In this paper, the problem of time-varying parameter identification is studied. To this aim, two identification algorithms are developed in order to identify time-varying parameters in a finite time or prescribed time (fixed-time). The convergence proofs are based on a notion of finite-time stability over finite intervals of time, i.e., short-finite-time stability, homogeneity for time-varying systems, and Lyapunov-based approach. The results are obtained under injectivity of the regressor term, which is related to the classical identifiability condition. The case of bounded disturbances (noise of measurements) is analyzed for both algorithms. Simulation results illustrate the feasibility of the proposed algorithms.
Bibliographical noteFunding Information:
Manuscript received November 29, 2016; revised November 29, 2016; accepted February 16, 2017. Date of publication February 23, 2017; date of current version June 26, 2017. This work was supported in part by HoTSMoCE Inria associate team program, in part by ANR Finite4SoS (ANR 15 CE23 0007), in part by the Government of Russian Federation under Grant 074-U01, and in part by the Ministry of Education and Science of Russian Federation under Project 14.Z50.31.0031. The work of H. Ríos was supported by CONACyT 270504. Recommended by Associate Editor M. Verhaegen.
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- Finite/Fixed-time (FT/FxT)
- parameter identification
- time-varying systems