Chaos Control of Lorenz System Using Small Gain Theorem

Wang, Lei; Xu, Jian-Hao; Wang, Ti-Biao

doi:10.1007/978-3-642-01510-6_133

Cited by 1 publication

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“…Generally speaking, the problem of controlling Lorenz system is challenged from the following three points. i) Since the Lorenz system is a nonlinear dynamical system, the methods using linear state feedback cannot guarantee the global stability for the system in some situations [17]. ii) Compared to the active control (i. e., the system parameters are known), it is more difficult to control chaos in the presence of uncertainty in system parameters [18].…”

Section: Introductionmentioning

confidence: 99%

Research on a New Singularity-Free Controller for Uncertain Lorenz System

Chen

2019

IEEE Access

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It is a challenge problem to stably control the well-known Lorenz system with uncertain parameters because of its nonlinearity and singularity. In this paper, by combining Zhang dynamics (ZD) and gradient-algorithm, a novel Zhang-Gradient (ZG) controller is designed and developed for solving the controlling problem of the uncertainty Lorenz system. In order to improve computing efficiency, the stochastic parallel gradient descent algorithm is also introduced to perform an incremental adjustment of the unknown parameters for the uncertain Lorenz system. The presented theoretical analysis in this paper shows that our such presented method could conquer the possible singularity which is a difficult problem in typical backstepping controller design. The computer simulation results exhibit that, the controlled system can be stable globally and the tracking error converges to zero asymptotically, which are further demonstrate the effectiveness and feasibility of our presented ZG controller.

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Section: Introductionmentioning

confidence: 99%

Research on a New Singularity-Free Controller for Uncertain Lorenz System

Chen

2019

IEEE Access

View full text Add to dashboard Cite

show abstract

Chaos Control of Lorenz System Using Small Gain Theorem

Cited by 1 publication

References 12 publications

Research on a New Singularity-Free Controller for Uncertain Lorenz System

Research on a New Singularity-Free Controller for Uncertain Lorenz System

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