Nonlinear optimal control: principle of local optimality

In this paper, it is shown that a nonlinear regulator constructed by using a state-dependent Riccati equation (SDRE) is a local optimal solution of the original optimal control problem. In order to prove this fact, the conventional methods-Lagrange multiplier method, minimum principle and dynamic programming are used-and an idea of the principle of local optimality is introduced by modifying the principle of optimality of dynamic programming.