Networked Boundary Control of Damped Wave Equations

This chapter considers the boundary control of damped wave equations using a boundary measurement in a networked control system (NCS) setting. In this networked boundary control system, the induced delays can be lumped as the boundary measurement delay. The Smith predictor is applied to the networked boundary control problem and the instability problem due to large delays is solved and the scheme is proved to be robust against a small difference between the assumed delay and the actual delay. In addition, we analyze the robustness of the time-fractional order 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, again 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.

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