Finite-time state-feedback control for a class of stochastic high-order nonlinear systems

Zha, Wenting; Zhai, Junyong; Ai, Weiqing; Fei, Shumin

doi:10.1080/00207160.2014.906585

Cited by 28 publications

(22 citation statements)

References 25 publications

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“…Thus, it is easy to observe that

false| f_{2} false(\cdot false) false| = \frac{1}{4} false| \sin x_{1} false| = \frac{1}{4} false| \sin x_{1} {false|}^{\frac{4}{21}} false| \sin x_{1} {false|}^{\frac{17}{21}} \leq \frac{1}{4} false| x_{1} {false|}^{\frac{17}{21}}

false| {sans-serifg}_{3} false(\cdot false) false| = \frac{2}{3} false| \sin x_{3} false| = \frac{2}{3} false| \sin x_{3} {false|}^{\frac{3}{17}} false| \sin x_{3} {false|}^{\frac{14}{17}} \leq \frac{2}{3} false| x_{3} {false|}^{\frac{14}{17}}

, which implies that Assumption is satisfied. (ii)It is remarkable that system greatly extends the relevant results in other works . Specifically, when d i ( t )=0, q i ≥ 1, system reduces to the systems considered in the aforementioned works and Assumption becomes assumption 3.1 in the work of Gao and Wu . The growth conditions in the works of Wang and Zhu and Zha et al are

false| f_{i} false({\overset{x}{true}}_{i} false) false| \leq ϕ_{i} false({\overset{x}{true}}_{i} false) true \sum_{j = 1}^{i} false| x_{j} false| and false‖ {sans-serifg}_{}

…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 65%

“…It can be found that the stabilization problem for such a kind of nonlinear stochastic system faces many difficulties. Fortunately, the state‐feedback stabilization problem of high‐order stochastic nonlinear systems may be solved by the adding a power integrator method and the Lyapunov‐based recursive design technique . However, it should be noted that the fractional powers of the high‐order systems considered in the existing literature are all required to be not less than one.…”

Section: Introductionmentioning

confidence: 99%

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Robust finite‐time stabilization of a class of high‐order stochastic nonlinear systems subject to output constraint and disturbances

Fang

Ding

et al. 2019

Intl J Robust & Nonlinear

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Summary In this paper, the robust stabilization problem is addressed for a class of high‐order stochastic nonlinear systems with output constraints and disturbances by using finite‐time control technique. One of the features of the considered stochastic systems is that the fractional powers are allowed to be any positive odd rational numbers, rather than grater than or equal to one. By constructing a novel tan‐type barrier Lyapunov function and using the adding a power integrator technique, the explicit steps on how to construct a backstepping‐like finite‐time controller have been developed to handle the robust stabilization and output constraint. Rigorous mathematical proof shows that the system states will finite‐time converge to a small region of the origin and the output constraint can be kept. Finally, a simulation example is given to illustrate the effectiveness of the proposed approach.

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“…Thus, it is easy to observe that

false| f_{2} false(\cdot false) false| = \frac{1}{4} false| \sin x_{1} false| = \frac{1}{4} false| \sin x_{1} {false|}^{\frac{4}{21}} false| \sin x_{1} {false|}^{\frac{17}{21}} \leq \frac{1}{4} false| x_{1} {false|}^{\frac{17}{21}}

false| {sans-serifg}_{3} false(\cdot false) false| = \frac{2}{3} false| \sin x_{3} false| = \frac{2}{3} false| \sin x_{3} {false|}^{\frac{3}{17}} false| \sin x_{3} {false|}^{\frac{14}{17}} \leq \frac{2}{3} false| x_{3} {false|}^{\frac{14}{17}}

false| f_{i} false({\overset{x}{true}}_{i} false) false| \leq ϕ_{i} false({\overset{x}{true}}_{i} false) true \sum_{j = 1}^{i} false| x_{j} false| and false‖ {sans-serifg}_{}

…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 65%

Section: Introductionmentioning

confidence: 99%

Robust finite‐time stabilization of a class of high‐order stochastic nonlinear systems subject to output constraint and disturbances

Fang

Ding

et al. 2019

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

show abstract

“…Furthermore, Khoo, Yin, Man, and Yu (2013) develops the finite-time stabilisation theory for non-linear stochastic systems in the strict-feedback form. More recent results on the finite-time control of non-linear stochastic systems can be found in Zheng, Chen, andWang (2011), Zha, Zhai, Ai, andFei (2014) and so on.…”

Section: Introductionmentioning

confidence: 98%

Finite-timeH_∞filtering for non-linear stochastic systems

Hou

Deng

Duan

2015

International Journal of Systems Science

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This paper describes the robust H ∞ filtering analysis and the synthesis of general non-linear stochastic systems with finite settling time. We assume that the system dynamic is modelled by Itô-type stochastic differential equations of which the state and the measurement are corrupted by state-dependent noises and exogenous disturbances. A sufficient condition for non-linear stochastic systems to have the finite-time H ∞ performance with gain less than or equal to a prescribed positive number is established in terms of a certain Hamilton-Jacobi inequality. Based on this result, the existence of a finite-time H ∞ filter is given for the general non-linear stochastic system by a second-order non-linear partial differential inequality, and the filter can be obtained by solving this inequality. The effectiveness of the obtained result is illustrated by a numerical example.

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“…But in practical systems, such as communication network systems, biochemistry reaction systems, and robot control systems, where operating times are often of finite duration, it is important that the systems achieve some desired performance in a specified finite time [12]- [14]. In this sense it appears reasonable to investigate the switching MJLSs whose states, given some initial conditions, remain within the prescribed bounds in the fixed time interval.…”

Section: Introductionmentioning

confidence: 98%

Observer-based finite-time controller for Markov jump systems with deterministic switches

Chaojie

Luan

Fei

2015

2015 34th Chinese Control Conference (CCC)

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The observer-based controller with finite-time bounded property design technique for a class of discrete-time Markov jump linear systems governed by deterministic switches is presented in this paper. Less conservative conditions are derived to ensure the state trajectories of the closed-loop systems keep within the desired bound in given-time interval by allowing the Lyapunov function to increase at every switching instant with a limited increasing rate. Meanwhile, considering the effect of time-delay on the transient performance of the systems, the analytic form of the relationship among time-delay, average dwell time and given finite time horizon are obtained through an average dwell time constraint. A numeric example is given to verify the results we derived.

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Finite-time state-feedback control for a class of stochastic high-order nonlinear systems

Cited by 28 publications

References 25 publications

Robust finite‐time stabilization of a class of high‐order stochastic nonlinear systems subject to output constraint and disturbances

Robust finite‐time stabilization of a class of high‐order stochastic nonlinear systems subject to output constraint and disturbances

Finite-timeH_∞filtering for non-linear stochastic systems

Observer-based finite-time controller for Markov jump systems with deterministic switches

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Finite-time state-feedback control for a class of stochastic high-order nonlinear systems

Cited by 28 publications

References 25 publications

Robust finite‐time stabilization of a class of high‐order stochastic nonlinear systems subject to output constraint and disturbances

Robust finite‐time stabilization of a class of high‐order stochastic nonlinear systems subject to output constraint and disturbances

Finite-timeH∞filtering for non-linear stochastic systems

Observer-based finite-time controller for Markov jump systems with deterministic switches

Contact Info

Product

Resources

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Finite-timeH_∞filtering for non-linear stochastic systems