Nonlinear fixed-time control protocol for uniform allocation of agents on a segment

Parsegov, Sergei; Polyakov, Andrey; Shcherbakov, Pavel

doi:10.1109/cdc.2012.6426570

Cited by 122 publications

(66 citation statements)

References 26 publications

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“…From the above analysis, it can be concluded that the double-integrator system with output feedback control law (19) does not escape in any finite time interval. Following the analysis at the beginning of the proof, one has that the closed-loop system under (2), (11) and (19) is fixed-time stable.…”

Section: Casementioning

confidence: 99%

“…Furthermore, if the system trajectory under the output feedback control law does not escape during the interval t ∈ [0, T 1 ], it follows from Theorem 11 that there exists a finite time, i.e., T 2 , uniformly in x(T 1 ) to ensure the fixed-time stability of double-integrator system. Therefore, the condition that the closed-loop system under output feedback control law (19) does not escape in finite time is sufficient to derive the conclusion of Theorem 13. It should be noted that the method in [11] can not be applied here, since the right hand side of the closed-loop system under (2), (11) and (19) does not satisfy the linear growth condition.…”

Section: Theorem 13mentioning

confidence: 99%

“…In addition, it looks promising for a system if a controller or an observer can be designed to ensure that the convergence is achieved in a fixed-time duration regardless of initial conditions. A sufficient condition for the fixed-time stability of nonlinear systems was provided in [13] and some fixed-time control laws, such as [18] and [19], were derived based on this condition. However, it is nontrivial to construct a Lyapunov function satisfying particular conditions for high-order systems.…”

Section: Introductionmentioning

confidence: 99%

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A fixed-time output feedback control scheme for double integrator systems

et al. 2017

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A continuous output feedback control scheme rendering the closed-loop double integrator system globally stable in finite-time is presented. In particular, the convergence time is independent of initial conditions. The bi-limit homogeneous technique is used for controller and observer designs with fixed-time convergence. Then, a continuous output feedback control law is proposed for nominal double-integrator system and its perturbed version. The homogeneity and Lyapunov techniques are used to ensure the fixed-time stability of the closed-loop system under output feedback control framework. Finally, the efficiency of the proposed algorithms are illustrated by numerical simulations.

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Section: Casementioning

confidence: 99%

Section: Theorem 13mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A fixed-time output feedback control scheme for double integrator systems

et al. 2017

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“…Based on the study of Parsegov and Polyakov [32] , we choose an alternate variable z i = e i 1 γ . Then, we obtain…”

Section: B Preliminariesmentioning

confidence: 99%

Adaptive nonsingular terminal sliding mode control design for near space hypersonic vehicles

Zhang

Dong

Sun

2014

IEEE/CAA J. Autom. Sinica

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This paper presents an adaptive nonsingular terminal sliding mode approach for the attitude control of near space hypersonic vehicles (NSHV) in the presence of parameter uncertainties and external disturbances. Firstly, a novel nonsingular terminal sliding surface is developed and its finitetime convergence is analyzed. Then, an adaptive nonsingular terminal sliding mode control law is proposed, which is chattering free. In the proposed approach, all parameter uncertainties and external disturbances are lumped into one term, which is estimated by an adaptive uncertainty estimation for eliminating the boundary requirement needed in the conventional control design. Subsequently, stability of the closed-loop system is proven based on Lyapunov theory. Finally, the proposed approach is applied to the attitude control design for NSHV. Simulation results show that the proposed approach attains a satisfactory performance in the presence of parameter uncertainties and external disturbances.

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“…To this end, the class of systems

\overset{x}{true} = - {false(α false| x {false|}^{p} + β false| x {false|}^{q} false)}^{k} sign false(x false), x false(0 false) = x_{0},

where x is a scalar state variable and the real numbers α , β , p , q , k >0 are system parameters, which satisfy the constraints kp <1, and kq >1, was proposed in the works of Polyakov and Andrieu et al and has been extensively used. Indeed, it represents a wide class of systems, which present the fixed‐time stability property through homogeneity and Lyapunov analysis frameworks . However, it is still difficult to derive a relatively simple relationship between the system parameters and the upper bound of the settling time .…”

Section: Introductionmentioning

confidence: 99%

Enhancing the settling time estimation of a class of fixed‐time stable systems

Aldana‐López

Gómez‐Gutiérrez

Jiménez‐Rodríguez

et al. 2019

Intl J Robust & Nonlinear

185

155

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Summary In this paper, we provide a new nonconservative upper bound for the settling time of a class of fixed‐time stable systems. To expose the value and the applicability of this result, we present four main contributions. First, we revisit the well‐known class of fixed‐time stable systems, to show the conservatism of the classical upper estimate of its settling time. Second, we provide the smallest constant that the uniformly upper bounds the settling time of any trajectory of the system under consideration. Third, introducing a slight modification of the previous class of fixed‐time systems, we propose a new predefined‐time convergent algorithm where the least upper bound of the settling time is set a priori as a parameter of the system. At last, we design a class of predefined‐time controllers for first‐ and second‐order systems based on the exposed stability analysis. Simulation results highlight the performance of the proposed scheme regarding settling time estimation compared to existing methods.

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Nonlinear fixed-time control protocol for uniform allocation of agents on a segment

Cited by 122 publications

References 26 publications

A fixed-time output feedback control scheme for double integrator systems

A fixed-time output feedback control scheme for double integrator systems

Adaptive nonsingular terminal sliding mode control design for near space hypersonic vehicles

Enhancing the settling time estimation of a class of fixed‐time stable systems

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