In this paper, we consider the problem of tracking a reference trajectory for a simplified car model based on unicycle kinematics, whose position only is measured, and where the control input and the measurements are corrupted by independent Gaussian noises. To tackle this problem we devise a novel observer-controller: the invariant Linear Quadratic Gaussian controller (ILQG). It is based on the Linear Quadratic Gaussian controller, but the equations are slightly modified to account for, and to exploit, the symmetries of the problem. The gain tuning exhibits a reduced dependency on the estimated trajectory, and is thus less sensitive to misestimates. Beyond the fact the invariant approach is sensible (there is no reason why the controller performance should depend on whether the reference trajectory is heading west or south), we show through simulations that the ILQG outperforms the conventional LQG controller in case of large noises or large initial uncertainties.

We introduce a new plan repair method for problems cast as Mixed Integer Programs. In order to tackle the inherent complexity of these NP-hard problems, our approach relies on the use of Supervised Learning method for the offline construction of a predictor which takes the problem's parameters as input and infers values for the discrete optimization variables. This way, the online resolution time of the plan repair problem can be greatly decreased by avoiding a large part of the combinatorial search among discrete variables. This contribution was motivated by the large-scale problem of intra-daily recourse strategy computation in electrical power systems. We report and discuss results on this benchmark, illustrating the different aspects and mechanisms of this new approach which provided close-to-optimal solutions in only a fraction of the computational time necessary for existing solvers.