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Contraction Theory for Robust Learning-Based Control: Toward Aerospace and Robotic Autonomy


Tsukamoto, Hiroyasu (2023) Contraction Theory for Robust Learning-Based Control: Toward Aerospace and Robotic Autonomy. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/rznp-g568.


Machine learning and AI have been used for achieving autonomy in various aerospace and robotic systems. In next-generation research tasks, which could involve highly nonlinear, complicated, and large-scale decision-making problems in safety-critical situations, however, the existing performance guarantees of black-box AI approaches may not be sufficiently powerful. This thesis gives a mathematical overview of contraction theory, with some practical examples drawn from joint projects with NASA JPL, for enjoying formal guarantees of nonlinear control theory even with the use of machine learning-based and data-driven methods. This is not to argue that these methods are always better than conventional approaches, but to provide formal tools to investigate their performance for further discussion, so we can design and operate truly autonomous aerospace and robotic systems safely, robustly, adaptively, and intelligently in real-time.

Contraction theory is an analytical tool to study differential dynamics of a non-autonomous (i.e., time-varying) nonlinear system under a contraction metric defined with a uniformly positive definite matrix, the existence of which results in a necessary and sufficient characterization of incremental exponential stability of multiple solution trajectories with respect to each other. Its nonlinear stability analysis boils down to finding a suitable contraction metric that satisfies a stability condition expressed as a linear matrix inequality, resulting in many parallels drawn between linear systems theory and contraction theory for nonlinear systems. This yields much-needed safety and stability guarantees for neural network-based control and estimation schemes, without resorting to a more involved method of using uniform asymptotic stability for input-to-state stability. Such distinctive features permit the systematic construction of a contraction metric via convex optimization, thereby obtaining an explicit exponential bound on the distance between a time-varying target trajectory and solution trajectories perturbed externally due to disturbances and learning errors. The first two parts of this thesis are about a theoretical overview of contraction theory and its advantages, with an emphasis on deriving formal robustness and stability guarantees for deep learning-based 1) feedback control, 2) state estimation, 3) motion planning, 4) multi-agent collision avoidance and robust tracking augmentation, 5) adaptive control, 6) neural net-based system identification and control, for nonlinear systems perturbed externally by deterministic and stochastic disturbances. In particular, we provide a detailed review of techniques for finding contraction metrics and associated control and estimation laws using deep neural networks.

In the third part of the thesis, we present several numerical simulations and empirical validation of our proposed approaches to assess the impact of our findings on realizing aerospace and robotic autonomy. We mainly focus on the two joint projects with NASA JPL: 1) Science-Infused Spacecraft Autonomy for Interstellar Object Exploration and 2) Constellation Autonomous Space Technology Demonstration of Orbital Reconfiguration (CASTOR), where we also perform hardware demonstrations of our methods using our thruster-based spacecraft simulators (M-STAR) and in high-conflict, distributed, intelligent UAV swarm reconfiguration with up to 20 UAVs (crazyflies).

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Nonlinear Control; Robust and Adaptive Control; Optimal Control; Machine Learning; Aerospace Autonomy; Robotics Autonomy; Contraction Theory
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Space Engineering
Awards:William F. Ballhaus Prize, 0223. IEEE Conference on Decision and Control (CDC) Student Travel Support Award, Dec. 2021. IEEE American Control Conference (ACC) Student Travel Support Award, May 2021. IEEE CDC Student Travel Support Award, Dec. 2020. Honjo International Scholarship Award, Aug. 2020. Caltech Vought Fellowship, Oct. 2017. Funai Overseas Scholarship Award.
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Chung, Soon-Jo
Thesis Committee:
  • Pellegrino, Sergio (chair)
  • Doyle, John C.
  • Murray, Richard M.
  • Watkins, Michael M.
  • Chung, Soon-Jo
Defense Date:15 May 2023
Funding AgencyGrant Number
Defense Advanced Research Projects Agency (DARPA)UNSPECIFIED
Funai Foundation for Information TechnologyUNSPECIFIED
Honjo International Scholarship FoundationUNSPECIFIED
Projects:Science-Infused Spacecraft Autonomy for Interstellar Object Exploration, Constellation Autonomous Space Technology Demonstration of Orbital Reconfiguration (CASTOR)
Record Number:CaltechTHESIS:05262023-141116640
Persistent URL:
Related URLs:
URLURL TypeDescription adapted for Chapters 2 - 8. adapted for Chapters 3 - 4. adapted for Chapters 5 - 6. adapted for Chapters 5 - 6. adapted for Chapter 7.
Tsukamoto, Hiroyasu0000-0002-6337-266
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:15210
Deposited By: Hiroyasu Tsukamoto
Deposited On:06 Jun 2023 15:09
Last Modified:16 Jun 2023 16:27

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