Continuous finite- and fixed-time high-order regulators

Abstract-This paper addresses the fixed-time leader-follower consensus problem for high-order integrator multi-agent systems subject to matched external disturbances. A new cascade control structure, based on a fixedtime distributed observer, is developed to achieve the fixed-time consensus tracking control. A simulation example is included to show the efficacy and the performance of the proposed control structure with respect to different initial conditions.

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“…Similarly, the proof could be also derived by following the same line as the proof of Theorem 2 given in the recent work [31].…”

Section: A Definitions and Lemmasmentioning

confidence: 85%

Fixed-Time Consensus Tracking for Multiagent Systems With High-Order Integrator Dynamics

Zuo

Tian

Defoort

et al. 2018

IEEE Trans. Automat. Contr.

559

240

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“…*The current result on fixed-time stabilization of a nth-order integrator chain, in which some fixed-time leader-follower consensus protocols are based (see, eg, the works of Zuo et al 53 and Tian et al 54 ), was given in the work of Basin et al 56 However, such a controller, which is based on the homogeneity approach, presents two drawbacks for the design under time constraints. Firstly, the result only holds for functions |x| 1− 1 sign(x) + |x| 1+ 2 sign(x),with…”

Section: Robust Predefined-time Consensus Algorithmsmentioning

confidence: 99%

A class of robust consensus algorithms with predefined‐time convergence under switching topologies

Aldana‐López

Gómez‐Gutiérrez

Defoort

et al. 2019

Intl J Robust & Nonlinear

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Summary This paper addresses the robust consensus problem under switching topologies. Contrary to existing methods, the proposed approach provides decentralized protocols that achieve consensus for networked multiagent systems in a predefined time. Namely, the protocol design provides a tuning parameter that allows setting the convergence time of the agents to a consensus state. An appropriate Lyapunov analysis exposes the capability of the current proposal to achieve predefined‐time consensus over switching topologies despite the presence of bounded perturbations. Finally, this paper presents a comparison showing that the suggested approach subsumes existing fixed‐time consensus algorithms, which allows to provide extra degrees of freedom to obtain predefined‐time consensus protocols with improved convergence characteristics, for instance, to reduce the slack between the true convergence time and the predefined upper bound. Numerical results are given to illustrate the effectiveness and advantages of the proposed method.

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“…Regarding the controller design problem for fixed‐time stability, the existing methodologies exhibit the following drawbacks. First, in methodologies like those proposed by Basin et al 32 and Tian et al, 28,29 which are based on the homogeneity property, 3 the UBST is unknown.Second, autonomous controllers derived based on Lyapunov analysis 1,16,26,34-36 may provide non‐conservative estimates of the UBST for the scalar case (see, eg, the work from Sanchez‐Torres et al 2 and Aldana‐López et al 34 ), but the estimate of the UBST becomes very conservative in high‐order systems (see, eg, section 5 in Zimenko et al 15 ). Third, in nonautonomous controllers based on time‐varying gains, 22,23,37 the origin is reached exactly at the desired time, but the time‐varying gain tends to infinity as the time approaches the desired convergence time.…”

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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Continuous finite- and fixed-time high-order regulators

Cited by 108 publications

References 23 publications

Fixed-Time Consensus Tracking for Multiagent Systems With High-Order Integrator Dynamics

Fixed-Time Consensus Tracking for Multiagent Systems With High-Order Integrator Dynamics

A class of robust consensus algorithms with predefined‐time convergence under switching topologies

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

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