Fixed-time sliding mode controller design for synchronization of complex dynamical networks

Khanzadeh, Alireza; Pourgholi, Mahdi

doi:10.1007/s11071-017-3400-x

Cited by 70 publications

(27 citation statements)

References 46 publications

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“…Recently, there has been a great deal of attention in the control community on the analysis of a class of systems, known as fixed‐time stable systems, because they exhibit finite‐time convergence with an upper bound of the settling time (UBST) that is independent of the initial conditions of the system 1-5 . This effort has produced many contributions on algorithms with the fixed‐time convergence property, such as multiagent coordination, 6-9 distributed resource allocation, 10 synchronization of complex networks, 11,12 stabilizing controllers, 1,13-16 state observers, 17 and online differentiation algorithms 18,19 …”

Section: Introductionmentioning

confidence: 99%

On the design of nonautonomous fixed‐time controllers with a predefined upper bound of the settling time

Gómez‐Gutiérrez

2020

Intl J Robust & Nonlinear

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Recently, there has been a great deal of attention in a class of finite-time stable dynamical systems, called fixed-time stable, that exhibit uniform convergence with respect to its initial condition, that is, there exists an upper bound for the settling-time (UBST) function, independent of the initial condition of the system. Of particular interest is the development of stabilizing controllers where the desired UBST can be selected a priori by the user since it allows the design of controllers to satisfy real-time constraints. Unfortunately, existing methodologies for the design of controllers for fixed-time stability exhibit the following drawbacks: on the one hand, in methods based on autonomous systems, either the UBST is unknown or its estimate is very conservative, leading to over-engineered solutions; on the other hand, in methods based on time-varying gains, the gain tends to infinity, which makes these methods unrealizable in practice. To bridge these gaps, we introduce a design methodology to stabilize a perturbed chain of integrators in a fixed-time, with the desired UBST that can be set arbitrarily tight. Our approach consists of redesigning autonomous stabilizing controllers by adding time-varying gains. However, unlike existing methods, we provide sufficient conditions such that the time-varying gain remains bounded, making our approach realizable in practice. K E Y W O R D Sfixed-time control, predefined-time control, predefined-time stabilization, prescribed-time control INTRODUCTIONRecently, there has been a great deal of attention in the control community on the analysis of a class of systems, known as fixed-time stable systems, because they exhibit finite-time convergence with an upper bound of the settling time (UBST) that is independent of the initial conditions of the system. 1-5 This effort has produced many contributions on algorithms with the fixed-time convergence property, such as multiagent coordination, 6-9 distributed resource allocation, 10 synchronization of complex networks, 11,12 stabilizing controllers, 1,13-16 state observers, 17 and online differentiation algorithms. 18,19 The fixed-time stability property is of great interest in the development of algorithms for scenarios where real-time constraints need to be satisfied. In fault detection, isolation, and recovery schemes, 20 failing to recover from the fault on time may lead to an unrecoverable mode. In missile guidance, 21 the impact time control guidance laws require stabilization in a desired time. 22,23 In hybrid dynamical systems, it is frequently required that the observer (respectively, controller) Int J Robust Nonlinear Control. 2020;30:3871-3885.wileyonlinelibrary.com/journal/rnc

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Section: Introductionmentioning

confidence: 99%

On the design of nonautonomous fixed‐time controllers with a predefined upper bound of the settling time

Gómez‐Gutiérrez

2020

Intl J Robust & Nonlinear

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“…As we know, although SMC behaves the characteristic of robustness, the chattering problem is its main disadvantage. A lot of approaches are applied to eliminate the chattering problem, such as high-order SMC, the replacement of sign function with sigmoid function or saturated function, reaching law-based control [15,40]. The reaching law-based control achieves the improvement of the dynamic performance for the reaching phase and alleviates the chattering problem to some extent.…”

Section: Introductionmentioning

confidence: 99%

Finite-time control for uncertain systems and application to flight control

Wang

et al. 2020

NAMC

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In this paper, the finite-time control design problem for a class of nonlinear systems with matched and mismatched uncertainty is addressed. The finite-time control scheme is designed by integrating multi power reaching (MPR) law and finite-time disturbance observer (FTDO) into integral sliding mode control, where a novel sliding surface is designed, and the FTDO is applied to estimate the uncertainty. Then the fixed-time reachability of the MPR law is analyzed, and the finite-time stability of the closed-loop system is proven in the framework of Lyapunov stability theory. Finally, numerical simulation and the application to the flight control of hypersonic vehicle (HSV) are provided to show the effectiveness of the designed controller.Proof. We carry out the analysis into two cases, one is s 0 > 0, another is s 0 < 0.Case 1: s 0 > 0. Without loss of generality, assume that s 0 > β 1 , the reaching phase of s can be completed through four phases as follows:

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“…In order to overcome these shortcomings, a new concept named fixed-time synchronization was firstly taken into account in [19]. Hints for future research on the fixed-time synchronization problem can be found in [20][21][22][23][24][25]. By designing a sliding mode controller, the fixed-time synchronization issue for complex dynamical networks was addressed in [21].…”

Section: Introductionmentioning

confidence: 99%

“…Hints for future research on the fixed-time synchronization problem can be found in [20][21][22][23][24][25]. By designing a sliding mode controller, the fixed-time synchronization issue for complex dynamical networks was addressed in [21]. Robust fixed-time synchronization for uncertain complex-valued neural networks with discontinuous activation functions was introduced in [23].…”

Section: Introductionmentioning

confidence: 99%

Fixed-time synchronization of semi-Markovian jumping neural networks with time-varying delays

Zhao

2018

Adv Differ Equ

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This paper is concerned with the global fixed-time synchronization issue for semi-Markovian jumping neural networks with time-varying delays. A novel state-feedback controller, which includes integral terms and time-varying delay terms, is designed to realize the fixed-time synchronization goal between the drive system and the response system. By applying the Lyapunov functional approach and matrix inequality analysis technique, the fixed-time synchronization conditions are addressed in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are provided to illustrate the feasibility of the proposed control scheme and the validity of theoretical results.

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Fixed-time sliding mode controller design for synchronization of complex dynamical networks

Cited by 70 publications

References 46 publications

On the design of nonautonomous fixed‐time controllers with a predefined upper bound of the settling time

On the design of nonautonomous fixed‐time controllers with a predefined upper bound of the settling time

Finite-time control for uncertain systems and application to flight control

Fixed-time synchronization of semi-Markovian jumping neural networks with time-varying delays

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