. The focus is on constrained linear systems and constrained linear hybrid systems. The applicability of the theory is demonstrated through two experimental case studies: a mechanical laboratory process and a traction control system developed jointly with the Ford Motor Company in Michigan.


Automatic Control in Aerospace 1992

Automatic Control in Aerospace 1992

Author: D.B. DeBra

Publisher: Elsevier

Published: 2017-01-11

Total Pages: 573

ISBN-13: 1483298744

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Space vehicles have become increasingly complex in recent years, and the number of missions has multiplied as a result of extending frontiers in the exploration of our planetary system and the universe beyond. The advancement of automatic control in aerospace reflects these developments. Key areas covered in these proceedings include: the size and complexity of spacecrafts and the increasingly stringent performance requirements to be fulfilled in a harsh and unpredictable environment; the merger of space vehicles and airplanes into space planes to launch and retrieve payloads by reusable winged vehicles; and the demand to increase space automation and autonomy to reduce human involvement as much as possible in manned, man-tended and unmanned missions. This volume covers not only the newly evolving key technologies but also the classical issues of guidance, navigation and control.


Computational Optimal Control

Computational Optimal Control

Author: Roland Bulirsch

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 382

ISBN-13: 3034884974

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Resources should be used sparingly both from a point of view of economy and eco logy. Thus in controlling industrial, economical and social processes, optimization is the tool of choice. In this area of applied numerical analysis, the INTERNATIONAL FEDERATION OF AUTOMATIC CONTROL (IFAC) acts as a link between research groups in universities, national research laboratories and industry. For this pur pose, the technical committee Mathematics of Control of IFAC organizes biennial conferences with the objective of bringing together experts to exchange ideas, ex periences and future developments in control applications of optimization. There should be a genuine feedback loop between mathematicians, computer scientists, engineers and software developers. This loop should include the design, application and implementation of algorithms. The contributions of industrial practitioners are especially important. These proceedings contain selected papers from a workshop on CONTROL Ap PLICATIONS OF OPTIMIZATION, which took place at the Fachhochschule Miinchen in September 1992. The workshop was the ninth in a series of very successful bien nial meetings, starting with the Joint Automatic Control Conference in Denver in 1978 and followed by conferences in London, Oberpfaffenhofen, San Francisco, Ca pri, Tbilisi and Paris. The workshop was attended by ninety researchers from four continents. This volume represents the state of the art in the field, with emphasis on progress made since the publication of the proceedings of the Capri meeting, edited by G. di Pillo under the title 'Control Applications of Optimization and Nonlinear Programming'.


Calculus of Variations and Optimal Control Theory

Calculus of Variations and Optimal Control Theory

Author: Daniel Liberzon

Publisher: Princeton University Press

Published: 2012

Total Pages: 255

ISBN-13: 0691151873

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This textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a self-contained resource for graduate students in engineering, applied mathematics, and related subjects. Designed specifically for a one-semester course, the book begins with calculus of variations, preparing the ground for optimal control. It then gives a complete proof of the maximum principle and covers key topics such as the Hamilton-Jacobi-Bellman theory of dynamic programming and linear-quadratic optimal control. Calculus of Variations and Optimal Control Theory also traces the historical development of the subject and features numerous exercises, notes and references at the end of each chapter, and suggestions for further study. Offers a concise yet rigorous introduction Requires limited background in control theory or advanced mathematics Provides a complete proof of the maximum principle Uses consistent notation in the exposition of classical and modern topics Traces the historical development of the subject Solutions manual (available only to teachers) Leading universities that have adopted this book include: University of Illinois at Urbana-Champaign ECE 553: Optimum Control Systems Georgia Institute of Technology ECE 6553: Optimal Control and Optimization University of Pennsylvania ESE 680: Optimal Control Theory University of Notre Dame EE 60565: Optimal Control


Dynamic Optimization, Second Edition

Dynamic Optimization, Second Edition

Author: Morton I. Kamien

Publisher: Courier Corporation

Published: 2013-04-17

Total Pages: 402

ISBN-13: 0486310280

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Since its initial publication, this text has defined courses in dynamic optimization taught to economics and management science students. The two-part treatment covers the calculus of variations and optimal control. 1998 edition.