Advances In Dynamics, Optimization And Computation: A Volume Dedicated To Michael Dellnitz On The Occasion Of His 60th Birthday (studies In Systems, Decision And Control (304))

This book presents a collection of papers on recent advances in problems concerning dynamics, optimal control and optimization. In many chapters, computational techniques play a central role. Set-oriented techniques feature prominently throughout the book, yielding state-of-the-art algorithms for computing general invariant sets, constructing globally optimal controllers and solving multi-objective optimization problems. Front Matter ....Pages i-xv Front Matter ....Pages 1-1 A Continuation Approach to Computing Phase Resetting Curves (Peter Langfield, Bernd Krauskopf, Hinke M. Osinga)....Pages 3-30 Input-Output Networks, Singularity Theory, and Homeostasis (Martin Golubitsky, Ian Stewart, Fernando Antoneli, Zhengyuan Huang, Yangyang Wang)....Pages 31-65 The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems (Raphael Gerlach, Adrian Ziessler)....Pages 66-85 Set-Oriented and Finite-Element Study of Coherent Behavior in Rayleigh-Bénard Convection (Anna Klünker, Christiane Schneide, Gary Froyland, Jörg Schumacher, Kathrin Padberg-Gehle)....Pages 86-108 Singular Value Decomposition of Operators on Reproducing Kernel Hilbert Spaces (Mattes Mollenhauer, Ingmar Schuster, Stefan Klus, Christof Schütte)....Pages 109-131 A Weak Characterization of Slow Variables in Stochastic Dynamical Systems (Andreas Bittracher, Christof Schütte)....Pages 132-150 Analysis and Simulation of Extremes and Rare Events in Complex Systems (Meagan Carney, Holger Kantz, Matthew Nicol)....Pages 151-182 Dynamical Systems Theory and Algorithms for NP-hard Problems (Tuhin Sahai)....Pages 183-206 Front Matter ....Pages 207-207 Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach (Kathrin Flaßkamp, Sina Ober-Blöbaum, Sebastian Peitz)....Pages 209-237 POD-Based Mixed-Integer Optimal Control of Evolution Systems (Christian Jäkle, Stefan Volkwein)....Pages 238-264 From Bellman to Dijkstra: Set-Oriented Construction of Globally Optimal Controllers (Lars Grüne, Oliver Junge)....Pages 265-294 An Optimal Control Derivation of Nonlinear Smoothing Equations (Jin Won Kim, Prashant G. Mehta)....Pages 295-311 Front Matter ....Pages 313-313 Structural Properties of Pareto Fronts: The Occurrence of Dents in Classical and Parametric Multiobjective Optimization Problems (Katrin Witting, Mirko Hessel-von Molo, Michael Dellnitz)....Pages 315-336 An Image Set-Oriented Method for the Numerical Treatment of Bi-Level Multi-objective Optimization Problems (Alessandro Dell’Aere)....Pages 337-354 The Gradient Subspace Approximation and Its Application to Bi-objective Optimization Problems (Oliver Schütze, Lourdes Uribe, Adriana Lara)....Pages 355-390 Back Matter ....Pages 391-392 A continuation approach to computing phase resetting curves -- Input-output networks, singularity theory, and homeostasis -- The approximation of invariant sets in infinite dimensional dynamical systems -- Set-oriented and finite-element study of coherent behavior in Rayleigh-Benard convection -- Singular value decomposition of operators on Reproducing Kernel Hilbert Spaces -- A weak characterization of slow variables in stochastic dynamical systems -- Analysis and simulation of extremes and rare events in complex systems -- Dynamical systems theory and algorithms for NP-hard problems