Adaptive State-Feedback Stabilization of Stochastic High-Order Nonlinear Systems With Time-Varying Powers and Stochastic Inverse Dynamics

Li, Guangju; Xie, Xue‐Jun

doi:10.1109/tac.2020.2969547

Cited by 27 publications

(13 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since for any a ∈ R and ε > 0, − a tanh(a/ε) ≤ 0 holds from Lemma 6, by [34], we get z n g n ω ≤ 0. As…”

Section: Remarkmentioning

confidence: 81%

“…Recently, the authors in [31] studied nonlinear systems with unknown constant powers, and the stabilization of nonlinear systems with a single unknown time-varying power was discussed in [32]. In the presence of multiple unknown time-varying powers, Cui, Xie, and Lie [33,34] deeply investigated finite-time stabilization and adaptive stabilization. Subsequently, [35][36][37][38][39][40] proposed the constrained control methods for nonlinear systems with multiple unknown powers.…”

Section: Introductionmentioning

confidence: 99%

“…(2) Compared with [1-19, 22-28, 35-40, 43, 44] on nonlinear constrained control, the considered system is more general since it possesses parametric uncertainties, multiple unknown timevarying powers, and asymmetric time-varying output constraint simultaneously. (3) Compared with [20][21][22][23][24][25][26][27][28][31][32][33][34][35][36][37][38][39][40] on the continuous sampling control of nonlinear systems, more attractive adaptive event-triggered control is firstly adopted to reduce redundant data transmissions and consume less communication resources in the constrained control framework; see Example 2 for the detailed discussion.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Adaptive Event‐Triggered Finite‐Time Tracking of Output‐Constrained High‐Order Nonlinear Systems with Time‐Varying Powers

Liu

2022

Complexity

View full text Add to dashboard Cite

This paper studies the adaptive event-triggered finite-time tracking of output-constrained high-order nonlinear systems with time-varying powers. Due to the presence of multiple unknown powers and the consideration of event-triggered control, all the existing control methods of output-constrained nonlinear systems are inapplicable. By introducing nonlinear mappings, finite-time performance functions, and low-power and high-power terms into adding a power integrator technique and the relative threshold strategy, an adaptive state-feedback controller is designed to eliminate the effects caused by the output constraint and time-varying powers. It is proved that all the closed-loop signals are bounded, the asymmetric time-varying output constraint is not violated, and the tracking error converges to a prescribed arbitrarily small region around zero in a preassigned finite time. Furthermore, the Zeno phenomenon can be avoided. Two simulation examples demonstrate the effectiveness of this control scheme.

show abstract

“…Since for any a ∈ R and ε > 0, − a tanh(a/ε) ≤ 0 holds from Lemma 6, by [34], we get z n g n ω ≤ 0. As…”

Section: Remarkmentioning

confidence: 81%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Adaptive Event‐Triggered Finite‐Time Tracking of Output‐Constrained High‐Order Nonlinear Systems with Time‐Varying Powers

Liu

2022

Complexity

View full text Add to dashboard Cite

show abstract

“…2) At present, only some state‐feedback control problems are solved in our works 5,16,18,29‐33,39 . Another future work is to consider preassigned finite‐time output‐feedback control for constrained nonlinear systems with time‐varying powers.…”

Section: Discussionmentioning

confidence: 99%

“…Remark For each

i = 1, \dots, n

, Assumption 1 means that unknown powers

p_{i} (t) \geq 1

have a common known upper bound p . Compared with References 16,24,39 and other articles, the restrictive relation

p_{1} (t) \geq p_{2} (t) \geq \dots \geq p_{n} (t)

is no longer needed.…”

Section: Problem Statement and Preliminariesmentioning

confidence: 99%

Adaptive preassigned finite‐time stability of nonlinear systems with time‐varying powers and full‐state constraints

Xie

2021

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

This article discusses adaptive preassigned finite‐time stability of nonlinear systems with unknown time‐varying powers and full‐state constraints. By introducing a concept of practical preassigned finite‐time stable, constructing finite‐time performance functions and nonlinear transformed functions, and integrating high‐power and low‐power terms into dynamic surface control design, an adaptive state‐feedback controller is designed to eliminate the effects of unknown powers and serious unknown parameters in system dynamics, and decrease the computational burden in previous design methods. It is proved that all the signals of the closed‐loop system are bounded, asymmetric time‐varying full‐state constraints are not transgressed, and system states converge to a prescribed arbitrarily small region around zero after a preassigned settling time. Two simulation examples show the effectiveness and advantages of this control scheme.

show abstract

Predefined‐time adaptive neural dynamic surface tracking control for high‐order nonlinear switched systems

Meng,

Ma,

Wang

2024

Asian Journal of Control

View full text Add to dashboard Cite

In this article, the issue of adaptive predefined‐time control for high‐order switched systems is researched. Neural networks (NNs) are introduced to approximate the uncertain nonlinear functions. In particular, a novel predefined‐time convergence filter is proposed to refrain from the problem of repeated differentiation of virtual controllers. On the basis of the backstepping recursion technique and the common Lyapunov function (CLF) approach, a neural adaptive predefined‐time dynamic surface control (DSC) scheme is proposed that can demonstrate all the signals in closed‐loop systems are bounded and the tracking error can converge to a small area near zero within predefined time. The simulation results illustrate the effectiveness of the proposed control scheme.

show abstract

Adaptive State-Feedback Stabilization of Stochastic High-Order Nonlinear Systems With Time-Varying Powers and Stochastic Inverse Dynamics

Cited by 27 publications

References 25 publications

Adaptive Event‐Triggered Finite‐Time Tracking of Output‐Constrained High‐Order Nonlinear Systems with Time‐Varying Powers

Adaptive Event‐Triggered Finite‐Time Tracking of Output‐Constrained High‐Order Nonlinear Systems with Time‐Varying Powers

Adaptive preassigned finite‐time stability of nonlinear systems with time‐varying powers and full‐state constraints

Predefined‐time adaptive neural dynamic surface tracking control for high‐order nonlinear switched systems

Contact Info

Product

Resources

About