Numerical Optimal Control: Solving 1D HJB Equations

Dynamic engineering systems require precise control strategies, but finding analytical solutions for optimal control problems is often impossible. This text-based course guides you through the fundamentals of the Hamilton-Jacobi-Bellman (HJB) equation in one dimension, showing you how to formulate and numerically solve control problems. You will start with essential terminology, basic control concepts, and foundational definitions before moving into practical discretization techniques. By reading through detailed explanations and structured code snippets, you will gain the confidence to implement robust numerical solvers. What you'll learn: - Understand the mathematical foundations of optimal control and the HJB equation; - Formulate 1D dynamic programming problems for engineering and chemical processes; - Implement finite difference schemes to discretize and solve HJB equations numerically; - Apply modern scientific computing practices using clean, structured Python and MATLAB code patterns; - Analyze boundary conditions, stability, and convergence of your numerical solvers; - Practice translating theoretical control laws into working numerical algorithms. The course begins with core theoretical concepts and governing equations, then guides you step-by-step through discretization, algorithm design, and code implementation. It is designed for beginners in numerical optimization and engineering, requiring only basic calculus and introductory programming concepts. Start reading today to master the essentials of numerical optimal control.