A New Algorithm for the LQR Problem with Partially Unknown Dynamics

We consider an LQR optimal control problem with partially unknown dynamics. We propose a new model-based online algorithm to obtain an approximation of the dynamics and the control at the same time during a single simulation. The iterative algorithm is based on a mixture of Reinforcement Learning and optimal control techniques. In particular, we use Gaussian distributions to represent model uncertainty and the probabilistic model is updated at each iteration using Bayesian regression formulas. On the other hand, the control is obtained in feedback form via a Riccati differential equation. We present some numerical tests showing that the algorithm can efficiently bring the system towards the origin.