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<p>The traditional barrier Lyapunov function (BLF) method has proven effective for the adaptive control problem of time-invariant state constrained fractional-order systems (FOSs). However, it is difficult to extend this method directly to the case with time-varying state constraints (TVSCs). This is because the composite function has a complicated fractional-order derivative. In this paper, by constructing fractional-order auxiliary filters and using the properties of fractional-order calculus, the BLF is used to address the adaptive control problem of incommensurate fractional-order nonlinear systems with TVSCs. The proposed control scheme in this paper can be used to control FOSs with time-invariant state constraints. It also encompasses adaptive control schemes for integer-order systems with TVSCs as a special case. In addition, the numerical examples are presented to confirm the control method proposed in this article.</p>

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Design of Adaptive Control Scheme for Time-Varying State Constrained Incommensurate Fractional-Order Systems

  • 期刊论文

  • 发表日期：

    2025年8月14日

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  • Boqiang Cao,
  • Ting Kang,
  • Xudong Hai

摘要

The traditional barrier Lyapunov function (BLF) method has proven effective for the adaptive control problem of time-invariant state constrained fractional-order systems (FOSs). However, it is difficult to extend this method directly to the case with time-varying state constraints (TVSCs). This is because the composite function has a complicated fractional-order derivative. In this paper, by constructing fractional-order auxiliary filters and using the properties of fractional-order calculus, the BLF is used to address the adaptive control problem of incommensurate fractional-order nonlinear systems with TVSCs. The proposed control scheme in this paper can be used to control FOSs with time-invariant state constraints. It also encompasses adaptive control schemes for integer-order systems with TVSCs as a special case. In addition, the numerical examples are presented to confirm the control method proposed in this article.