Robust finite-time stabilizers for five-degree-of-freedom active magnetic bearing system

Finite-time sliding mode control for a 3-DOF fully actuated autonomous surface vehicle

“…According to the local finite-time stability of x = 0 , all states of system (1) exactly reach zero for t ≥ T conv where T conv ≤ π ρ 3 ( ρ 1 ρ 2 ) − 1 . Similar to the previous lemma, the global finite-time stability of x = 0 is guaranteed if V ( bold-italicx ) is radially unbounded onto Γ = R n (Abooee and Arefi, 2019; Abooee et al, 2017; Bhat and Bernstein, 2000) ▪.…”

“…In addition, the global finite-time stability of x = 0 is ensured if V ( bold-italicx ) is radially unbounded onto Γ = R n (Abooee and Arefi, 2019; Abooee et al, 2017; Bhat and Bernstein, 2000; Wang et al, 2019a) ▪.…”

“…In addition, assume that A ∈ R 3 × 3 is a positive definite matrix. Therefore, three following inequalities ( I ), ( II ) and ( III ) expressed by (14) are always valid (Abooee and Arefi, 2019; Abooee et al, 2019).…”

“…On the other hand, in current researches regarding the finite-time stability (Abooee and Arefi, 2018, 2019; Abooee et al, 2017, 2019; Basin, 2019; Chen and Sun, 2020; Ma et al, 2019; Yang et al, 2018; Zhao et al, 2019,), three basic control methods have been represented and established to deal with the nonlinear systems’finite-time stabilization problem, including the direct Lyapunov method, along with several applicable lemmas (Bhat and Bernstein, 1998, 2000; Feng et al, 2020; Polyakov and Poznyak, 2009), the creative method based on the geometric homogeneity conception (Bhat and Bernstein, 1998) and the terminal sliding mode control (TSMC) method (Abooee and Arefi, 2019; Abooee et al, 2017, 2019; Moradi Zirkohi, 2019; Zuo and Tie, 2014). Advantages and disadvantages of these finite-time stabilization techniques have been explained and discussed comprehensively in Abooee and Arefi (2019), Abooee et al (2017, 2019) and Sun et al (2019).…”

“…According to the aforementioned applications of ASVs, the accurate path-following problem of these vehicles has recently become an active and interesting research topic in control and ocean engineering societies. Therefore, a large number of scientific investigations have focused on this problem (Abooee and Arefi, 2019; Ertogan et al, 2015; Huang et al, 2015; Li et al, 2015; Ngo et al, 2017; Skjetne et al, 2005; Sun et al, 2017b; Witkowska and Smierzchalski, 2009) and researchers have applied many different control methods such as PID or PD control (Fang et al, 2012; Larrazabal and Peñas, 2016; Su et al, 2017), sliding mode control (SMC) (Ashrafiuon et al, 2008; Chwa, 2011; Koshkouei et al, 2007; Perera and Soares, 2012; Zhang et al, 2000), backstepping method (Do and Pan, 2006; Huang et al, 2015), model predictive control (MPC) (Li and Sun, 2012; Saari and Djemai, 2012; Tzeng, 1999), adaptive-SMC method (Sun et al, 2017b; Zhang and Zhang, 2015; Zhang et al, 2017; Zheng et al, 2017), adaptive-backstepping method (Do, 2016; Du et al, 2007; Hu et al, 2017; Yin and Xiao, 2017), feedback linearization control (Consolini and Tosques, 2012), adaptive-neural networks method (He et al, 2016, Zhang et al, 2015), adaptive-fuzzy approach (Wang et al, 2016), fuzzy-SMC strategy (Ngo et al, 2017) and fuzzy-neural networks method (Fang and Lee, 2016, Wang and Er, 2014).…”