Numerical Methods for Optimal Control Problems

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 "e;space race"e; 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.

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.

1 M. Assellaou and A. Picarelli, A Hamilton-Jacobi-Bellman approach for the numerical computation of probabilistic state constrained reachable sets.- 2. A. Britzelmeier,  A. De Marchi, and M. Gerdts, An iterative solution approach for a bi-level optimization problem for congestion avoidance on road networks.- 3 S. Cacace, R. Ferretti, and Z. Rafiei, Computation of Optimal Trajectories for Delay Systems: an Optimize-Then-Discretize Strategy for General-Purpose NLP Solvers.-  4 L. Mechelli and S. Volkwein, POD-Based Economic Optimal Control of Heat-Convection Phenomena.- 5 A. Alla and V. Simoncini, Order reduction approaches for the algebraic Riccati equation and the LQR problem.- 6 F. Durastante and S. Cipolla, Fractional PDE constrained optimization: box and sparse constrained problems.- 7 M. C. Delfour, Control, Shape, and Topological Derivatives via Minimax Differentiability of Lagrangians.- 8 A. J. Krener, Minimum Energy Estimation Applied to the Lorenz Attractor.- 9 M. Akian and E. Fodjo, Probabilistic max-plus schemes for solving Hamilton-Jacobi-Bellman equations.- 10 P. M. Dower, An adaptive max-plus eigenvector method for continuous time optimal control problems.- 11 W. Mc Eneaney and R. Zhao, Diffusion Process Representations for a Scalar-Field Schr¨odinger Equation Solution in Rotating Coordinates.