OPERATOR THEORETIC METHODS FOR DATA-DRIVEN CONTROL SYNTHESIS
Abstract
The United States Air Force (USAF) April 2019 Science and Technology Strategy report identifies the need for the USAF to “develop and deliver transformational capabilities” while “maintaining the ability to dominate time, space, and complexity in future conflict across all operating domains to project power and defend the homeland. To achieve said dominance, the report emphasizes operational strategies that increase the speed and the complexity of the battlespace by transforming the “current force structure, which emphasizes relatively low numbers of high value assets,” into one that overwhelms hostile forces through augmentation of high-end platforms with larger numbers of inexpensive, low-end systems capable of rapid and effective decision making. While artificial intelligence, as an asset to support rapid and effective decision making, is invaluable, the decision-making challenges that stem from limited availability of training data in ever-evolving battlespaces necessitate the development of learning tools that incorporate prior knowledge into the learning process. Moreover, computationally efficient methods for numerical optimization of decisions and trajectories are necessary for coordinated deployment of a large volume of assets. In response, this project aims to develop a novel operator theoretic framework to facilitate fast data-and-model-driven decision making that will lead to improved command and control methods for coordinated deployment of large teams of autonomous assets. The PIs propose to develop novel operator theoretic techniques for data and modeldriven synthesis of control policies through synthesis of control Lyapunov functions (CLFs) and solution of optimal control problems. The proposed technical tasks focus on the use of trajectories (i.e., time-series) as the fundamental unit of data for the resolution of control synthesis and certification problems in dynamical systems. Trajectory information in the dynamical systems is embedded in a reproducing kernel Hilbert space (RKHS) through what will be called occupation kernels. The occupation kernels are tied to the dynamics of the system through the densely defined Liouville operator. The pairing of Liouville operators and occupation kernels results in an operator theoretic framework that allows for nontrivial information concerning the dynamical systems to be extracted from the RKHS. If successful, the efforts in this project will lead to mathematically rigorous methods, that admit efficient linear and/or quadratic programming based numerical approximations, for construction of CLFs and solution of optimal control problems using data-driven black-box and gray-box models.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 12, 2021
- Source ID
- FA95502010127
Entities
People
- Rushikesh Kamalapurkar
Organizations
- Air Force Office of Scientific Research
- Oklahoma State University–Stillwater
- United States Air Force