Observer-based boundary control of semi-linear parabolic PDEs with non-collocated distributed event-triggered observation |
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| Authors: | Jun-Wei Wang |
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| Institution: | Key Laboratory of Knowledge Automation for Industrial Processes of Ministry of Education, School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, PR China |
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| Abstract: | This paper deals with the problem of boundary control for a class of semi-linear parabolic partial differential equations (PDEs) with non-collocated distributed event-triggered observation. A semi-linear Luenberger PDE observer with an output error based event-triggering condition is constructed by using the event-triggered observation to exponentially track the PDE state. By the estimated state, a feedback controller is proposed. It has been shown by the Lyapunov technique, and a variant of Poincaré–Wirtinger inequality that the resulting closed-loop coupled PDEs is exponentially stable if a sufficient condition presented in terms of standard linear matrix inequality (LMI) is satisfied. Moreover, a rigorous proof is provided for existence of a minimal dwell-time between two triggering times. Finally, numerical simulation results are given to show the effectiveness of the proposed design method. |
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