Hamilton-Jacobi-Bellman equations

En savoir plus sur le livre

Optimal feedback control is crucial across various fields, including aerospace engineering, chemical processing, and resource economics. Dynamic programming techniques are essential for solving fully nonlinear Hamilton-Jacobi-Bellman equations. This book explores advanced numerical approximation methods for these equations, covering topics such as post-processing of Galerkin methods, high-order methods, boundary treatment in semi-Lagrangian schemes, and reduced basis methods. It also discusses comparison principles for viscosity solutions, max-plus methods, and the numerical approximation of Monge-Ampère equations. Applications highlighted include simulations of adaptive controllers and the control of nonlinear delay differential equations. Key topics include the development of a monotone probabilistic scheme and a probabilistic max-plus algorithm for Hamilton-Jacobi-Bellman equations, enhancing policies through postprocessing, and a viability approach for adaptive controller simulation. The book also addresses Galerkin approximations for optimal control of nonlinear delay differential equations and efficient higher-order time discretization schemes based on diagonally implicit symplectic Runge-Kutta methods. Additionally, it examines numerical solutions for the simple Monge-Ampère equation with nonconvex Dirichlet data and discusses boundary conditions in comparison principles for viscosity solutions, along with boundary mesh