Adaptive control was originally proposed to control systems, the model of which changes over time. However, traditionally, classical adaptive control has been developed for systems with constant parameters. This chapter surveys the so-called congelation of variables method to overcome the obstacle of time-varying parameters. Two examples, illustrating how to deal with time-varying parameters in the feedback path and in the input path, respectively, are first presented. Then n-dimensional lower triangular systems to show how to combine the congelation of variables method with adaptive backstepping are discussed. Finally, we study how to control a class of nonlinear systems via output feedback: this is a problem that cannot be solved directly due to the coupling between the input and the time-varying perturbation. It turns out that if we assume a strong minimum-phase property, namely, ISS of the inverse dynamics, such a coupling is converted into a coupling between the output and the time-varying perturbation. Then, a small-gain-like analysis, which takes all subsystems into account, yields a controller that achieves output regulation and boundedness of all closed-loop signals. Simulation results to demonstrate that the proposed controller achieves asymptotic output regulation and outperforms the classical adaptive controller in the presence of time-varying parameters are presented.

Chen, K., Astolfi, A. (2021). Adaptive Control for Systems with Time-Varying Parameters—A Survey. In C.P. Zhong-Ping Jiang (a cura di), Trends in Nonlinear and Adaptive Control (pp. 217-247). Springer [10.1007/978-3-030-74628-5_8].

Adaptive Control for Systems with Time-Varying Parameters—A Survey

Astolfi A.
2021-09-01

Abstract

Adaptive control was originally proposed to control systems, the model of which changes over time. However, traditionally, classical adaptive control has been developed for systems with constant parameters. This chapter surveys the so-called congelation of variables method to overcome the obstacle of time-varying parameters. Two examples, illustrating how to deal with time-varying parameters in the feedback path and in the input path, respectively, are first presented. Then n-dimensional lower triangular systems to show how to combine the congelation of variables method with adaptive backstepping are discussed. Finally, we study how to control a class of nonlinear systems via output feedback: this is a problem that cannot be solved directly due to the coupling between the input and the time-varying perturbation. It turns out that if we assume a strong minimum-phase property, namely, ISS of the inverse dynamics, such a coupling is converted into a coupling between the output and the time-varying perturbation. Then, a small-gain-like analysis, which takes all subsystems into account, yields a controller that achieves output regulation and boundedness of all closed-loop signals. Simulation results to demonstrate that the proposed controller achieves asymptotic output regulation and outperforms the classical adaptive controller in the presence of time-varying parameters are presented.
set-2021
Settore ING-INF/04 - AUTOMATICA
English
Rilevanza internazionale
Capitolo o saggio
Chen, K., Astolfi, A. (2021). Adaptive Control for Systems with Time-Varying Parameters—A Survey. In C.P. Zhong-Ping Jiang (a cura di), Trends in Nonlinear and Adaptive Control (pp. 217-247). Springer [10.1007/978-3-030-74628-5_8].
Chen, K; Astolfi, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/303063
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