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A novel adaptive control algorithm based on non-linear Laguerre—Volterra observer

Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, P.R. China, Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK, hz254{at}cam.ac.uk

Larissa Tischenko

Judge Business School, University of Cambridge, Trumpington Street, Cambridge CB2 1AG, UK

Pin-Ze Yu

Department of Optoelectronics Science and Technology, Chinese Naval University of Engineering, Wuhan 430033, P.R. China

By expanding each kernel using an orthonormal Laguerre series, a Volterra functional series is used to represent the input—output relation of a non-linear dynamic system. When Volterra series and Laguerre series truncations are allowed, an appropriate choice of the Laguerre filter pole permits a description of the process dynamics with a small number of parameters. Feeding back the error of the outputs of the plant and the model, we design a novel non-linear state observer, based on which a stable output feedback control law is derived for both regulator and tracking problems. To support this algorithm, we present the theoretical analyses of its nominal stability, which allows us to obtain the state feedback gain and the observer gain solely by solving two linear matrix inequalities (LMIs). In addition, another theorem is also given to show its capability of minimizing the steady-state tracking errors. To handle more complex dynamics, we improve the standard recursive least square estimation (RLSE) identification method to a normalized one with guaranteed convergence. Finally, control simulations on a benchmark problem — a continuous stirring tank reactor (CSTR) process — and experiments on a chemical reactor temperature control system are performed. This method, especially its essential idea of a Volterra non-linear observer, has shown great potential for the control of a large class of non-linear dynamic systems.

Key Words: Laguerre series • linear matrix inequality • LMI • non-linear observer • recursive least square estimation • RLSE • Volterra series

Transactions of the Institute of Measurement and Control, Vol. 31, No. 2, 129-151 (2009)
DOI: 10.1177/0142331207088192


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