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arXiv · 2602.04656

Safe Adaptive Control of Parabolic PDE-ODE Cascades

Yun Jiang·Ji Wang
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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.

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Yun Jiang, Ji Wang. 2026-02-04. Safe Adaptive Control of Parabolic PDE-ODE Cascades. https://arxiv.org/abs/2602.04656

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