Optimal control of a third order nonlinear system based on an inverse optimality method

In this paper, a nonlinear optimal control problem for a third order system is defined and solved. The optimal control law is found using an inverse optimality approach to solve the Hamilton-Jacobi-Bellman equation, where the solution is obtained directly for the control input without needing to assume or compute a value function first. However, the value function can be obtained after one solves for the control input and it is shown to be at least a local Lyapunov function. The developed controller is applied to a path following control of a wheeled mobile robot.