The Tracking Control of the Variable-Order Fractional Differential Systems by Time-Varying Sliding-Mode Control Approach
Open Access
- 22 April 2022
- journal article
- research article
- Published by MDPI AG in Fractal and Fractional
- Vol. 6 (5), 231
- https://doi.org/10.3390/fractalfract6050231
Abstract
This paper is concerned with the problem of tracking control for a class of variable-order fractional uncertain system. In order to realize the global robustness of systems, two types of controllers are designed by the global sliding-mode control method. The first one is based on a full-order global sliding-mode surface with variable-order fractional type, and the control law is continuous, which is free of chattering. The other one is a novel time-varying control law, which drives the error signals to stay on the proposed reduced-order sliding-mode surface and then converges to the origin. The stability of the controllers proposed is proved by the use of the variable-order fractional type Lyapunov stability theorem and the numerical simulation is given to validate the effectiveness of the theoretical results.Keywords
Funding Information
- Shandong University of Technology (ZR2020QA037)
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