The use of Lyapunov functions is generally limited to proving the stability of a system with a given control law. In this presentation, Lyapunov functions are used to formulate optimal control problems as pointwise nonlinear programmes. These optimisation problems are equivalent to inverse optimal control problems. This approach is applied to satellite attitude control. The optimal attitude control problems under consideration will be the minimisation of the norm of the control torque subject to constraints on the convergence rate of a Lyapunov function. This approach improves the tradeoff between rapidity and energy consumption compared to a benchmark controller, which is taken to be a PD type controller without loss of generality. The phase space trajectories show that the solutions to some fundamental open loop optimization problems are particular cases of optimal control problem formulations based on the convergence rates of Lyapunov functions. This is the case of the minimum time single axis attitude control problem, which is a special case of the problem of maximizing the convergence rate of a Lyapunov function under maximum torque limitations. It is also the case of the problem of minimising toque for fixed manoeuvre time. The solution to this problem is a particular case of the problem of minimizing the norm of the control torque under a Lyapunov convergence rate constraint.

### Séminaire d'Automatique du Plateau de Saclay : Optimal control and Lyapunov functions applied to the satellite attitude control

Séminaire le 24 Mai 2016, 11h00 à CentraleSupelec (Gif-sur-Yvette) Salle du conseil du L2S - B4.40

**Nadjim Horri (Coventry University)**