Output-Feedback Stabilization of an Underactuated Network of N Interconnected n plus m Hyperbolic PDE Systems

• 成果类型: Article
• 署名作者: Auriol, Jean
• 署名单位: Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3462633
• 发表日期: 2025
• 页码: 1563-1575
• 关键词: Couplings; observers; mathematical models; Extremities; Backstepping; vectors; trajectory; difference systems; partial differential equations (PDEs) networks; predictor; tracking

摘要

In this article, we detail the design of an output feedback stabilizing control law for an underactuated network of N subsystems of n+m heterodirectional linear first-order hyperbolic partial differential equations interconnected through their boundaries. The network has a chain structure, as only one of the subsystems is actuated. The available measurements are located at the opposite extremity of the chain. The proposed approach introduces a new type of integral transformation to tackle in-domain couplings in the different subsystems while guaranteeing a clear actuation path between the control input and the different subsystems. Then, it is possible to state several essential properties of each subsystem: output trajectory tracking, input-to-state stability, and predictability (the possibility of designing a state prediction). We recursively design a stabilizing state-feedback controller by combining these properties. We then design a state observer that reconstructs delayed values of the states. This observer is combined with the state-feedback control law to obtain an output-feedback controller. Simulations complete the presentation.