Huan Yu

Yuanyuan Shi, Zongyi Li, Huan Yu et al.

State estimation is important for a variety of tasks, from forecasting to substituting for unmeasured states in feedback controllers. Performing real-time state estimation for PDEs using provably and rapidly converging observers, such as those based on PDE backstepping, is computationally expensive and in many cases prohibitive. We propose a framework for accelerating PDE observer computations using learning-based approaches that are much faster while maintaining accuracy. In particular, we employ the recently-developed Fourier Neural Operator (FNO) to learn the functional mapping from the initial observer state and boundary measurements to the state estimate. By employing backstepping observer gains for previously-designed observers with particular convergence rate guarantees, we provide numerical experiments that evaluate the increased computational efficiency gained with FNO. We consider the state estimation for three benchmark PDE examples motivated by applications: first, for a reaction-diffusion (parabolic) PDE whose state is estimated with an exponential rate of convergence; second, for a parabolic PDE with exact prescribed-time estimation; and, third, for a pair of coupled first-order hyperbolic PDEs that modeling traffic flow density and velocity. The ML-accelerated observers trained on simulation data sets for these PDEs achieves up to three orders of magnitude improvement in computational speed compared to classical methods. This demonstrates the attractiveness of the ML-accelerated observers for real-time state estimation and control.

Tianming Wang, Wenjie Lu, Huan Yu et al.

Underwater robots in shallow waters usually suffer from strong wave forces, which may frequently exceed robot's control constraints. Learning-based controllers are suitable for disturbance rejection control, but the excessive disturbances heavily affect the state transition in Markov Decision Process (MDP) or Partially Observable Markov Decision Process (POMDP). Also, pure learning procedures on targeted system may encounter damaging exploratory actions or unpredictable system variations, and training exclusively on a prior model usually cannot address model mismatch from the targeted system. In this paper, we propose a transfer learning framework that adapts a control policy for excessive disturbance rejection of an underwater robot under dynamics model mismatch. A modular network of learning policies is applied, composed of a Generalized Control Policy (GCP) and an Online Disturbance Identification Model (ODI). GCP is first trained over a wide array of disturbance waveforms. ODI then learns to use past states and actions of the system to predict the disturbance waveforms which are provided as input to GCP (along with the system state). A transfer reinforcement learning algorithm using Transition Mismatch Compensation (TMC) is developed based on the modular architecture, that learns an additional compensatory policy through minimizing mismatch of transitions predicted by the two dynamics models of the source and target tasks. We demonstrated on a pose regulation task in simulation that TMC is able to successfully reject the disturbances and stabilize the robot under an empirical model of the robot system, meanwhile improve sample efficiency.