We present a control design method for nonlinear partial differential equations (PDEs) based on a combination of gain scheduling and backstepping theory for linear PDEs. A benchmark first-order hyperbolic system with a destabilizing in-domain nonlinearity is considered first. For this system a nonlinear feedback law based on gain scheduling is derived explicitly, and a statement of stability is presented for the closed-loop system. Control designs are then presented for a string and shear beam PDE, both with Kelvin-Voigt damping and potentially destabilizing free-end nonlinearities. String and beam simulation results illustrate the merits of the gain scheduling approach over the linearization-based design.
- Dynamic Systems and Control Division
Gain Scheduling-Inspired Control for Nonlinear Partial Differential Equations
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Siranosian, AA, Krstic, M, Smyshlyaev, A, & Bement, M. "Gain Scheduling-Inspired Control for Nonlinear Partial Differential Equations." Proceedings of the ASME 2009 Dynamic Systems and Control Conference. ASME 2009 Dynamic Systems and Control Conference, Volume 2. Hollywood, California, USA. October 12–14, 2009. pp. 509-516. ASME. https://doi.org/10.1115/DSCC2009-2532
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