Prescribed-Time Stabilization of a Class of Nonlinear Systems by Linear Time-Varying Feedback

Zhou, Bin; Shi, Yang

doi:10.1109/tac.2021.3061645

Cited by 110 publications

(48 citation statements)

References 41 publications

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“…To solve this problem, a novel design scheme was proposed. By using the idea of scalarization, 24,32,35 the prescribed‐time stabilization problem of the vector‐valued system is transformed into the stability analysis problem of a scalar‐valued differential equation. It has been shown that all of the closed‐loop trajectories convergence to the origin in prescribed time.…”

Section: Discussionmentioning

confidence: 99%

Prescribed‐time stabilization of p‐normal nonlinear systems by bounded time‐varying feedback

Zhang

Zhou

Hou

et al. 2021

Intl J Robust & Nonlinear

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This article studies the prescribed‐time stabilization problem of p‐normal nonlinear systems by bounded time‐varying high‐gain feedback. A time‐varying bounded controller, which can achieve prescribed‐time stabilization, is designed via backstepping. Because of the usage of time‐varying high‐gain functions which grow unbounded as the time tends to the prescribed time, the usual separation technique is invalid. To solve this problem, a novel design scheme is proposed. It is shown that all of the closed‐loop trajectories convergence to the origin in prescribed time. Finally, a numerical example verifies the effectiveness of the proposed method.

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Section: Discussionmentioning

confidence: 99%

Prescribed‐time stabilization of p‐normal nonlinear systems by bounded time‐varying feedback

Zhang

Zhou

Hou

et al. 2021

Intl J Robust & Nonlinear

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“…such that the FTLOR problem can be achieved in finite-time T 0 by the bounded LTV state controller (18) where 𝛾(t) satisfies (40). Proof.…”

Section: The Second Approachmentioning

confidence: 99%

“…The function 𝛾(t) in Theorem 2 satisfies lim t↑T 0 𝛾(t) = +∞, which implies that the gain matrix in the bounded LTV controller of Theorem 2 approaches infinity at finite-time T 0 and is thus not well defined for all t ≥ T 0 . To avoid possible problems in implementation, we can replace (40) by 𝜆 min (P(𝛾 max )) , and the system state x(t) satisfies…”

Section: [ T Tmentioning

confidence: 99%

“…For this reason, linear feedback is the best choice, since it is easy to implement, and, as we know, it is robust with respect to uncertainties. 39,40 However, as far as we know, when the controller is restricted to be linear, the finite-time output regulation problem for linear systems has not been well solved in the literature, to say nothing the presence of input constrains. From a mathematical point of view, we believe that the finite time output regulation problem for input-constrained linear systems mainly has the following two difficulties.…”

Section: Introductionmentioning

confidence: 99%

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Finite‐time output regulation by bounded linear time‐varying controls with applications to the satellite formation flying

Zhang

Zhou

Jiang

et al. 2021

Intl J Robust & Nonlinear

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This article studies the finite-time output regulation problem for linear time-invariant continuous-time systems. By using the solution to a parametric Lyapunov equation (PLE) and regulator equations, three bounded linear time-varying (LTV) state controllers composed of the LTV feedback gain and the LTV feedforward gain are designed, such that (prescribed) finite-time output regulation is solved. As a further result, a linear LTV observer-based controller is also designed. The most significant advantages of this article are that the system under consideration is more general and the output regulation problem is achieved within a user-chosen regulation time. Finally, the developed LTV state controllers are utilized to the design of the satellite formation flying control system and simulation results verify the effectiveness of the proposed approaches.

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“…In addition, by using temporal scale transformation, a triangularly stable controller is proposed for the perturbed system in [31], a dynamic highgain feedback algorithm is established for strict-feedback-like systems in [19], and some distributed algorithms are developed for multi-agent systems in [32]- [34]. Based upon parametric Lyapunov equation, a finite-time controller and a prescribedtime controller are studied for linear systems in [1] and [21], and then generalized to nonlinear systems in [35].…”

Section: Introductionmentioning

confidence: 99%

Prescribed-time Control for Linear Systems in Canonical Form Via Nonlinear Feedback

Song¹

2022

Preprint

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For systems in canonical form with nonvanishing uncertainties/disturbances, this work presents an approach to full state regulation within prescribed time irrespective of initial conditions. By introducing the smooth hyperbolic-tangent-like function, a nonlinear and time-varying state feedback control scheme is constructed, which is further extended to address output feedback based prescribed-time regulation by invoking the prescribed-time observer, all are applicable over the entire operational time zone. As an alternative to full state regulation within user-assignable time interval, the proposed method analytically bridges the divide between linear and nonlinear feedback based prescribed-time control, and is able to achieve asymptotic stability, exponential stability and prescribed-time stability with a unified control structure.

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Prescribed-Time Stabilization of a Class of Nonlinear Systems by Linear Time-Varying Feedback

Cited by 110 publications

References 41 publications

Prescribed‐time stabilization of p‐normal nonlinear systems by bounded time‐varying feedback

Prescribed‐time stabilization of p‐normal nonlinear systems by bounded time‐varying feedback

Finite‐time output regulation by bounded linear time‐varying controls with applications to the satellite formation flying

Prescribed-time Control for Linear Systems in Canonical Form Via Nonlinear Feedback

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