Adaptive tracking control for switched strict-feedback nonlinear systems with time-varying delays and asymmetric saturation actuators

Yu, Zhensheng; Dong, Yan; Li, Shugang; Li, Fangfei

doi:10.1016/j.neucom.2017.01.060

Cited by 57 publications

(60 citation statements)

References 38 publications

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“…In other works, it has been shown that saturation, backlash, and dead zone nonlinearities can be expressed by .Definition Consider the following nonlinear system:

\overset{x}{true} = h ((), x, t), x ((), t_{0}) = x_{0},

where x ( t ) ∈ ℝ n denotes the system state, h : ℝ n × [ t 0 , ∞] → ℝ n is a continuous vector‐valued function, and x 0 ∈ ℝ n and t 0 denote the initial state vector and the initial time, respectively. For all x 0 ∈ U with a compact set U ∈ ℝ n , if there exists a w > 0 and a number T ( w , x 0 ) such that ‖ x ( t )‖ < w holds, for all t ≥ T ( w , x 0 ) + t 0 , it is said the solution of this system is semiglobally uniformly ultimately bounded (SGUUB).…”

Section: Preliminaries and Problem Statementmentioning

confidence: 99%

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Adaptive prescribed performance control of switched MIMO uncertain nonlinear systems subject to unmodeled dynamics and input nonlinearities

Malek

Shahrokhi

Vafa

et al. 2018

Intl J Robust & Nonlinear

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Summary In this paper, the design of an adaptive tracking control for a class of switched uncertain multiple‐input–multiple‐output nonlinear systems in the strict‐feedback form with unmodeled dynamics in the presence of three types of input nonlinearity under arbitrary switching has been addressed. By means of an intelligent approximator like a fuzzy logic system or a neural network, the unknown dynamics are estimated. The unmodeled dynamics have been tackled with a dynamic signal. A universal framework for describing different types of input nonlinearity including saturation, backlash, and dead zone has been utilized. By applying the backstepping approach and the common Lyapunov function method, virtual and actual controllers and the adaptive law for each subsystem have been constructed. Finally, it has been shown that the closed‐loop system is semiglobally uniformly ultimately bounded and the tracking errors converge to their predefined bounds. The effectiveness of the proposed control scheme has been shown through simulation study.

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“…In other works, it has been shown that saturation, backlash, and dead zone nonlinearities can be expressed by .Definition Consider the following nonlinear system:

\overset{x}{true} = h ((), x, t), x ((), t_{0}) = x_{0},

Section: Preliminaries and Problem Statementmentioning

confidence: 99%

“…Nevertheless, there exists a substantial drawback regarding this technique called “explosion of complexity” caused by the repeated differentiations of virtual controllers. To overcome this problem, the dynamic surface control may be used or the virtual controllers derivatives can be estimated by an intelligent approximator …”

Section: Introductionmentioning

confidence: 99%

Adaptive prescribed performance control of switched MIMO uncertain nonlinear systems subject to unmodeled dynamics and input nonlinearities

Malek

Shahrokhi

Vafa

et al. 2018

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

show abstract

“…Switched systems as a class of hybrid systems consist of a number of subsystems that orchestrated by a switching rule to determine which subsystem is active at each time instant . Due to their numerous applications in a wide range of control systems such as chemical process, near space vehicle, human muscular control systems, and networked control systems, considerable attention has been attracted to control and stabilization of these systems …”

Section: Introductionmentioning

confidence: 99%

“…In the last decade, by applying the backstepping‐based approaches, several adaptive control methods have been proposed for pure‐ and strict‐feedback switched nonlinear systems with delay and without delay . In other works, dynamic surface control (DSC) procedure has been utilized to overcome the “explosion of complexity” due to repetitive differentiation of virtual controller in each step of the backstepping approach. In order to compensate unknown time‐delay terms, other authors have exploited the Lyapunov‐Krasovskii functional.…”

Section: Introductionmentioning

confidence: 99%

Prescribed performance adaptive neural output control for a class of switched nonstrict‐feedback nonlinear time‐delay systems: State‐dependent switching law approach

Kamali

Tabatabaei

Arefi

et al. 2019

Intl J Robust & Nonlinear

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Summary This paper investigates the tracking problem for a class of uncertain switched nonlinear delayed systems with nonstrict‐feedback form. To address this problem, by introducing a new common Lyapunov function (CLF), an adaptive neural network dynamic surface control is proposed. The state‐dependent switching rule is designed to orchestrate which subsystem is active at each time instance. In order to compensate unknown delay terms, an appropriate Lyapunov‐Krasovskii functional is considered in the constructing of the CLF. In addition, a novel switched neural network–based observer is constructed to estimate system states through the output signal. To maintain the tracking error performance within a predefined bound, a prescribed performance bound approach is employed. It is proved that by the proposed output‐feedback control, all the signals of the closed‐loop system are bounded under the switching law. Moreover, the transient and steady‐state tracking performance is guaranteed by the prescribed performance bound. Finally, the effectiveness of the proposed method is illustrated by two numerical and practical examples.

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“…And there are also a large number of researches on the stability of predator-prey systems with time delays. The time delays have very complex impact on the dynamic behaviors of nonlinear dynamic systems [2,3,11,15,[17][18][19]. Zhang [16] produced a general example of such generalized model, that is to say, he investigated a threespecies model, and the results showed that the positive equilibrium is locally stable when the system has two same time delays.…”

Section: Introductionmentioning

confidence: 99%

Hopf bifurcation analysis and its preliminary control in a Hasting-Powell food chain model with two different delays

Zhang¹,

Lu²,

Du³

et al. 2017

J. Nonlinear Sci. Appl.

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Keeping the balance of nature is important, and it is very significant to effectively control the number of species for ecosystem stability. In this paper, we propose a tritrophic Hastings-Powell (HP) model with two different time delays, and the local stability of equilibrium, Hopf bifurcation, and the existence and uniqueness of the positive equilibrium are analyzed in detail. Besides, we obtain the stable conditions for the system and prove that Hopf bifurcation will occur when the delay pass through the critical value. And the stability and direction of the Hopf bifurcation are also investigated by using the center manifold theorem and normal form theorem. Finally, some numerical examples are given to illustrate the results.

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Adaptive tracking control for switched strict-feedback nonlinear systems with time-varying delays and asymmetric saturation actuators

Cited by 57 publications

References 38 publications

Adaptive prescribed performance control of switched MIMO uncertain nonlinear systems subject to unmodeled dynamics and input nonlinearities

Adaptive prescribed performance control of switched MIMO uncertain nonlinear systems subject to unmodeled dynamics and input nonlinearities

Prescribed performance adaptive neural output control for a class of switched nonstrict‐feedback nonlinear time‐delay systems: State‐dependent switching law approach

Hopf bifurcation analysis and its preliminary control in a Hasting-Powell food chain model with two different delays

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