This talk presents an inverse optimality method to solve the Hamilton-Jacobi-Bellman equation for a class of nonlinear problems for which the cost is quadratic and the dynamics are affine in the input. The method is inverse optimal because 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. Additionally, the value function can also be obtained after one solves for the control input. A Lyapunov function that proves stability of the feedback connection of the inverse optimal controller with the nonlinear system is also obtained. Several applications of the methodology will be presented, such as spring-mass damper systems, Van der Pol oscillators, path following of unicycles and backstepping.
Groupe d’études et de recherche en analyse des décisions