Falcone M., Ferretti R., Grüne L., McEneaney W.M. (Eds.) Numerical Methods for Optimal Control Problems

Springer, 2019. — 275 p. — (Springer INdAM Series 29). — ISBN: 3030019586.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.A Hamilton-Jacobi-Bellman Approach for the Numerical Computation of Probabilistic State Constrained Reachable Sets
An Iterative Solution Approach for a Bi-level Optimization Problem for Congestion Avoidance on Road Networks
Computation of Optimal Trajectories for Delay Systems: An Optimize-Then-Discretize Strategy for General-Purpose NLP Solvers
POD-Based Economic Optimal Control of Heat-Convection Phenomena
Order Reduction Approaches for the Algebraic Riccati Equation and the LQR Problem
Fractional PDE Constrained Optimization: Box and Sparse Constrained Problems
Control, Shape, and Topological Derivatives via Minimax Differentiability of Lagrangians
Minimum Energy Estimation Applied to the Lorenz Attractor
Probabilistic Max-Plus Schemes for Solving Hamilton-Jacobi-Bellman Equations
An Adaptive Max-Plus Eigenvector Method for Continuous Time Optimal Control Problems
Diffusion Process Representations for a Scalar-Field Schrödinger Equation Solution in Rotating Coordinates