A Linear Time-Varying Inequality Approach for Prescribed Time Stability and Stabilization

Zhou, Bin; Zhang, Kang-Kang

doi:10.1109/tcyb.2022.3164658

Cited by 27 publications

(10 citation statements)

References 40 publications

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“…If

T

can be prescribed as any number (usual in the design), then prescribed‐time control will be used instead of finite‐ and fixed‐time control. The problem of predefining the settling time in finite‐time control, which might be referred to as the prescribed‐time control problem, was investigated in many references such as References 44,46,48–51. Though the constant

T

in the fixed‐time control scheme can be assigned in advance by suitably assigning control parameters, the true settling time still depends on the initial condition, which is different from the prescribed‐time control scheme where the true settling time is independent of the initial condition.…”

Section: Preliminaries and Problem Formulationmentioning

confidence: 99%

“…Hence, the issue of finite/fixed/predefined-time output feedback control for nonlinear systems and multiagent systems has been widely concerned by scholars. 10,19,[38][39][40][41][42][43] Several effective methods have been developed for achieving finite/fixed/prescribed-time stability for nonlinear systems and multiagent systems, including sliding mode control method, [44][45][46][47][48] time-varying function technique, 33,[49][50][51] and so on. For example, in Reference 39, the problem of global finite-time stabilization by output feedback for a class of nonlinear systems was considered and an output feedback controller was proposed by using the homogeneous domination approach, in Reference 41 a novel continuous and nonsingular practical prescribed-time consensus control law was designed on the basis of the distributed practical prescribed-time observer and the problem of practical prescribed-time stability of multiagent systems under the directed topology based on output-feedback consensus control was achieved.…”

Section: Introductionmentioning

confidence: 99%

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An adaptive observer based output feedback prescribed‐time control of a class of nonlinear systems with unknown parameters

Wang,

Jiang,

Zhang

2024

Intl J Robust & Nonlinear

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SummaryIn this paper, an adaptive observer based output feedback prescribed‐time control is designed for a class of nonlinear systems with unknown parameters. According to the characteristics of the nonlinear systems, a novel adaptive observer is first designed. Then by imposing parametric Lyapunov equations, a time‐varying high‐gain observer based output feedback adaptive controller is constructed, by which, it is proven that the states of both the observer and the original system can be driven to zero within any prescribed time. Moreover, the control signal is proven uniformly bounded by a scalar. Two numerical examples are illustrated to verify the effectiveness of the proposed method.

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“…If

T

T

Section: Preliminaries and Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An adaptive observer based output feedback prescribed‐time control of a class of nonlinear systems with unknown parameters

Wang,

Jiang,

Zhang

2024

Intl J Robust & Nonlinear

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“…In view of these problems, prescribed-time stabilization has been proposed, where the settlingtime can be chosen in advance. Existing Lyapunov-based criteria that can achieve prescribed-time stabilization are mainly based on time varying high-gain feedback (see, for example, [5], [22], [27], [30], [32], [33] and [34]).…”

Section: Introductionmentioning

confidence: 99%

Strong Prescribed-Time Stabilization of Uncertain Nonlinear Systems by Periodic Delayed Feedback

Ding,

Zhou,

Zhang

et al. 2024

IEEE Trans. Automat. Contr.

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In this paper, a novel Lyapunov-based approach for strong prescribed-time stabilization by periodic delayed feedback is established. Since the comparison lemma cannot be directly applied to time-delay systems, their proofs rely on trajectory analysis. Based on this approach, a novel control law for strong prescribed-time stabilization of uncertain scalar nonlinear systems is obtained, with the appealing properties that i) singularity problems inherent to time-varying high gain approaches are avoided, ii) strong prescribed-time stabilization is achieved with control terms exhibiting a linear growth rate in the combined current and delayed state variable, iii) the achieved fixed-time stability is preserved under classes of additive perturbations, and iv) the setting time of the closedloop system equals the prescribed value for some admissible uncertainties. Subsequently, using the backstepping procedure, a strongly prescribedtime stabilizing control law for strict feedback uncertain nonlinear systems is designed. Numerical simulations are shown to verify the effectiveness of the proposed approaches.

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“…And the convergence time of transient error cannot be determined. Although the prescribed time control method [46, 47] proposed in recent years can solve the problem of transient error convergence time, it will ignore overshoot, steady-state error, and other factors. Therefore, it is necessary to design a unified predetermined performance control strategy considering overshoot, transient convergence time, transient error, and steady-state error.…”

Section: Introductionmentioning

confidence: 99%

Broad learning control of a two-link flexible manipulator with prescribed performance and actuator faults

Niu

Kong

et al. 2023

Robotica

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In this paper, we present a broad learning control method for a two-link flexible manipulator with prescribed performance (PP) and actuator faults. The trajectory tracking errors are processed through two consecutive error transformations to achieve the constraints in terms of the overshoot, transient error, and steady-state error. And the barrier Lyapunov function is employed to implement constraints on the transition state variable. Then, the improved radial basis function neural networks combined with broad learning theory are constructed to approximate the unknown model dynamics of flexible robotic manipulator. The proposed fault-tolerant PP control cannot only ensure tracking errors converge into a small region near zero within the preset finite time but also address the problem caused by actuator faults. All the closed-loop error signals are uniformly ultimately bounded via the Lyapunov stability theory. Finally, the feasibility of the proposed control is verified by the simulation results.

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A Linear Time-Varying Inequality Approach for Prescribed Time Stability and Stabilization

Cited by 27 publications

References 40 publications

An adaptive observer based output feedback prescribed‐time control of a class of nonlinear systems with unknown parameters

An adaptive observer based output feedback prescribed‐time control of a class of nonlinear systems with unknown parameters

Strong Prescribed-Time Stabilization of Uncertain Nonlinear Systems by Periodic Delayed Feedback

Broad learning control of a two-link flexible manipulator with prescribed performance and actuator faults

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