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Robustness of fractional-order boundary control of time fractional wave equations with delayed boundary measurement using the simple predictor. (English) Zbl 1125.93029
Sabatier, J. (ed.) et al., Advances in fractional calculus. Theoretical developments and applications in physics and engineering. Dordrecht: Springer (ISBN 978-1-4020-6041-0/hbk; 978-1-4020-6042-7/e-book). 543-552 (2007).
Summary: We analyse the robustness of the fractional wave equation with a fractional-order boundary controller subject to delayed boundary measurement. Conditions are given to guarantee stability when the delay is small. For large delays, the Smith predictor is applied to solve the instability problem and the scheme is proved to be robust against a small difference between the assumed delay and the actual delay. The analysis shows that fractional-order controllers are better than integer order controllers in the robustness against delays in the boundary measurement.
MSC:
93C20Control systems governed by PDE
35K60Nonlinear initial value problems for linear parabolic equations
93D21Adaptive or robust stabilization
35B37PDE in connection with control problems (MSC2000)