Safe Adaptive Control of Parabolic PDE-ODE Cascades

TL;DR

This paper introduces a safe adaptive boundary control method for parabolic PDE-ODE systems with uncertainties, ensuring safety and convergence through an adaptive CBF framework and finite-time parameter identification.

Contribution

It develops a novel adaptive control strategy combining high-relative-degree CBFs with batch least-squares identification for PDE-ODE cascades with uncertainties.

Findings

Guarantees safety if initially safe, or drives system into safe set within finite time.

Achieves convergence of all plant states to zero.

Numerical simulations confirm effectiveness of the control approach.

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.