Adaptive finite-time control of nonlinear systems with parametric uncertainty

Ye, Hong; Wang, Jiankui; Cheng, Daizhan

doi:10.1109/tac.2006.875006

Cited by 411 publications

(209 citation statements)

References 8 publications

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“…It should be pointed out that the adaptive law depends on the switching signal, which is different from that of [37].…”

Section: Remarkmentioning

confidence: 99%

“…Adaptive control is one of the effective ways to deal with control systems with parametric uncertainty [29][30][31][32][33][34][35][36]. Some adaptive finite-time control results have been reported, for example, Hong et al [37] have investigated the problem of the global FTS for a class of nonlinear systems in p (being odd positive integers) normal form with parametric uncertainties; by following backstepping methodology, an adaptive finite-time control law was obtained in the form of continuous time-invariant feedback. More recently, adaptive FTS of nonlinearly parameterized nonholonomic systems was studied in [38].…”

Section: Introductionmentioning

confidence: 99%

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Global adaptive finite‐time stabilization of a class of switched nonlinear systems with parametric uncertainty

Cai

Xiang

2015

Adaptive Control & Signal

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This paper investigates the global adaptive finite-time stabilization of a class of switched nonlinear systems, whose subsystems are all in p (p 6 1) normal form with unknown control coefficients and parametric uncertainties. The restrictions on the power orders and the nonlinear perturbations are relaxed. By using the parameter separation technique, the uncertain parameters are separated from nonlinear functions. A systematic design procedure for a common state feedback controller and a switching adaptive law is presented by employing the backstepping methodology. It is proved that the closed-loop system is finite-time stable under arbitrary switching by utilizing the common Lyapunov function. Finally, with the application to finite-time control of chemical reactor systems, the effectiveness of the proposed method is demonstrated.

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“…It should be pointed out that the adaptive law depends on the switching signal, which is different from that of [37].…”

Section: Remarkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Global adaptive finite‐time stabilization of a class of switched nonlinear systems with parametric uncertainty

Cai

Xiang

2015

Adaptive Control & Signal

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show abstract

“…When p i ≥ 1, [23] studied the adaptive finite-time control of nonlinear systems with parametric uncertainty and [24,25] demonstrated the global finite-time stabilization of system (1) with low-order nonlinearity. For stochastic systems, considerable effort has been made to study the finite-time stability and stabilization in recent years.…”

Section: Introductionmentioning

confidence: 99%

Finite‐Time Stabilization of Stochastic High‐Order Nonlinear Systems

Zhang

Xie

2016

Asian Journal of Control

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This paper considers the problem of global finite-time stabilization in probability for stochastic high-order nonlinear systems in which the power order is greater than or equal to one and the drift and diffusion terms satisfy weaker growth conditions. Based on stochastic Lyapunov theorem on finite-time stability, via the combined adding one power integrator and sign function method, constructing a  2 Lyapunov function and verifying the existence and uniqueness of solution, a continuous state feedback controller is designed to guarantee the closed-loop system globally finite-time stable in probability.

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“…Compared with ASC, the FTSC offers some superior properties such as fast response, high tracking precision, strong disturbance rejection and insensitivity to system uncertainty [18][19][20][21][22]. These properties are particularly useful for high precision control of robot manipulators.…”

Section: Introductionmentioning

confidence: 99%

“…The second is, for theory, finite-time convergence has been an important and challenging topic in theoretical studying. Recently, finite-time stability control for nonlinear systems has been extensively studied [20][21][22]. Hopefully, to establish a basis for further development, the study can provide a new insight and application incentive in aspect of the theoretical development.…”

Section: Introductionmentioning

confidence: 99%