On the strict-feedback form of hyperbolic distributed-parameter systems
This work addresses the structural understanding and control design for distributed-parameter systems, specifically hyperbolic PDEs, by extending backstepping methods from ODEs, though it is incremental as it builds on existing results without presenting new stabilization outcomes.
The paper tackled the problem of mapping exactly controllable heterodirectional hyperbolic PDEs and PDE-ODE systems into a strict-feedback form, which is a structural property not previously established for such systems, enabling a recursive backstepping control design.
The paper is concerned with the strict-feedback form of hyperbolic distributed-parameter systems. Such a system structure is well known to be the basis for the recursive backstepping control design for nonlinear ODEs and is also reflected in the Volterra integral transformation used in the backstepping-based stabilization of parabolic PDEs. Although such integral transformations also proved very helpful in deriving state feedback controllers for hyperbolic PDEs, they are not necessarily related to a strict-feedback form. Therefore, the paper looks at structural properties of hyperbolic systems in the context of controllability. By combining and extending existing backstepping results, exactly controllable heterodirectional hyperbolic PDEs as well as PDE-ODE systems are mapped into strict-feedback form. While stabilization is not the objective in this paper, the obtained system structure is the basis for a recursive backstepping design and provides new insights into coupling structures of distributed-parameter systems that allow for a simple control design. In that sense, the paper aims to take backstepping for PDEs back to its ODE origin.