An inverse optimality method to solve a class of second order optimal control problems

This paper presents an inverse optimality method to solve the Hamilton-Jacobi-Bellman equation for a class of second order nonlinear problems for which the cost is quadratic and the dynamics are affine in the input. The running cost that renders the control input optimal is also explicitly determined. One special feature of this method, as compared to other methods in the literature, is the fact that the solution is obtained directly for the control input without needing to assume or compute a value function first. Additionaly, the value function can also be obtained after one solves for the control input. A Lyapunov function that proves stability of the controller is also obtained for a subclass of problems.