Hamilton-Jacobi-Bellman equations

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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