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Exponential Stabilization of the Uncertain Wave Equation via Distributed Dynamic Input Extension

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3 Author(s)
Orlov, Y. ; Dept. of Electr. & Electron. Eng., Univ. of Cagliari, Cagliari, Italy ; Pisano, A. ; Usai, E.

The wave equation is studied under the effect of a persistent external perturbation. A dynamical distributed controller is suggested, based on an infinite-dimensional generalization of second-order sliding-mode control techniques, that provides the exponential attainment of a sufficiently smooth arbitrary reference of the state trajectory. The control system comprises of both feedforward and feedback parts, the latter being a discontinuous term directly connected to the plant input through a dynamical filter that augments the system state smoothing out the discontinuity of the feedback control loop. As a result, a continuous input is applied to the plant. A constructive Lyapunov-based proof of convergence of the proposed control algorithm is carried out and supporting numerical results are presented.

Published in:

Automatic Control, IEEE Transactions on  (Volume:56 ,  Issue: 1 )