A New Algorithm for Finding Numerical Solutions of Optimal Feedback Control Law

A new algorithm for finding numerical solutions of optimal feedback control of a class of general finite dimensional systems with multi-input is developed. The algorithm is based on the fact that the value function of the optimal control problem is the viscosity solution of its associated Hamilton-Jacobi-Bellman equation. An example that the closed form solutions of optimal feedback control-trajectory pairs are available is validated. It is shown that the numerical solutions completely tally with the analytical solutions.