Adaptive fractional-order switching-type control method design for 3D fractional-order nonlinear systems

Abstract

In this paper, an adaptive sliding mode technique based on a fractional-order (FO) switching-type control law is designed to guarantee robust stability for uncertain 3D FO nonlinear systems. A novel FO switching-type control law is proposed to ensure the existence of the sliding motion in finite time. Appropriate adaptive laws are shown to tackle the uncertainty and external disturbance. The calculation formula of the reaching time is analyzed and computed. The reachability analysis is visualized to show how to obtain a shorter reaching time. A stability criterion of the FO sliding mode dynamics is derived based on indirect approach to Lyapunov stability. posed control scheme are illustrated through numerical simulations.

A comparative study of the vibro-impact capsule systems with one-sided and two-sided constraints

“…It is also worth to develop a general control method for such type of nonlinear systems, e.g. [31,32], particularly when the number of nonlinearities increases, the dynamics of the system will become more complex from periodic motion to chaos.…”

Extended dissipative state estimation for memristive neural networks with time-varying delay

“…Numerical examples and their simulations are given to illustrate the usefulness and effectiveness of the proposed results. In future, the employed methods can be developed to study MNNs' other dynamical behaviors such as finite-time stability, state bounding analysis, fractional dynamics [38,39], uncertainty mining [40,41] and so on.…”

Robust Control of Uncertain Nonlinear Systems: A Nonlinear DOBC Approach

“…Rather than directly estimating the uncertain parameters as in many adaptive control algorithms [21], as shown in Eq. (2), it estimates the total difference between the nominal model and the physical system, which may include both structured or unstructured uncertainty.…”