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Mission
Mission
LINC seeks to develop machine introspection and learning technologies that continually compare the real-time behavior of a physical system – as measured by on-board sensors – with a learned model of the platform, determine whether the observed behavior differs from that model in ways that might compromise stability and control, and implement an updated control law when required and effectively communicate those updates to the operator.
How do we design autonomous vehicles to operate in the face of unexpected changes in the system dynamics that lie outside their design envelope, such as physical attacks, unforeseen conditions, or unanticipated use? Current practices consider model-based methods that summarize the expected changes in the system dynamics, however, it is intractable to explicitly model a range of systems, their components, & their dynamics in every possible state. The Learning Introspective Control (LINC) program aims to develop machine learning enabled & adaptive controllers that enable physical systems that continually monitor and learn a model of the current system from on-board sensor measurements to update control laws in situ to maintain the stability and control of the vehicle, all the while communicating with the operator of the changes to improve situational awareness and trust.
Our lab, in collaboration with Saab and Dr. Mahmoudian, Dr. Sundaram, and Dr. Mou’s laboratories in Purdue University, is developing a control framework which integrates data-driven and classical optimal control methodologies to achieve these aims. Specifically, we leverage the Koopman operator, which describes a nonlinear system as a linear system in a high-dimensional lifted state space, to model the changed system dynamics online using only onboard sensor measurements. Our demonstration platform is an autonomous surface vehicle called the Wave Adaptive Modular Vehicle (WAM-V), on which we test and evaluate our proposed control framework.
Research Topics and Products
Research Topics and Products
1) Data-driven Models
1) Data-driven Models
Figure: Performance of a Luenberger observer of a pendulm on a cart system, where the outputs are the bearing angles from two observation points. The Luenberger observer is designed using a data-driven Koopman model identified using the OC-EDMD with only output data.
Observability of the Koopman Representation
Observability of the Koopman Representation
The Koopman operator has gained considerable attention due to its ability to represent a nonlinear system as a high-dimensional linear system through nonlinear lifting of the state space. While many algorithms have been proposed to approximate a Koopman representation from data, most assume full knowledge of the state information, whereas, in many applications, only the system’s output may be available. System identification with output data relies on the observability of the system in question, however, whether the Koopman representation is observable for an observable nonlinear system remains an open question. In this work, we bridge the gap by showing the existence of a locally faithful, observable Koopman representation for a nonlinear system that is locally weakly observable. Furthermore, based on the theoretic framework, we propose a data-driven algorithm, called Observable Canonical Extended Dynamic Mode Decomposition (OC-EDMD), which can approximate the Koopman representation directly from output data. Instead of lifting the state of the nonlinear system, we lift the output of the nonlinear system to a higher dimension and construct a finite-dimensional Koopman representation that is observable.
Publications:
H. Park and I. Hwang, “Observability of Koopman Representations and Output Canonical Extended Dynamic Mode Decomposition,” In the Proceedings of the 63rd IEEE Conference on Decision and Control, Milan, Italy, December 16-19, 2024 (accepted)
2) Data-driven Control
2) Data-driven Control
Data-driven Control and Reachability Analysis
Data-driven Control and Reachability Analysis
In collaboration with lcollaboration with Saab and Dr. Mahmoudian, Dr. Sundaram, and Dr. Mou’s laboratories in Purdue University, we have developed a robust data-driven autonomous system for an unmanned surface vessel capable of performing waypoint following and station-keeping of under unknown dynamic conditions. Our approach is based on modular design for ease of transfer of autonomy across different maritime surface vessel platforms. Our proposed learning-based platform comprises a deep Koopman model that learns a linear representation of the nonlinear dynamics of the system using on-board measurements, a change point detector that provides guidance on domain shifts prompting relearning under severe exogenous and endogenous perturbations, and an optimal controller design that recalculate the optimal gain using the learned deep Koopman model. We also developed a algorithm for reachability analysis which uses the learned deep Koopman model to monitor the safety of the autonomous vehicle under changed dynamics.
RefleXAI-demo-stationkeeping.movVideo: Wave Adaptive Modular Vehicle (WAM-V) performing a station-keeping task
RefleXAI-demo-reachability.movVideo: Real-time calculation of forward reachable sets using the learned deep Koopman model
Publication:
J. Li, H. Park, W. Hao, L. Xin, J. Chavez-Galaviz, A. Chaudhary, M. Bloss, C. Vo, K. Pattison, D. Upadhyay, S. Sundaram, S. Mou, I. Hwang, N. Mahmoudian, “C3DKL: Cascade Control with Change Point Detection and Deep Koopman Learning for Time-Varying Systems,” 8th Annual Workshop on Naval Applications of Machine Learning, San Diego, CA, March 11-14, 2024
Publications
H. Park, V. Vijay, and I. Hwang, “Data-driven Reachability Analysis for Nonlinear Systems,” IEEE Control Systems Letters, Vol.8, pp. 2661-2666, December 2 2024, DOI: 10.1109/LCSYS.2024.3510595
H. Park and I. Hwang, “Observability of Koopman Representations and Output Canonical Extended Dynamic Mode Decomposition,” In the Proceedings of the 63rd IEEE Conference on Decision and Control, Milan, Italy, December 16-19, 2024
J. Li, H. Park, W. Hao, L. Xin, J. Chavez-Galaviz, A. Chaudhary, M. Bloss, C. Vo, K. Pattison, D. Upadhyay, S. Sundaram, S. Mou, I. Hwang, N. Mahmoudian, “C3DKL: Cascade Control with Change Point Detection and Deep Koopman Learning for Time-Varying Systems,” 8th Annual Workshop on Naval Applications of Machine Learning, San Diego, CA, March 11-14, 2024
People
Hyunsang Park, Ph.D. student
Joonwon Choi, Ph.D. student
Sponsor
Sponsor
This material is based upon work supported by the Defense Advanced Research Projects Agency (DARPA) via Contract No. N65236-23-C-8012 and under subcontract to Saab, Inc. as part of the RefleXAI project. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the DARPA, the U.S. Government, or Saab, Inc.
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