Addressing the relative degree restriction in nonlinear adaptive observers: A high-gain observer approach |
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| Institution: | 1. Shanghai University of Engineering Science, Shanghai, 201620, China;2. Shanghai Electric Automation Group, Shanghai, 200023, China;3. Key Laboratory of Smart Manufacturing in Energy Chemical Process (East China University of Science and Technology), Ministry of Education, Shanghai, 200237, China;1. College of Electrical Power and Engineering, Taiyuan University of Technology, 79 Yingze West Street, Taiyuan, China;2. Agricultural Bank of China Changzhi Branch, Changzhi, Shanxi, China;3. Department of Chemical Engineering, Chung-Yuan Christian University, Taoyuan, Taiwan, R.O.C.;4. School of Electrical and Electronic Engineering, University of Adelaide, Adealide SA, 5005, Australia;1. Division of Electrical and Electronic Engineering, Graduate School of Engineering, Mie University, Tsu 514-8507, Japan;2. School of Electronics and Information Engineering, Suzhou University of Science and Technology, Suzhou 215009, China;1. State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, Liaoning, 110819, China;2. School of Electrical and Electronic Engineering, Nanyang Technological University, 639798, Singapore;3. College of Sciences, Northeastern University, Shenyang, Liaoning, 110819, China |
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| Abstract: | The design of adaptive observers is a common approach for the joint state and parameter-estimation problem. Nonetheless, there are still some obstacles that have to be solved to improve the design of adaptive observers and extend its implementability to a larger class of systems. First, the separation of the state-estimation and the parameter-estimation requires a relative degree one or zero between some known signal and the parameters to be estimated. Second, standard stability proofs for adaptive observers cannot be easily extended to consider the unavoidable presence of sensor noise and unmodeled system uncertainty. Consequently, on the one hand, this work proposed a methodology to relax the relative degree condition through the use of a high-gain observer that will be coupled with the adaptive observer. On the other hand, the stability and performance of the proposed observer scheme will be analyzed by the use of a strict Lyapunov function based on the Mazenc construction, which allows to have provable convergence and to study the effect of sensor noise and model uncertainty through common Lyapunov theory. Finally, the proposed approach is validated in a compartmental epidemiology model. |
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