Wei Kang

Tenavi Nakamura-Zimmerer, Qi Gong, Wei Kang

Recent research shows that supervised learning can be an effective tool for designing near-optimal feedback controllers for high-dimensional nonlinear dynamic systems. But the behavior of neural network controllers is still not well understood. In particular, some neural networks with high test accuracy can fail to even locally stabilize the dynamic system. To address this challenge we propose several novel neural network architectures, which we show guarantee local asymptotic stability while retaining the approximation capacity to learn the optimal feedback policy semi-globally. The proposed architectures are compared against standard neural network feedback controllers through numerical simulations of two high-dimensional nonlinear optimal control problems: stabilization of an unstable Burgers-type partial differential equation, and altitude and course tracking for an unmanned aerial vehicle. The simulations demonstrate that standard neural networks can fail to stabilize the dynamics even when trained well, while the proposed architectures are always at least locally stabilizing and can achieve near-optimal performance.

Wei Kang

In this paper, a new definition of observability is introduced for PDEs. It is a quantitative measure of partial observability. The quantity is proved to be consistent if approximated using well posed approximation schemes. A first order approximation of an unobservability index using empirical gramian is introduced. For linear systems with full state observability, the empirical gramian is equivalent to the observability gramian in control theory. The consistency of the defined observability is exemplified using a Burgers' equation.

Tianwei Xia, Kai Sun, Wei Kang

Microgrids have more operational flexibilities as well as uncertainties than conventional power grids, especially when renewable energy resources are utilized. An energy storage based feedback controller can compensate undesired dynamics of a microgrid to improve its stability. However, the optimal feedback control of a microgrid subject to a large disturbance needs to solve a Hamilton-Jacobi-Bellman problem. This paper proposes a machine learning-based optimal feedback control scheme. Its training dataset is generated from a linear-quadratic regulator and a brute-force method respectively addressing small and large disturbances. Then, a three-layer neural network is constructed from the data for the purpose of optimal feedback control. A case study is carried out for a microgrid model based on a modified Kundur two-area system to test the real-time performance of the proposed control scheme.