Locally optimal controllers and globally inverse optimal controllers

In this paper we consider the problem of global asymptotic stabilization with prescribed local behavior. We show that this problem can be formulated in terms of control Lyapunov functions. Moreover, we show that if the local control law has been synthesized employing a LQ approach, then the associated Lyapunov function can be seen as the value function of an optimal problem with some specific local properties. We illustrate these results on two specific classes of systems: backstepping and feedforward systems. Finally, we show how this framework can be employed when considering the orbital transfer problem

Forwarding design with prescribed local behavior

International audienceAmong the non-linear control techniques, some Lyapunov design methods (Forwarding / Backstepping) take advantage of the structure of the system (Feedforward-form / Feedback-form) to formulate a continuous control law which stabilizes globally and asymptotically the equilibrium. In addition to stabilization, we focus on the local behaviour of the closed loop system, providing conditions under which we can predetermine the behaviour around the origin for Feedforward systems

Adding an integration with prescribed local behavior

International audienceAmong the non-linear control techniques, some Lyapunov design methods (Forwarding / Backstepping) take advantage of the structure of the system (Feedforward-form / Feedback-form) to formulate a continuous control law which stabilizes globally and asymptotically the equilibrium. In addition to stabilization, we focus on the local behaviour of the closed loop system, providing conditions under which we can predetermine the behaviour around the origin for Feedforward systems