Optimal control and the Dynamic Programming Principle

This entry illustrates the application of Bellman’s dynamic programming principle within the context of optimal control problems for continuous-time dynamical systems. The approach leads to a characterization of the optimal value of the cost functional, over all possible trajectories given the initial conditions, in terms of a partial differential equation called the Hamilton–Jacobi–Bellman equation. Importantly, this can be used to synthesize the corresponding optimal control input as a state-feedback law.