Predefined-Time Convergence Control for High-Order Integrator Systems Using Time Base Generators

Becerra, Héctor M.; Vázquez, Carlos; Arechavaleta, Gustavo; Delfin, Josafat

doi:10.1109/tcst.2017.2734050

Cited by 121 publications

(86 citation statements)

References 19 publications

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“…However, unlike existing methods based on time‐base generators, 22,23,37 we provide sufficient conditions such that our time‐varying gains remain bounded. Moreover, contrary to Becerra et al, 39 no initial state is explicitly used in the feedback law; and unlike Song et al 23 and Becerra et al, 39 predefined‐time convergence is guaranteed even in the presence of external disturbances.…”

Section: Introductionmentioning

confidence: 92%

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: 92%

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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“…Time base generators are parametric functions of time, particularly designed to stabilize a system in such a way that its state describes a convenient transient profile. TBGs have been previously used to achieve predefined-time convergence of first and higher order dynamics for single systems in [35]. For the case of single first-order systems, TBGs have been used for the control of robots at kinematic level [43].…”

Section: Time Base Generator (Tbg)mentioning

confidence: 99%

“…A time base generator (TBG) is a continuous and differentiable time-dependent polynomial function ℎ( ) described as [35]…”

Section: Time Base Generator (Tbg)mentioning

confidence: 99%

“…In [35], a couple of procedures for calculating the coefficients C, fulfilling the required constraints, have been introduced. In particular, when a high degree polynomial is used, an optimization procedure can be applied to find the best coefficients.…”

Section: Time Base Generator (Tbg)mentioning

confidence: 99%

“…By using a motion planning strategy, predefinedtime consensus protocols based on a time-varying sampling sequence convergent to a specified settling time are proposed in [32,33]. Preliminary versions of a couple of predefinedtime protocols were proposed in [34], taking advantage of time base generators (TBGs), which are parametric time signals that converge to zero in a specified time [35], and can be tracked using feedback controllers.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Predefined-Time Consensus of Nonlinear First-Order Systems Using a Time Base Generator

Colunga

Vázquez

Becerra

et al. 2018

Mathematical Problems in Engineering

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This paper proposes a couple of consensus algorithms for multiagent systems in which agents have first-order nonlinear dynamics, reaching the consensus state at a predefined time independently of the initial conditions. The proposed consensus protocols are based on the so-called time base generators (TBGs), which are time-dependent functions used to build time-varying control laws. Predefined-time convergence to the consensus is proved for connected undirected communication topologies and directed topologies having a spanning tree. Furthermore, one of the proposed protocols is based on the super-twisting controller, providing robustness against disturbances while maintaining the predefined-time convergence property. The performance of the proposed methods is illustrated in simulations, and it is compared with finite-time, fixed-time, and predefined-time consensus protocols. It is shown that the proposed TBG protocols represent an advantage not only in the possibility to define a settling time but also in providing smoother and smaller control actions than existing finite-time, fixed-time, and predefined-time consensus.

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Adaptive output‐feedback stabilization in prescribed time for nonlinear systems with unknown parameters coupled with unmeasured states

Krishnamurthy

Khorrami

Krstić

2020

Adaptive Control & Signal

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Summary The prescribed‐time output‐feedback stabilization (ie, regulation of the state and control input to zero within a “prescribed” time picked by the control designer irrespective of the initial state) of a general class of uncertain nonlinear strict‐feedback‐like systems is considered. Unlike prior results, the class of systems considered in this article allows crossproducts of unknown parameters (without any required magnitude bounds on unknown parameters) and unmeasured state variables in uncertain state‐dependent nonlinear functions throughout the system dynamics. We show that prescribed‐time output‐feedback stabilization (ie, both prescribed‐time state estimation and prescribed‐time regulation) is achieved through a novel output‐feedback control design involving specially designed dynamics of an adaptation state variable and a high‐gain scaling parameter in combination with a temporal transformation and a dual high‐gain scaling based observer and controller design. While standard dynamic adaptation techniques cannot be applied due to crossproducts of unknown parameters and unmeasured states, we show that instead, the dynamics of the high‐gain scaling parameter and adaptation parameter can be designed with temporal forcing terms to ensure that unknown parameters in system dynamics are dominated by a particular fractional power of the high‐gain scaling parameter and the adaptation parameter after a subinterval (of unknown length) of the prescribed time interval. We show that the control law can be designed such that the system state and input are regulated to zero in the remaining subinterval of the prescribed time interval.

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Predefined-Time Convergence Control for High-Order Integrator Systems Using Time Base Generators

Cited by 121 publications

References 19 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

Predefined-Time Consensus of Nonlinear First-Order Systems Using a Time Base Generator

Adaptive output‐feedback stabilization in prescribed time for nonlinear systems with unknown parameters coupled with unmeasured states

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