Fuzzy-Based Tracking Control for a Class of Fractional-Order Systems with Time Delays

Abstract

This paper focuses on the tracking control problem for a family of fractional-order systems with unknown drift functions and unknown time delays. By employing fuzzy logic systems (FLSs), the unknown functions are approximated and compensated. Meanwhile, with the help of a hyperbolic tangent function and a sign function, the adverse effects of time-varying delays and FLSs approximation error are mitigated simultaneously. It should be stressed that the proposed method eliminates the assumption that the time delay is bounded by a known function. The stability analysis shows that the tracking error can converge to a small neighborhood of the origin. Finally, simulation is conducted to confirm the effectiveness of the presented control strategy.

Keywords

• fractional-order systems
• fuzzy logic systems
• time delays
• unknown nonlinear functions
• hyperbolic tangent function