15.2.1 Hamilton-Jacobi-Bellman Equation

The HJB equation is a central result in optimal control theory. Many other principles and design techniques follow from the HJB equation, which itself is just a statement of the dynamic programming principle in continuous time. A proper derivation of all forms of the HJB equation would be beyond the scope of this book. Instead, a time-invariant formulation that is most relevant to planning will be given here. Also, an informal derivation will follow, based in part on [95].