Thesis title: Energy-Based and Machine Learning Approaches to Passivity-Preserving and Safety-Critical Control
This thesis advances the synthesis and analysis of nonlinear, safety‑aware controllers by leveraging an energy/passivity viewpoint and modern computational tools. Across three studies, we (i) compare how distinct Control Barrier Function (CBF) designs reshape energy flows and closed‑loop performance in safety‑critical control of robotic systems, (ii) develop a Physics‑Informed Neural Networks (PINNs) framework to automate the core partial differential equation (PDE) step of Interconnection and Damping Assignment Passivity‑Based Control (IDA‑PBC), and (iii) introduce a model‑based machine‑learning method to synthesize CBFs that preserve passivity of the closed loop under input saturation. Collectively, the results provide a structured path to controllers that guarantee invariance or stabilization while making explicit the energetic mechanisms, shaping, dissipation, and transfer, through which those guarantees are realized.
Two research streams run through all three articles. An energy/passivity‑centric perspective as a unifying language for design and analysis. The first study shows how energy‑based and exponential CBFs alter energy transfers and impact performance in safety‑critical tasks. The second exploits the port‑Hamiltonian structure of IDA‑PBC to assign a desired energetic architecture and achieve asymptotic stability through damping, with PINNs solving the kinetic‑energy PDE up to small residuals. The third enforces safety with CBFs while ensuring that passivity, a property fundamentally tied to energy balance, is retained even with actuator limits. Constructive, computation‑ready synthesis validated on realistic systems. We move beyond existence results by providing methods and evidence that scale to nonlinear and underactuated systems: a comparative CBF study on obstacle avoidance with simulations on a 3R planar robot and a 7‑DoF manipulator plus hardware tests; a PINN‑based IDA‑PBC pipeline that reduces reliance on restrictive solvability assumptions and attains stabilization via appropriate damping when the kinetic‑energy PDE is solved to a small error; and a passivity‑preserving, learning‑assisted CBF design evaluated on cart‑pole and 2R manipulators under input saturation.
Together these contributions clarify the trade‑offs among safety, performance, and energetic behavior; expand the toolbox for energy‑shaping and safety‑critical design with machine‑learning.