Safe Adaptive Control of Parabolic PDE-ODE Cascades
Abstract
In this paper, we propose a safe adaptive boundary control strategy for a class of parabolic partial differential equation-ordinary differential equation (PDE-ODE) cascaded systems with parametric uncertainties in both the PDE and ODE subsystems. The proposed design is built upon an adaptive Control Barrier Function (aCBF) framework that incorporates high-relative-degree CBFs together with a batch least-squares identification (BaLSI)-based adaptive control that guarantees exact parameter identification in finite time. The proposed control law ensures that: (i) if the system output state initially lies within a prescribed safe set, safety is maintained for all time; otherwise, the output is driven back into the safe region within a preassigned finite time; and (ii) convergence to zero of all plant states is achieved. Numerical simulations are provided to demonstrate the effectiveness of the proposed approach.
Keywords
Cite
@article{arxiv.2602.04656,
title = {Safe Adaptive Control of Parabolic PDE-ODE Cascades},
author = {Yun Jiang and Ji Wang},
journal= {arXiv preprint arXiv:2602.04656},
year = {2026}
}