This work presents recent mathematical methods in the area of optimal control with a particular emphasis on the computational aspects and applications. Optimal control theory concerns the determination of control strategies for complex dynamical systems, in order to optimize some measure of their performance. Started in the 60's under the pressure of the "space race" between the US and the former USSR, the field now has a far wider scope, and embraces a variety of areas ranging from process control to traffic flow optimization, renewable resources exploitation and management of financial markets. These emerging applications require more and more efficient numerical methods for their solution, a very difficult task due the huge number of variables. The chapters of this volume give an up-to-date presentation of several recent methods in this area including fast dynamic programming algorithms, model predictive control and max-plus techniques. This book is addressed to researchers, graduate students and applied scientists working in the area of control problems, differential games and their applications.

Nonlinear Model Predictive Control is a thorough and rigorous introduction to nonlinear model predictive control (NMPC) for discrete-time and sampled-data systems. NMPC is interpreted as an approximation of infinite-horizon optimal control so that important properties like closed-loop stability, inverse optimality and suboptimality can be derived in a uniform manner. These results are complemented by discussions of feasibility and robustness. NMPC schemes with and without stabilizing terminal constraints are detailed and intuitive examples illustrate the performance of different NMPC variants. An introduction to nonlinear optimal control algorithms gives insight into how the nonlinear optimisation routine - the core of any NMPC controller - works. An appendix covering NMPC software and accompanying software in MATLAB (R) and C++(downloadable from www.springer.com/ISBN) enables readers to perform computer experiments exploring the possibilities and limitations of NMPC.

This book provides an approach to the study of perturbation and discretization effects on the long-time behavior of dynamical and control systems. It analyzes the impact of time and space discretizations on asymptotically stable attracting sets, attractors, asumptotically controllable sets and their respective domains of attractions and reachable sets. Combining robust stability concepts from nonlinear control theory, techniques from optimal control and differential games and methods from nonsmooth analysis, both qualitative and quantitative results are obtained and new algorithms are developed, analyzed and illustrated by examples.

This book contains a selection of the papers presented at the 3rd NCN Workshop which was focused on "Dynamics, Bifurcations and Control". The peer-reviewed papers describe a number of ways how dynamical systems techniques can be applied for analysis and design problems in control with topics ranging from bifurcation control via stability and stabilizaton to the global dynamical behaviour of control systems. The book gives an overview of the current status of the field.

Lyapunov methods have been and are still one of the main tools to analyze the stability properties of dynamical systems. In this monograph, Lyapunov results characterizing the stability and stability of the origin of differential inclusions are reviewed. To characterize instability and destabilizability, Lyapunov-like functions, called Chetaev and control Chetaev functions in the monograph, are introduced. Based on their definition and by mirroring existing results on stability, analogue results for instability are derived. Moreover, by looking at the dynamics of a differential inclusion in backward time, similarities and differences between stability of the origin in forward time and instability in backward time, and vice versa, are discussed. Similarly, the invariance of the stability and instability properties of the equilibria of differential equations with respect to scaling are summarized. As a final result, ideas combining control Lyapunov and control Chetaev functions to simultaneously guarantee stability, i.e., convergence, and instability, i.e., avoidance, are outlined. The work is addressed at researchers working in control as well as graduate students in control engineering and applied mathematics.

Model Predictive Control (MPC) can be dated back to the 1960s, and can now be regarded as a mature control method, which has had significant impact on industrial process control. It is applied in many control systems and has been extended to include non-linear dynamics and non-convex constraints. Of increasing importance in all such control systems in the economic benefits within the design of the system. Traditionally, the so-called control pyramid has been the main technique to do this, whereby economic targets are translated into setpoints and reference trajectories, which are in turn stabilized by control techniques such as MPC. At the same time, in process systems engineering and other fields of application, one aims at economic process operation and much attention has been given to this and the term Economic Model Predictive Control (EMPC) has been coined. Economic Nonlinear Model Predictive Control provides a concise overview of different approaches on the question of stability and optimality in different formulations of EMPC. It is the first monograph to cover approaches both with and without terminal constraints and end penalties, and turnpike/dissipativity-based settings as well as Lyapunov-based approaches. This monograph is an accessible tutorial on the state-of-the-art in model predictive control. Students and researchers will find a clear exposition of current knowledge upon which they can build their own research.

Das Buch bietet eine kompakte, grundlegende Einfuhrung in die Theorie gewoehnlicher Differentialgleichungen aus der Perspektive der dynamischen Systeme im Umfang einer einsemestrigen Vorlesung. UEber die Diskussion der Loesungstheorie und der Theorie linearer Systeme hinaus werden insbesondere einfache analytische und numerische Loesungsverfahren, Konzepte der Theorie dynamischer Systeme, Stabilitat, Verzweigungen und Hamilton-Systeme behandelt. Der Stoff wird durchgangig anhand von Beispielen, Fragen, UEbungsaufgaben und Computerexperimenten illustriert und vertieft. Das Buch ist besonders fur das Bachelor-Studium gut geeignet, sowohl vorlesungsbegleitend zum Modul "Gewoehnliche Differentialgleichungen" als auch zum Selbststudium. Es werden nur die Grundvorlesungen in Analysis und Linearer Algebra vorausgesetzt.