Finite-time $$H_{\infty }$$ control of uncertain fractional-order neural networks

Abstract

The problem of finite-time H ∞ control for uncertain fractional-order neural networks is investigated in this paper. Using finite-time stability theory and the Lyapunov-like function method, we first derive a new condition for problem of finite-time stabilization of the considered fractional-order neural networks via linear matrix inequalities (LMIs). Then a new sufficient stabilization condition is proposed to ensure that the resulting closed-loop system is not only finite-time bounded but also satisfies finite-time H ∞ performance. Three examples with simulations have been given to demonstrate the validity and correctness of the proposed methods. Keywords Fractional order neural networks • Finite-time boundedness • H ∞ control problem • Linear matrix inequalities

Robust adaptive self‐structuring neural networks tracking control of unmanned surface vessels with uncertainties and time‐varying disturbances

“…Remark 1. In this article, the main objective is to analyze a high-performance controller (22) for USVs to ensure that the closed-loop system is FTS and to obtain a L 2 gain less or equal to than 𝛾. Controller ( 22) is robust and has good interference attenuation performance.…”

Output feedback finite‐time dissipative control for uncertain nonlinear fractional‐order systems

“…Remark The finite‐time ( R , T , S )‐dissipative w.r.t ( a 1 , a 2 , T f , N , h ) provided in this paper proposed an input–output energy‐related feature to analyze and design of static output feedback controller over a finite‐time interval [26]. When , the finite‐time ( R , T , S )‐dissipative w.r.t ( a 1 , a 2 , T f , N , h ) is reduced to the finite‐time H ∞ performance level α [17]. When , the finite‐time ( R , T , S )‐dissipative w.r.t ( a 1 , a 2 , T f , N , h ) is simplified to the finite‐time strictly passivity.…”

“…The FS problem for the delayed FOS was first studied by M. P. Lazarević [10] by using the Gronwall inequality. Then, by many various techniques such as using Laplace transform, extended Gronwall inequality, and linear matrix inequality (LMI) techniques, many valuable researches on this field have been announced [11][12][13][14][15][16][17][18].…”

Output feedback passification of a class of fractional-order static neural networks

“…Since the NN model described by the fractional-order differential systems can describe the characteristics and properties of dynamical systems more efficiently and accurately, fractional-order NNs have received considerable attention. Many important and interesting problems on fractional-order neural networks (FONNs) such as Lyapunov stability (Yang et al, 2018; Yao et al, 2020; Zhang et al, 2017), finite-time stability (Yang et al, 2021; Wu et al, 2015), passivity analysis (Ding et al, 2019; Padmaja and Balasubramaniam, 2021; Sau et al, 2020; Thuan et al, 2020), synchronization (Wang et al, 2019a), state estimation (Nagamani et al, 2020), guaranteed cost control (Thuan and Huong, 2019), and H ∞ control problems (Sau et al, 2021; Thuan et al, 2020) have been studied by many authors. Note that almost all research investigation concentrated on the fractional-order local field NNs (Ding et al, 2019; Nagamani et al, 2020; Padmaja and Balasubramaniam, 2021; Sau et al, 2020; Thuan and Huong, 2019; Thuan et al, 2020; Wang et al, 2019a; Wu et al, 2015; Yang et al, 2018; Zhang et al, 2017), while relatively few of them concentrated on the fractional-order static neural networks (FOSNNs) (Wu et al, 2016a, 2016b, 2018; Wu and Zou, 2014; Yao et al, 2020; Yang et al, 2021).…”