Adaptive error feedback regulation problem for 1D wave equation
Wei Guo
School of Statistics, University of International Business and Economics, Beijing, China
Search for more papers by this authorCorresponding Author
Hua-cheng Zhou
School of Electrical Engineering, Tel Aviv University, Tel Aviv, Israel
Correspondence
Hua-cheng Zhou, School of Electrical Engineering, Tel Aviv University, Tel Aviv 69978, Israel.
Email: [email protected]
Search for more papers by this authorMiroslav Krstic
Department of Mechanical and Aerospace Engineering, University of California, San Diego, CA, USA
Search for more papers by this authorWei Guo
School of Statistics, University of International Business and Economics, Beijing, China
Search for more papers by this authorCorresponding Author
Hua-cheng Zhou
School of Electrical Engineering, Tel Aviv University, Tel Aviv, Israel
Correspondence
Hua-cheng Zhou, School of Electrical Engineering, Tel Aviv University, Tel Aviv 69978, Israel.
Email: [email protected]
Search for more papers by this authorMiroslav Krstic
Department of Mechanical and Aerospace Engineering, University of California, San Diego, CA, USA
Search for more papers by this authorSummary
By using the adaptive control approach, we solve the error feedback regulator problem for the one-dimensional wave equation with a general harmonic disturbance anticollocated with control and with two types of disturbed measurements, ie, one collocated with control and the other anti-collocated with control. Different from the classical error feedback regulator design, which is based on the internal mode principle, we give the adaptive servomechanism design for the system by making use of the measured tracking error (and its time derivative) and the estimation mechanism for the parameters of the disturbance and of the unknown reference. Constructing auxiliary systems and observer and applying the backstepping method for infinite-dimensional system play important roles in the design. The control objective, which is to regulate the tracking error to zero and to keep the states bounded, is achieved.
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