Numerical solution to the optimal feedback control of continuous casting process
Journal of Global Optimization
Application of Optimal Control techniques and Advanced Computing to the study of enzyme kinetics
Mathematics and Computers in Simulation
Convergence Rate for a Curse-of-Dimensionality-Free Method for a Class of HJB PDEs
SIAM Journal on Control and Optimization
Stable Numerical Schemes for Solving Hamilton-Jacobi-Bellman-Isaacs Equations
SIAM Journal on Scientific Computing
An Adaptive Sparse Grid Semi-Lagrangian Scheme for First Order Hamilton-Jacobi Bellman Equations
Journal of Scientific Computing
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In this paper we develop a new version of the semi-Lagrangian algorithm for first order Hamilton–Jacobi equations. This implementation is well suited to deal with problems in high dimension, i.e. in Rm with m≥3, which typically arise in the study of control problems and differential games. Our model problem is the evolutive Hamilton–Jacobi equation related to the optimal control finite horizon problem. We will give a step-by-step description of the algorithm focusing our attention on two critical routines: the interpolation in high dimension and the search for the global minimum. We present some numerical results on test problems which range from m=3 to m=5 and deal with applications to front propagation, aerospace engineering, ecomomy and biology.