Feedback control of hyperbolic PDE systems

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Abstract
This article deals with distributed parameter systems described by first‐order hyperbolic partial differential equations (PDEs), for which the manipulated input, the controlled output, and the measured output are distributed in space. For these systems, a general output‐feedback control methodology is developed employing a combination of theory of PDEs and concepts from geometric control. A concept of characteristic index is introduced and used for the synthesis of distributed state‐feedback laws that guarantee output tracking in the closed‐loop system. Analytical formulas of distributed output‐feedback controllers are derived through combination of appropriate distributed state observers with the developed state‐feedback controllers. Theoretical analogies between our approach and available results on stabilization of linear hyperbolic PDEs are also identified. The developed control methodology is implemented on a nonisothermal plug‐flow reactor and its performance is evaluated through simulations.