Safe Control of Hyperbolic PDE-ODE Cascades

Motivated by control of a delivery unmanned aerial vehicle with a cable-suspended load, with the purpose of avoiding collision of the payload with the surrounding environment, we design safe control for a cascade system consisting of hyperbolic PDEs and ODEs. The considered class of plants is 2×2 hyperbolic PDEs sandwiched by a strict-feedback nonlinear ODE and a linear ODE. This is the first safe control design for hyperbolic PDEs, where we apply the backstepping method and introduce the concept of PDE control barrier function (CBF) whose non-negativity as well as the ODE CBF's non-negativity are ensured to achieve the safety goal. The designed controller guarantees: 1) the safety of the state furthermost from the control input; 2) the exponential regulation of the overall plant state to zero. The effectiveness of the proposed method is illustrated by numerical simulation.