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arXiv · 2409.10087

Output-feedback stabilization of an underactuated network of N interconnected n + m hyperbolic PDE systems

Jean Auriol
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Abstract

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.

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Jean Auriol. 2024-09-16. Output-feedback stabilization of an underactuated network of N interconnected n + m hyperbolic PDE systems. https://arxiv.org/abs/2409.10087

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