Saturated Delayed Controls for Feedforward Nonlinear Systems

Ye, Huawen

doi:10.1109/tac.2013.2293411

Cited by 27 publications

(42 citation statements)

References 31 publications

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“…Remark Some mechanical systems such as the PVTOL aircraft model system and the translational oscillators with rotating actuator (TORA) system can be transformed into feedforward nonlinear systems with nonlinear perturbations satisfying Assumption . For example, after some suitable transformations, the TORA system is in the following form:

\{\begin{matrix} {\overset{x}{true}}_{1} = x_{2}, \\ {\overset{x}{true}}_{2} = - x_{1} + x_{3} + ((), \sin x_{3} - x_{3}), \\ {\overset{x}{true}}_{3} = x_{4}, \\ {\overset{x}{true}}_{4} = u, \end{matrix}

where the nonlinear perturbation satisfies

|\sin x_{3} - x_{3}| \leq 3 x_{3}^{2}, whenever |x_{3}| \leq 1 .

…”

Section: Problem Formulationmentioning

confidence: 99%

“…For system , when h i = 0, i ∈ I [2, p ], and r = 0, Problem has been investigated in the work of Ye based on a canonical form introduced by Teel . However, since the control is subject to time delay, the decoupling property in the work of Teel is no longer valid in the recursive design, which makes the analysis in the work of Ye rather involved. In this paper, we will construct a novel canonical form containing not only time delay in the input but also time delays in its state, which can keep the decoupling property in the recursive design.…”

Section: Problem Formulationmentioning

confidence: 99%

“…The proposed controllers contain some free parameters that can be designed to improve the control performance. Moreover, such a special canonical form permits us to handle feedforward systems containing delayed states, which were not considered in the work of Ye . Besides, when the nonlinear terms in vanish, a modified saturated feedback will be established to the corresponding global stabilization problem.…”

Section: Problem Formulationmentioning

confidence: 99%

“…Particularly, in order to guarantee that the saturation functions will operate in linear region after a finite time (see the proof of part A of Theorem ), a deeper analysis than that in the work of Zhou and Yang will be established. Compared with the results in the work of Ye, our proposed nonlinear control laws contain not only the current but also the delayed states, which allows us to cancel all the other state components at every step of the recursive design, which leads to a much more concise analysis than that in the work of Ye . Moreover, the approach proposed in this paper can deal with feedforward nonlinear systems containing not only the current states but also the delayed states, which was not considered in the work of Ye .…”

Section: Introductionmentioning

confidence: 96%

“…Compared with the results in the work of Ye, our proposed nonlinear control laws contain not only the current but also the delayed states, which allows us to cancel all the other state components at every step of the recursive design, which leads to a much more concise analysis than that in the work of Ye . Moreover, the approach proposed in this paper can deal with feedforward nonlinear systems containing not only the current states but also the delayed states, which was not considered in the work of Ye . Part of results in this paper (without proofs) has been presented at The 14th IFAC Workshop on Time Delay Systems held in Budapest, June 28‐30, 2018 …”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Bounded control of feedforward time‐delay systems with linearized systems consisting of chain of oscillators

Yang

Zhou

Lam³

2018

Intl J Robust & Nonlinear

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Summary For the global stabilization of a family of feedforward nonlinear time‐delay systems whose linearized systems consist of a chain of identical oscillators, a saturated feedback control is established based on a special canonical form. The proposed control laws use not only the current states but also the delayed states for feedback, which helps maintain the decoupling property in the recursive design. Moreover, explicit conditions guaranteeing the stability of the closed‐loop system are provided. When the nonlinear terms vanish and even the oscillators are distinct, a modified saturated feedback control can still be established for the corresponding global stabilization problem. Two numerical examples are given to illustrate the effectiveness of the proposed approaches.

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\{\begin{matrix} {\overset{x}{true}}_{1} = x_{2}, \\ {\overset{x}{true}}_{2} = - x_{1} + x_{3} + ((), \sin x_{3} - x_{3}), \\ {\overset{x}{true}}_{3} = x_{4}, \\ {\overset{x}{true}}_{4} = u, \end{matrix}

where the nonlinear perturbation satisfies

|\sin x_{3} - x_{3}| \leq 3 x_{3}^{2}, whenever |x_{3}| \leq 1 .

…”

Section: Problem Formulationmentioning

confidence: 99%

Section: Problem Formulationmentioning

confidence: 99%

Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Bounded control of feedforward time‐delay systems with linearized systems consisting of chain of oscillators

Yang

Zhou

Lam³

2018

Intl J Robust & Nonlinear

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New Saturated Delayed Control for a Chain of Integrators with Nonlinear Terms

Kang

et al. 2017

Asian Journal of Control

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This paper investigates the saturated delayed stabilization of a chain of integrators with higher‐order nonlinear terms. With the aid of a recent state transformation, the system is transformed into a canonical form in which time delay appears in both input and states. As a result, natural cancellations can be fully used in the saturation reduction analysis, and fewer terms need to be estimated in the asymptotical stability analysis of the reduced system. In addition, a single tuneable parameter is introduced to the special state transformation, which facilitates compensating an arbitrarily large input‐delay. As an example, a simplified inertia wheel pendulum system is provided with an explicit controller and numerical simulations are given to demonstrate the effectiveness of the suggested controller.

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Global stabilization via nested saturation function for high-order feedforward nonlinear systems with unknown time-varying delays

Song

Sun

Yang

et al. 2016

Int. J. Robust. Nonlinear Control

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Summary We consider the global stabilization problem for a class of high‐order feedforward time‐delay nonlinear systems. The nested saturation function method is inherently improved to develop a continuous controller, without the requirements on the memory of the past input and the prior information of the time‐varying delays. The proposed controller is less conservative in terms of the level of nonlinearities whose upper bounds include high‐order, low‐order, and linear terms. The design procedures are provided based on the sign function technique, the homogeneous domination idea, and the search of Lyapunov function. Finally, a simulation example is used to demonstrate the application of the obtained theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.

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Saturated Delayed Controls for Feedforward Nonlinear Systems

Cited by 27 publications

References 31 publications

Bounded control of feedforward time‐delay systems with linearized systems consisting of chain of oscillators

Bounded control of feedforward time‐delay systems with linearized systems consisting of chain of oscillators

New Saturated Delayed Control for a Chain of Integrators with Nonlinear Terms

Global stabilization via nested saturation function for high-order feedforward nonlinear systems with unknown time-varying delays

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