On parameter convergence in least squares identification and adaptive control

Funding information National Natural Science Foundation of China, Grant/Award Number: 61703295; Biomedical Engineering Programme, Agency for Science, Technology and Research, Singapore, Grant/Award Number: 1421480015; Fundamental Research Program of Jiangsu Province, China, Grant/Award Number: BK20181183 Summary Least squares estimation is appealing in performance and robustness improvements of adaptive control. A strict condition termed persistent excitation (PE) needs to be satisfied to achieve parameter convergence in least squares estimation. This paper proposes a least squares identification and adaptive control strategy to achieve parameter convergence without the PE condition. A modified modeling error that utilizes online historical data together with instant data is constructed as additional feedback to update parameter estimates, and an integral transformation is introduced to avoid the time derivation of plant states in the modified modeling error. On the basis of these results, a regressor filtering–free least squares estimation law is proposed to guarantee exponential parameter convergence by an interval excitation condition, which is much weaker than the PE condition. And then, an identification-based indirect adaptive control law is proposed to establish exponential stability of the closed-loop system under the interval excitation condition. Illustrative results considering both identification and control problems have verified the effectiveness and superiority of the proposed approach.

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