Fixed-Time Stabilization of Nonlinear System and its Application into General Neural Networks

Yu, Jiaju; Yu, Shuanghe; Yan, Yan

doi:10.1109/access.2020.2982204

Cited by 9 publications

(11 citation statements)

References 34 publications

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“…Remark 3.4: It is obvious that the settling time T f * is a bounded function on initial value V 0 , and it is easy to prove that T f * is less than T max . It is worthwhile noticing that T max is similar to that in [38], [39], but the result is concise. Thus, it brings convenience to adjust settling time even if initial states is unknown.…”

Section: Resultssupporting

confidence: 52%

A New Design to Finite-Time Stabilization of Nonlinear Systems With Applications to General Neural Networks

Chen

2021

IEEE Access

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The finite-time stabilization problem of nonlinear systems is investigated in this paper. Firstly, to improve the precision of settling time of nonlinear system, a new finite-time stability theorem is established, and a higher precision settling time is derived from it. Moreover, by theoretical derivation, we prove that the corresponding settling time is more accurate than the existing results. Secondly, as an application, a new class of finite-time protocol framework, which unifies continuous protocol and discontinuous ones into a uniform formula, is designed to solve the finite-time stabilization problem of the general neural network system, and it can bring to a continuous control protocol and a discontinuous control protocol through choosing different design parameters. It is shown that the convergence rate is improved and also the corresponding settling time is upper bounded by some positive constant independent of initial conditions, which makes it convenient and flexible to adjust the settling time by adjusting design parameters. Finally, two numerical examples are provided to illustrate the effectiveness of our theoretical results. INDEX TERMSFinite-time stability theorem; Filippov solution; General neural networks; Lyapunov function; Settling time function; Upper bound of settling time

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Section: Resultssupporting

confidence: 52%

A New Design to Finite-Time Stabilization of Nonlinear Systems With Applications to General Neural Networks

Chen

2021

IEEE Access

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“…Before moving on, we present some definitions of fixedtime stability. Definition 1: ( [35], [36]) Consider the system defined bẏ…”

Section: Preliminaries a System Modelingmentioning

confidence: 99%

“…, and T (z 0 ) is called the settling-time function. Definition 2: ( [35], [36]) If the system (5) is globally finitetime stable and there exists a positive constant T max such that T < T max , that is to say, the convergence time T is bounded. Therefore, it is said to be fixed-time stable.…”

Section: Preliminaries a System Modelingmentioning

confidence: 99%

“…Second, the convergence time T 1 can be preselected by the users, which is easily achievable and owns a better transient response than the traditional asymptotic rate in (12) and (13). Remark 4: In [35], new results about the settling time estimate of fixed-time stability are proposed, the Gamma function is introduced. In [35], the result is less conservative and more accurate by…”

Section: Fixed-time Prescribed Performance Tracking Control a Pmentioning

confidence: 99%

“…Remark 4: In [35], new results about the settling time estimate of fixed-time stability are proposed, the Gamma function is introduced. In [35], the result is less conservative and more accurate by…”

Section: Fixed-time Prescribed Performance Tracking Control a Pmentioning

confidence: 99%

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Trajectory Tracking Control of Surface Vehicles: A Prescribed Performance Fixed-Time Control Approach

Yang

2020

IEEE Access

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This article focuses on the fixed-time trajectory tracking problem for surface vehicles (SVs) with prescribed performance. First, to realize prescribed performance, the error transformation and fixedtime prescribed performance function are proposed. In this way, the constrained tracking error problem can be solved by the stabilization of the transformed system. Second, by introducing a reduced-order disturbance observer, a fixed-time sliding mode controller is developed to realize trajectory tracking control while satisfying both predefined performance and perturbance rejection. It notices that the associated settling time can be preselected by parameters and independent of system initial conditions. Finally, some simulation examples are provided to illustrate the effectiveness of our theoretical results.

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Adaptive neural network fixed‐time stabilization control for high‐order nonlinear systems

2021

Math Methods in App Sciences

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This paper investigates a neural network (NN) adaptive fixed‐time stabilization control problem for high‐order nonlinear systems. Radial basis function NNs (RBFNNs) are used to approximate unknown nonlinear function. A nonlinear filter is designed to solve the issue of “explosion of complexity.” Combining adaptive backstepping design and adding a power integrator, an adaptive NN fixed‐time control method is developed. It is proved that all the signals of the closed‐loop system are bounded in fixed time. Finally, simulation example is provided to confirm the effectiveness of the presented control method.

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Fixed-Time Stabilization of Nonlinear System and its Application into General Neural Networks

Cited by 9 publications

References 34 publications

A New Design to Finite-Time Stabilization of Nonlinear Systems With Applications to General Neural Networks

A New Design to Finite-Time Stabilization of Nonlinear Systems With Applications to General Neural Networks

Trajectory Tracking Control of Surface Vehicles: A Prescribed Performance Fixed-Time Control Approach

Adaptive neural network fixed‐time stabilization control for high‐order nonlinear systems

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