Learning-Based Optimal Control with Performance Guarantees for Unknown Systems with Latent States

As control engineering methods are applied to increasingly complex systems, data-driven approaches for system identification appear as a promising alternative to physics-based modeling. While many of these approaches rely on the availability of state measurements, the states of a complex system are often not directly measurable. It may then be necessary to jointly estimate the dynamics and a latent state, making it considerably more challenging to design controllers with performance guarantees. This paper proposes a novel method for the computation of an optimal input trajectory for unknown nonlinear systems with latent states. Probabilistic performance guarantees are derived for the resulting input trajectory, and an approach to validate the performance of arbitrary control laws is presented. The effectiveness of the proposed method is demonstrated in a numerical simulation.