Numerical Methods for Optimal Control Problems

✍ Scribed by Maurizio Falcone, Roberto Ferretti, Lars Grüne, William M. McEneaney

• Publisher: Springer International Publishing
• Year: 2018
• Tongue: English
• Leaves: 275
• Series: Springer INdAM Series 29
• Edition: 1st ed.
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages i-x
A Hamilton-Jacobi-Bellman Approach for the Numerical Computation of Probabilistic State Constrained Reachable Sets (Mohamed Assellaou, Athena Picarelli)....Pages 1-22
An Iterative Solution Approach for a Bi-level Optimization Problem for Congestion Avoidance on Road Networks (Andreas Britzelmeier, Alberto De Marchi, Matthias Gerdts)....Pages 23-38
Computation of Optimal Trajectories for Delay Systems: An Optimize-Then-Discretize Strategy for General-Purpose NLP Solvers (Simone Cacace, Roberto Ferretti, Zahra Rafiei)....Pages 39-62
POD-Based Economic Optimal Control of Heat-Convection Phenomena (Luca Mechelli, Stefan Volkwein)....Pages 63-87
Order Reduction Approaches for the Algebraic Riccati Equation and the LQR Problem (Alessandro Alla, Valeria Simoncini)....Pages 89-109
Fractional PDE Constrained Optimization: Box and Sparse Constrained Problems (Fabio Durastante, Stefano Cipolla)....Pages 111-135
Control, Shape, and Topological Derivatives via Minimax Differentiability of Lagrangians (Michel C. Delfour)....Pages 137-164
Minimum Energy Estimation Applied to the Lorenz Attractor (Arthur J. Krener)....Pages 165-182
Probabilistic Max-Plus Schemes for Solving Hamilton-Jacobi-Bellman Equations (Marianne Akian, Eric Fodjo)....Pages 183-209
An Adaptive Max-Plus Eigenvector Method for Continuous Time Optimal Control Problems (Peter M. Dower)....Pages 211-240
Diffusion Process Representations for a Scalar-Field Schrödinger Equation Solution in Rotating Coordinates (William M. McEneaney, Ruobing Zhao)....Pages 241-268

✦ Subjects

Mathematics; Systems Theory, Control; Numerical Analysis; Computational Science and Engineering; Engineering Mathematics; Game Theory