George Leitmann - Böcker

When the Tyrian princess Dido landed on the North African shore of the Mediterranean sea she was welcomed by a local chieftain. He offered her all the land that she could enclose between the shoreline and a rope of knotted cowhide. While the legend does not tell us, we may assume that Princess Dido arrived at the correct solution by stretching the rope into the shape of a circular arc and thereby maximized the area of the land upon which she was to found Carthage. This story of the founding of Carthage is apocryphal. Nonetheless it is probably the first account of a problem of the kind that inspired an entire mathematical discipline, the calculus of variations and its extensions such as the theory of optimal control. This book is intended to present an introductory treatment of the calculus of variations in Part I and of optimal control theory in Part II. The discussion in Part I is restricted to the simplest problem of the calculus of variations. The topic is entirely classical; all of the basic theory had been developed before the turn of the century. Consequently the material comes from many sources; however, those most useful to me have been the books of Oskar Bolza and of George M. Ewing. Part II is devoted to the elementary aspects of the modern extension of the calculus of variations, the theory of optimal control of dynamical systems.

The 11th International Workshop on Dynamics and Control brought together scientists and engineers from diverse fields and gave them a venue to develop a greater understanding of this discipline and how it relates to many areas in science, engineering, economics, and biology. The event gave researchers an opportunity to investigate ideas and techniques from outside their own fields of expertise, enabling a cross-pollination of dynamics and control perspectives. Now there is a book that documents the major presentations of the workshop, providing a foundation for further research.The range and diversity of papers in Dynamical Systems and Control demonstrate the remarkable reach of the subject. All of these contributed papers shed light on a multiplicity of physical, biological, and economic phenomena through lines of reasoning that originate and grow from this discipline.The editors divide the book into three parts. The first covers fundamental advances in dynamics, dynamical systems, and control. These papers represent ideas that can be applied to several areas of interest. The second part deals with new and innovative techniques and their application to a variety of interesting problems, from the control of cars and robots, to the dynamics of ships and suspension bridges, and the determination of optimal spacecraft trajectories. The third section relates to social, economic, and biological issues. It reveals the wealth of understanding that can be obtained through a dynamics and control approach to issues such as epidemics, economic games, neo-cortical synchronization, and human posture control.

This volume is a collection of contributions to the subject of multicriteria decision making and differential games, all of which are based wholly or in part on papers that have appeared in the Journal of Optimization Theory and Applications. The authors take this opportunity to revise, update, or enlarge upon their earlier publications. The theory of multicriteria decision making and differential games is concerned with situations in which a single decision maker is faced with a multiplicity of usually incompatible criteria, performance indices or payoffs, or in which a number of decision makers, or players, must take into account criteria each of which depends on the decisions of all the decision makers. The first six chapters are devoted to situations involving a single decision maker, or a number of decision makers in complete collaboration and thus being in effect a single decision maker. Chapters I -IV treat various topics in the theory of domination structures and nondominated decisions. Chapter V presents a discussion of efficient, or Pareto-optimal, decisions. The approach to multicriteria decision making via preference relations is explored in Chapter VI. When there is more than one decision maker, cooperation, as well as noncooperation, is possible. Chapters VII and VIII deal with the topic of coalitions in a dynamic setting, while Chapters IX and X address the situation of two unequal decision makers, a leader and a follower.

When the Tyrian princess Dido landed on the North African shore of the Mediterranean sea she was welcomed by a local chieftain. He offered her all the land that she could enclose between the shoreline and a rope of knotted cowhide. While the legend does not tell us, we may assume that Princess Dido arrived at the correct solution by stretching the rope into the shape of a circular arc and thereby maximized the area of the land upon which she was to found Carthage. This story of the founding of Carthage is apocryphal. Nonetheless it is probably the first account of a problem of the kind that inspired an entire mathematical discipline, the calculus of variations and its extensions such as the theory of optimal control. This book is intended to present an introductory treatment of the calculus of variations in Part I and of optimal control theory in Part II. The discussion in Part I is restricted to the simplest problem of the calculus of variations. The topic is entirely classical; all of the basic theory had been developed before the turn of the century. Consequently the material comes from many sources; however, those most useful to me have been the books of Oskar Bolza and of George M. Ewing. Part II is devoted to the elementary aspects of the modern extension of the calculus of variations, the theory of optimal control of dynamical systems.