Robust Fixed Time Control of a Class of Chaotic Systems with Bounded Uncertainties and Disturbances

Su, Haipeng; Luo, Runzi; Huang, Meng; Fu, Jiaojiao

doi:10.1007/s12555-020-0782-1

Cited by 10 publications

(12 citation statements)

References 27 publications

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“…In this section, the controllable PMSM chaotic system in Refs. [36, 37] is presented as follows:

\left\{\begin{array}{@{}l@{}}\begin{array}{rl}\hfill {\dot{y}}_{1}(t)\,=& -{y}_{1}(t)+{y}_{2}(t){y}_{3}(t)+{\Delta }{f}_{1}(y)+{\hslash }_{1}(t)+{u}_{1}(t),\hfill \\ \hfill {\dot{y}}_{2}(t)\,=& -{y}_{2}(t)-{y}_{1}(t){y}_{3}(t)+{\omega }_{1}{y}_{3}(t)+{\Delta }{f}_{2}(y)+{\hslash }_{2}(t)\hfill \\ \hfill & +{u}_{2}(t),\hfill \\ \hfill {\dot{y}}_{3}(t)\,=\,& {\omega }_{2}\left({y}_{2}(t)-{y}_{3}(t)\right)+{\Delta }{f}_{3}(y)+{\hslash }_{3}(t)+{u}_{3}(t),\hfill \end{array}\quad \hfill \end{array}\right.

where

Y (t) = [y_{1} false(t false), y_{2} false(t false) ...]

…”

Section: Application To the Control Of Chaotic Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Thereinto, OZNN, IEZNN and DIEZNN models are placed in the same linear noise environment. The DIEZNN model is applied to the control of the controllable permanent magnet synchronous motor (PMSM) chaotic system [36, 37] in Section 5. These are the major contributions of this research. For solving the inverse problem of the time‐varying matrix under linear noises, the novel ZNN design formula with the double integral item is deduced and proposed for the first time. Depending on the design formula of the double integral, an innovative ZNN model is first constructed and studied to deal with the TVMI problem.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Double integral‐enhanced Zeroing neural network with linear noise rejection for time‐varying matrix inverse

Liao

Han

Cao

et al. 2023

CAAI Trans on Intel Tech

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In engineering fields, time‐varying matrix inversion (TVMI) issue is often encountered. Zeroing neural network (ZNN) has been extensively employed to resolve the TVMI problem. Nevertheless, the original ZNN (OZNN) and the integral‐enhanced ZNN (IEZNN) usually fail to deal with the TVMI problem under unbounded noises, such as linear noises. Therefore, a neural network model that can handle the TVMI under linear noise interference is urgently needed. This paper develops a double integral‐enhanced ZNN (DIEZNN) model based on a novel integral‐type design formula with inherent linear‐noise tolerance. Moreover, its convergence and robustness are verified by derivation strictly. For comparison and verification, the OZNN and the IEZNN models are adopted to resolve the TVMI under multiple identical noise environments. The experiments proved that the DIEZNN model has excellent advantages in solving TVMI problems under linear noises. In general, the DIEZNN model is an innovative work and is proposed for the first time. Satisfyingly, the errors of DIEZNN are always less than 1 × 10−3 under linear noises, whereas the error norms of OZNN and IEZNN models are not convergent to zero. In addition, these models are applied to the control of the controllable permanent magnet synchronous motor chaotic system to indicate the superiority of the DIEZNN.

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“…In this section, the controllable PMSM chaotic system in Refs. [36, 37] is presented as follows:

\left\{\begin{array}{@{}l@{}}\begin{array}{rl}\hfill {\dot{y}}_{1}(t)\,=& -{y}_{1}(t)+{y}_{2}(t){y}_{3}(t)+{\Delta }{f}_{1}(y)+{\hslash }_{1}(t)+{u}_{1}(t),\hfill \\ \hfill {\dot{y}}_{2}(t)\,=& -{y}_{2}(t)-{y}_{1}(t){y}_{3}(t)+{\omega }_{1}{y}_{3}(t)+{\Delta }{f}_{2}(y)+{\hslash }_{2}(t)\hfill \\ \hfill & +{u}_{2}(t),\hfill \\ \hfill {\dot{y}}_{3}(t)\,=\,& {\omega }_{2}\left({y}_{2}(t)-{y}_{3}(t)\right)+{\Delta }{f}_{3}(y)+{\hslash }_{3}(t)+{u}_{3}(t),\hfill \end{array}\quad \hfill \end{array}\right.

where

Y (t) = [y_{1} false(t false), y_{2} false(t false) ...]

…”

Section: Application To the Control Of Chaotic Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Double integral‐enhanced Zeroing neural network with linear noise rejection for time‐varying matrix inverse

Liao

Han

Cao

et al. 2023

CAAI Trans on Intel Tech

View full text Add to dashboard Cite

show abstract

“…Based on the Lyapunov theorem and some inequality techniques, sliding mode surfaces were proposed to establish controllers that guarantee fixed-time stability independently of the system's initial conditions. In 2022, [34] proposed a criterion that determines a boundary for the fixed-time stability of chaotic dynamics with internal uncertainties and external disturbances. In that year, the article [35] addressed the topic of employing a dynamic sliding mode controller to stabilize interval type-2 fuzzy systems with uncertainties, time delays, and external disturbances.…”

Section: Introductionmentioning

confidence: 99%

Design of a Fixed-Time Stabilizer for Uncertain Chaotic Systems Subject to External Disturbances

et al. 2023

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This paper addresses the fixed-time stability problem of chaotic systems with internal uncertainties and external disturbances. To this end, new sliding-mode surfaces are introduced to design fixed-time controllers for the stabilization of perturbed chaotic systems. First, the required conditions for deriving fixed-time stability are determined. Then, using the obtained stability theorems and sliding mode techniques, the controllers are synthesized. The proposed controller enables the convergence of the trajectories of the chaotic system to the origin in finite time, independently of the initial conditions. The performance of the proposed approach is assessed using a simulation study of a PMSM system and the Matouk system. Among the advantages of the proposed controller are its robustness to external disturbances and the boundedness of the settling time to a constant value for any initial condition.

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“…[1][2][3][4][5][6][7]. It is well known that complex variable chaotic systems are an important branch of chaotic system [8], and Many control methods are used in practical applications, such as communication engineering [9], robust control [10,11], electrical engineering [12], etc. and have achieved good results in the problems of tracking control, antisynchronization, and stabilization.…”

Section: Introductionmentioning

confidence: 99%

Projection synchronization of complex variable nonlinear chaotic systems based on UDE

Song

Zhang²,

Pan³

et al. 2022

6th International Workshop on Advanced Algorithms and Control Engineering (IWAACE 2022)

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The projection synchronization issue of complex Lü chaotic systems is examined in this work. Firstly, the system is presented, the complex chaotic system is transformed into the equivalent real number system, on this basis, the existence of the projection synchronization problem is proved and solution is obtained by an algorithm. Secondly, combines feedback controller and uncertainty and disturbance estimator (UDE), where one is used to implement the projection synchronization of nominal complex chaotic systems and the UDE controller is used to remove uncertainty and disturbance. Finally, the validity of the proposed results is proved by numerical simulation.

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Robust Fixed Time Control of a Class of Chaotic Systems with Bounded Uncertainties and Disturbances

Cited by 10 publications

References 27 publications

Double integral‐enhanced Zeroing neural network with linear noise rejection for time‐varying matrix inverse

Double integral‐enhanced Zeroing neural network with linear noise rejection for time‐varying matrix inverse

Design of a Fixed-Time Stabilizer for Uncertain Chaotic Systems Subject to External Disturbances

Projection synchronization of complex variable nonlinear chaotic systems based on UDE

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