Improved Results on Asymptotic Stabilization for Stochastic Nonlinear Time-Delay Systems With Application to a Chemical Reactor System

Liu, Liang; Yin, Shen; Zhang, Lixian; Yin, Xunyuan; Yan, Hao

doi:10.1109/tsmc.2016.2608799

Cited by 90 publications

(44 citation statements)

References 54 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As a typical nonlinear system model, stochastic nonlinear system has received considerable attention during the past decades because stochastic noises are inevitably encountered in various practical dynamic systems. In particular, since backstepping technique was extended to a stochastic setting,() increasing efforts toward its stabilization issue have been made and fruitful results have been achieved (see other works() and the references therein). Meanwhile, the study of switched systems has also attracted extensive interests of researchers,() due to their significant applications in modeling many practical systems, such as aircraft multimode control,() chemical processes, and automotive engineering .…”

Section: Introductionmentioning

confidence: 99%

Finite‐time stabilization for a class of switched stochastic nonlinear systems with dead‐zone input nonlinearities

Gao

Liu

2018

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

Summary This paper studies the finite‐time stabilizing control problem for a class of switched stochastic nonlinear systems (SSNSs) in p‐normal form. The switched systems under consideration possess the powers of different positive rational numbers and the dead‐zone input nonlinearities. Based on the improving finite‐time stability theorem for SSNSs established in this paper, a general framework to address common state feedback for SSNSs is developed by adopting the common Lyapunov function–based adding a power integrator technique. It is proved that the proposed controller renders the trivial solution of the closed‐loop system uniformly finite‐time stable in probability under arbitrary switchings. Finally, simulation results are given to confirm the validity of the proposed approach.

show abstract

Section: Introductionmentioning

confidence: 99%

Finite‐time stabilization for a class of switched stochastic nonlinear systems with dead‐zone input nonlinearities

Gao

Liu

2018

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

show abstract

“…In this section, to verify the effectiveness of our proposed global output feedback regulation algorithm, we consider the following two‐stage chemical reactor system with delayed recycle streams

\{\begin{matrix} {\overset{x}{true}}_{1} = prefix- true \frac{1}{β_{1}} x_{1} prefix- ϖ_{1} x_{1} + \frac{1 prefix- υ_{2}}{ρ_{1}} x_{2} + δ_{1} false(t, x, x false(t prefix- d false(t false) false) false) \\ {\overset{x}{true}}_{2} = prefix- true \frac{1}{β_{2}} x_{2} prefix- ϖ_{2} x_{2} + \frac{υ_{1}}{ρ_{2}} x_{1} false(t prefix- d false(t false) false) + \frac{ς_{2}}{ρ_{2}} u + δ_{2} false(t, x, x false(t prefix- d false(t false) false) false) \\ y = ε false(t false) x_{1}, \end{matrix}

where x 1 ( t ), x 2 ( t ) are compositions ( m 3 ); β 1 , β 2 are reactor residence times (s); ϖ 1 , ϖ 1 are reaction parameters (1/ s ); υ 1 , υ 2 are recycle flow rates ( m 3 / s ); ς 2 is the feed rate ( m 3 / s ); ρ 1 , ρ 2 are reactor volumes ( m 3 ); δ 1 (·) and δ 2 (·) are the uncertain nonlinear functions for describing the system itself uncertainties; d ( t ) is the unknown time‐varying delay; ε ( t ) is the unknown measurement sensitivity fault.…”

Section: Simulation Examplementioning

confidence: 99%

“…In this section, to verify the effectiveness of our proposed global output feedback regulation algorithm, we consider the following two-stage chemical reactor system with delayed recycle streams. [34][35][36] ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩̇x d(t)))…”

Section: Simulation Examplementioning

confidence: 99%

Global output feedback regulation of nonlinear time delay systems subject to sensor measurement faults

Chen

Guan

2020

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

Summary This article studied the global output feedback regulation problem for a class of uncertain nonlinear time delay systems subject to unknown measurement faults on sensors. Different from the existing works, we consider the unknown time‐varying delays on the system states and relax their conservative condition on nonlinear functions. By introducing two novel time‐varying gains, a new global output feedback regulation algorithm is proposed, which ensures control parameters can be chosen flexibly. The proposed linear‐like controller is independent of the unknown time‐varying delays. Moreover, it has a simple structure, which is convenient for the implementation in practice. Based on the Lyapunov stability theory, it is strictly proved that all signals of the resulting closed‐loop system are globally bounded with the designed controller. Finally, a simulation example is presented to illustrate the effectiveness of the proposed output feedback regulation algorithm.

show abstract

“…The existence of time delays may deteriorate system performance and cause instability. Therefore, the control and design for stochastic nonlinear time-delay systems has been one of the active research topics and already obtained fruitful results [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. In [18][19][20][21][22], by using Lyapunov-Krasovskii functional method, the outputfeedback stabilization problems were solved for stochastic nonlinear systems with time delays only presenting in system output.…”

Section: Introductionmentioning

confidence: 99%

“…In addition, the adaptive control technique has been applied with neural network approximation approach to weaken the assumptions on system time-delay nonlinearities in [28][29][30][31][32] and the related references. Recently, the traditional pure growth assumptions were further relaxed for stochastic nonlinear time-delay systems in [33] with the help of parameter-based controller design method. Despite the remarkable efforts obtained on relaxing the growth assumptions, the existing results including [25][26][27][28][29][30][31][32][33] all failed to remove these nonlinear growth assumptions.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Stabilization of Stochastic Nonlinear Systems Disturbed by Unknown Time Delay and Covariance Noise

Duan

Min

Qin

2017

Mathematical Problems in Engineering

View full text Add to dashboard Cite

This paper considers a more general stochastic nonlinear time-delay system driven by unknown covariance noise and investigates its adaptive state-feedback control problem. As a remarkable feature, the growth assumptions imposed on delay-dependent nonlinear terms are removed. Then, with the help of Lyapunov-Krasovskii functionals and adaptive backstepping technique, an adaptive state-feedback controller is constructed by overcoming the negative effects brought by unknown time delay and covariance noise. Based on the designed controller, the closed-loop system can be guaranteed to be globally asymptotically stable (GAS) in probability. Finally, a simulation example demonstrates the effectiveness of the proposed scheme.

show abstract

Improved Results on Asymptotic Stabilization for Stochastic Nonlinear Time-Delay Systems With Application to a Chemical Reactor System

Cited by 90 publications

References 54 publications

Finite‐time stabilization for a class of switched stochastic nonlinear systems with dead‐zone input nonlinearities

Finite‐time stabilization for a class of switched stochastic nonlinear systems with dead‐zone input nonlinearities

Global output feedback regulation of nonlinear time delay systems subject to sensor measurement faults

Adaptive Stabilization of Stochastic Nonlinear Systems Disturbed by Unknown Time Delay and Covariance Noise

Contact Info

Product

Resources

About