2018
DOI: 10.1002/asjc.1924
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Continuous Fixed‐Time Convergent Super‐Twisting Algorithm in Case of Unknown State and Disturbance Initial Conditions

Abstract: This paper presents a fixed-time convergent super-twisting-like algorithm designed to provide a direct extension, without any additional terms, of the conventional super-twisting control system, whose state initial condition is unknown and the disturbance initial condition is bounded by a known constant or even completely unknown. The fixed-time convergent super-twisting-like algorithm is first designed for a scalar system and then generalized to a multivariable one. An upper estimate of its convergence (settl… Show more

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Cited by 31 publications
(13 citation statements)
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References 34 publications
(82 reference statements)
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“…Definition 4 (see [36]). The system (29) is called fixed-time convergent to the origin, if the origin is globally finite-time stable and the settling time function Tðx 0 Þ is bounded by positive constant T max > 0, i.e., the system state xðt, x 0 Þ ∈ R n is equal to zero, for all t ≥ T max , starting from any initial condition x 0 .…”
Section: Definition and Lemmasmentioning
confidence: 99%
“…Definition 4 (see [36]). The system (29) is called fixed-time convergent to the origin, if the origin is globally finite-time stable and the settling time function Tðx 0 Þ is bounded by positive constant T max > 0, i.e., the system state xðt, x 0 Þ ∈ R n is equal to zero, for all t ≥ T max , starting from any initial condition x 0 .…”
Section: Definition and Lemmasmentioning
confidence: 99%
“…As follows from Theorem 1, adding the fourth exponential term (6) in the control law (12), Àh (e jv(t)j À1) e jv(t)j (tf Àt) sign(v(t)), makes this finitetime convergence predefined for a time no greater than t f . Finally, as follows from Theorem 1 in Basin et al (2019), adding the second term in the control law (12), Àl 2 jv(t)j p sign(v(t)) with l 2 . 0, yields fixed-time convergence of system states (13) to the origin, if h = 0, and suppression of the disturbance _ z(t).…”
Section: Control Designmentioning
confidence: 99%
“…Fixed-time convergent algorithms, where the convergence times are independent of state initial conditions, are studied starting from Andrieu et al (2008) and Polyakov (2012). Continuous fixed-time convergent scalar and multi-variable control laws are proposed in Basin et al (2019) for a super-twisting system, whose state and disturbance initial conditions are unknown, and the upper estimates of their convergence times are calculated. A continuous fixed-time convergent control law driving the states of a stochastic super-twisting system at the origin for a fixed-time is designed in Guerra-Avellaneda and .…”
Section: Introductionmentioning
confidence: 99%
“…This difficulty in linear system is handled by assigning multi‐step sets associated with scaling parameters which guarantee the closed‐loop H∞ performance using random system trajectories 11 . Further, in Basin et al, 12 a direct extension is provided for the unknown state and disturbance initial conditions of a super‐twisting control algorithm by designing a fixed‐time convergent smooth second‐order observer. The developed approach identified the drawback of zero initial value for the disturbance while calculating the upper estimate of control algorithm convergence time and overcomes it by admitting a disturbance with unknown but bounded initial value.…”
Section: Introductionmentioning
confidence: 99%