National Science Foundation Project Page
Project Title: Hybrid Control Architectures Combining Physical Models and Real-time Learning
Institutions: Old Dominion University and University of Vermont
Abstract : Artificial neural networks have traditionally been the backbone of machine learning. While these biologically inspired learning systems certainly have their strengths, they also have limitations in the context of control engineering. For example, physics based models often provide key physical insight into the design of control systems for power grids, autonomous vehicles, and robots. So completely discarding such models in the context of learning based control systems is often counterproductive. This project aims to develop a new control architecture which combines the advantages of model based design methods with those of real-time learning. The proposed architecture is based on recent advances in the mathematical modeling of dynamical systems. While well suited for a variety of applications in engineering, biology, and ecology, the target application is the safe and reliable control of smart grids. The latter are clearly of vital importance for future economic development and the security of the nation's constantly evolving energy distribution system. Project outcomes will provide practical solutions to complex energy management problems involving uncertain power demands, energy limits, the insertion of renewable resources, and the utilization of grid resources such as virtual batteries, while at the same time maintaining grid stability and reliability.
The proposed hybrid control architecture involves a given system and an assumed physical model both driven by the same control input. The measured difference between their outputs defines an error system. The key idea is to use a generic input-output representation known as a Chen-Fliess functional series to describe this unknown error system. The series coefficients are estimated in real-time via a minimum mean-square error estimator. Effectively, the conventional artificial neuron is replaced here by this new type of learning unit to approximate the error system. The control problem is solved via predictive control using the assumed model and the learned error system. The enabling technology is recent advances in the numerical approximation of Chen-Fliess series which make it possible to implement the scheme in discrete-time. The specific objectives of the project are to (1) advance the theoretical foundations that underpin real-time learning for control applications, including the cascading of these new learning units for deep learning (2) optimize and adapt the novel theoretical results for real-time control of smart grids to provide a priori performance guarantees. The main problem here lies in the uncertainty coming from the over-simplified/poorly modeled dynamics of the grid in addition to the action of renewable resources.