Adaptive backstepping control for fractional order systems with input saturation

Approximation‐based adaptive fault compensation backstepping control of fractional‐order nonlinear systems: An output‐feedback scheme

“…Moreover, at larger γ i , the control action may become aggressive. Smaller values of the σ ‐modification parameter, that is, σ i , lead to a smaller ultimate bound in the adaptive laws, while it may result in a parametric drift. Remark The backstepping control approaches that are proposed in References for then nonlinear fractional‐order systems cannot meet the fault compensation and are only beneficial in uncertain fractional‐order systems. The adaptive controls are assessed with respect to a category of strict‐feedback systems containing fault compensation design in Reference , which cannot be applied in fractional‐order systems.…”

“…Moreover, the employment of the fractional‐order controllers increases the degree of freedom and enhances the system performance in dynamical systems . Some available strategies, such as adaptive, optimal, and proportional integral derivative (PID) controllers, are exploited to control the systems' fractional order . The stability of these systems is very essential in control systems and also is discussed in some recent works.…”

“…29 Some available strategies, such as adaptive, optimal, and proportional integral derivative (PID) controllers, are exploited to control the systems' fractional order. [30][31][32][33][34][35] The stability of these systems is very essential in control systems and also is discussed in some recent works. In this context, the unknown external disturbances are of concern for a category of these systems in Reference 36.…”

Sufficient and necessary conditions for stabilizing singular fractional order systems with partially measurable state

“…They often appear in various practical applications such as viscoelastic systems, electrochemistry, economy and biology systems [1][2][3]. Due to its importance in both theoretical study and practical applications, such systems attract increasing attention, especially with respect to system identification [4,5], stability analysis [6,7], controller synthesis [8,9] and numerical computing [10,11], etc.…”

Mittag-Leffler stabilization of fractional-order nonlinear systems with unknown control coefficients

“…The overparametrization and partial overparametrization problems were soon eliminated by elegantly introducing the tuning functions [33,35]. On the other hand, with the aids of this frequency distribute model and the indirect Lyapunov method, the adaptive backstepping control of fractional-order systems were established [37][38][39]. As far as we know, there are few results on the generalization of backstepping into fractional-order systems.…”