Output Feedback Finite-Time Stabilization of Systems Subject to Hölder Disturbances via Continuous Fractional Sliding Modes

الملخص EN

The problem of designing a continuous control to guarantee finite-time tracking based on output feedback for a system subject to a Hölder disturbance has remained elusive.

The main difficulty stems from the fact that such disturbance stands for a function that is continuous but not necessarily differentiable in any integer-order sense, yet it is fractional-order differentiable.

This problem imposes a formidable challenge of practical interest in engineering because (i) it is common that only partial access to the state is available and, then, output feedback is needed; (ii) such disturbances are present in more realistic applications, suggesting a fractional-order controller; and (iii) continuous robust control is a must in several control applications.

Consequently, these stringent requirements demand a sound mathematical framework for designing a solution to this control problem.

To estimate the full state in finite-time, a high-order sliding mode-based differentiator is considered.

Then, a continuous fractional differintegral sliding mode is proposed to reject Hölder disturbances, as well as for uncertainties and unmodeled dynamics.

Finally, a homogeneous closed-loop system is enforced by means of a continuous nominal control, assuring finite-time convergence.

Numerical simulations are presented to show the reliability of the proposed method.