Inverse Dynamic Control of Discrete-Time Latent Dynamic Systems

Controller design for dynamic systems with unknown dynamics using data driven approaches is a long standing problem. Most existing works study systems with observable low-dimensional state variables. As for latent dynamic systems where only high-dimensional observations are attainable, standard methods like reinforcement learning are sample inefficent and hard to generalize to new goals. In this paper, we study the problem of controller design for discrete-time latent dynamic systems. We first train an identifiable latent dynamic model to explicitly recover the latent variables and estimate the dynamic model. The latent variables are identified up to an affine transformation with blockwise diagonal structure even when the system is affine nonlinear and the mixing function is highly nonlinear. Then an inverse dynamic controller is used to ensure stable tracking in the test environment. The goals or desired trajectories are not needed in the training process, and the dynamics of the uncontrollable environmental latent variables may be different in the training and test environment. Simulation experiments are conducted to verify the proposed controller.