State-feedback optimal controllers for deterministic nonlinear systems

A full-state feedback optimal control problem is solved for a general deterministic nonlinear system. The solution method is based on transforming Hamilton-Jacobi equation into an algebraic equation using the pseudo-inverse. Then we interpret the value function in terms of the control Lyapunov function and provide the stabilizing controller and the stability margins. We also derive an optimal controller for a nonlinear system which requires a solution of the state dependent Riccati equation. Simple examples demonstrate each method.