Ordinary differential equations (ODEs) and differential-algebraic equations (DAEs) are widely used to model control systems in engineering, natural sciences, and economy. Optimal control plays a central role in optimizing such systems and to operate them effi ciently and safely. The intention of this textbook is to provide both, the theoretical and computational tools that are necessary to investigate and to solve optimal control problems with ODEs and DAEs. An emphasis is placed on the interplay between the optimal control problem, which typically is defi ned and analyzed in a Banach space setting, and discretizations thereof, which lead to finite dimensional optimization problems. The theoretical parts of the book require some knowledge of functional analysis, the numerically oriented parts require knowledge from linear algebra and numerical analysis. Practical examples are provided throughout the book for illustration purposes. The book addresses primarily master and Ph D students as well as researchers in applied mathematics, but also engineers or scientists with a good background in mathematics. The book serves as a reference in research and teaching and hopefully helps to advance the state-of-the-art in optimal control.
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Prof. Dr. Matthias Gerdts studied Mathematics with minor Computer Science at the University of Technology Clausthal, Germany, and graduated in 1997. He received his doctoral degree in 2001 and his Habilitation in 2006 from the University of Bayreuth (Germany). In 2003 he was a visiting professor at the University of California, San Diego (USA). From 2004 to 2007 he held a junior professorship for numerical optimal control at the Department of Mathematics of the University of Hamburg (Germany), and moved to a lecturer position for mathematical optimization at the University of Birmingham (U.K.) from 2007 to 2009. From 2009 to 2010 he was an associate professor for optimal control at the University of Würzburg (Germany). Since 2010 he is a full professor for engineering mathematics at the Department of Aerospace Engineering of the Universität der Bundeswehr München (Germany). His primary research interests are optimal control, optimization techniques, model-predictive control, differential-algebraic equations, and sensitivity analysis. The methods are applied in path planning and trajectory optimization tasks in automated driving, robotics, and aerospace engineering.
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