Nonlinear Analysis (Jan 2022)

Robust piecewise adaptive control for an uncertain semilinear parabolic distributed parameter systems

  • Yanfang Lei,
  • Junmin Li,
  • Ailiang Zhao

DOI
https://doi.org/10.15388/namc.2022.27.25195
Journal volume & issue
Vol. 27

Abstract

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In this study, we focus on designing a robust piecewise adaptive controller to globally asymptotically stabilize a semilinear parabolic distributed parameter systems (DPSs) with external disturbance, whose nonlinearities are bounded by unknown functions. Firstly, a robust piecewise adaptive control is designed against the unknown nonlinearity and the external disturbance. Then, by constructing an appropriate Lyapunov–Krasovskii functional candidate (LKFC) and using the Wiritinger’s inequality and a variant of the Agmon’s inequality, it is shown that the proposed robust piecewise adaptive controller not only ensures the globally asymptotic stability of the closed-loop system, but also guarantees a given performance. Finally, two simulation examples are given to verify the validity of the design method.

Keywords