Decentralized summation‐based triggering mechanism for Lipschitz nonlinear systems

Mousavi, Seyed Hossein; Marquez, Horacio J.

doi:10.1002/rnc.3794

Cited by 10 publications

(5 citation statements)

References 31 publications

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“…This is demonstrated in our example in Section 5.2. Assumption is the linear growth condition, but there are still many applicable practical systems, eg, an electromagnetic levitation system in our experiment and an inverted pendulum …”

Section: Resultsmentioning

confidence: 99%

Robust observer‐based output feedback controller for nonlinear systems with uncertain triangular and nontriangular nonlinearities and diagonal terms

Choi

2018

Intl J Robust & Nonlinear

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In this paper, we provide a robust observer-based output feedback control scheme for a class of nonlinear systems where there are uncertain triangular and nontriangular nonlinearities, nontrivial diagonal terms, and external disturbance. The presence of diagonal terms is the main generalized feature over the existing results. In order to handle the diagonal terms, there is a gain-scaling factor in the proposed controller. Through the analysis, we show that all states and observer errors of the controlled system remain bounded. Moreover, the ultimate bounds of some states and observer errors can be made (arbitrarily) small by adjusting the gain-scaling factor reflecting on the structure of nonlinearities and external disturbance. The validity of our control scheme is experimentally verified via the ball position control of an electromagnetic levitation system. KEYWORDSdiagonal terms, gain-scaling factor, observer-based output feedback control, triangular and nontriangular nonlinearities, ultimate bounds 1182

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Section: Resultsmentioning

confidence: 99%

Robust observer‐based output feedback controller for nonlinear systems with uncertain triangular and nontriangular nonlinearities and diagonal terms

Choi

2018

Intl J Robust & Nonlinear

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“…Therefore, Assumption 1 is more generalized over References 1,3. The following condition is imposed in Reference 7. There exist a function

γ (ϵ) \geq 0

such that for

ϵ > 0

\begin{align} true \sum_{i = 1}^{n} ϵ^{i prefix- 1} false| δ_{i} false(t, x, u false) false| \leq γ false(ϵ false) true \sum_{i = 1}^{n} ϵ^{i prefix- 1} false| x_{i} false|, i = 1, \dots, n . \end{align}

Over the condition (6), Assumption 1 becomes more general by adding the term

ϵ^{n} | u |

. Other conditions of (A3) can represent some models of the inverted pendulum system 13,26 with uncertain mass parameter:

{\dot{x}}_{1} = x_{2}

{\dot{x}}_{2} = {1 / (m_{0} + Δ m) l^{2}} u + (g / l) \sin x_{1}

and so on. However, the control method of References 1,3,7 cannot be applied to this inverted pendulum system due to the nonlinearity of input term

{1 / (m_{0} + Δ m) l^{2 ...}

…”

Section: System Formulation and Problem Statementmentioning

confidence: 99%

“…Other conditions of (A3) can represent some models of the inverted pendulum system 13,26 with uncertain mass parameter:

{\dot{x}}_{1} = x_{2}

{\dot{x}}_{2} = {1 / (m_{0} + Δ m) l^{2}} u + (g / l) \sin x_{1}

and so on. However, the control method of References 1,3,7 cannot be applied to this inverted pendulum system due to the nonlinearity of input term

{1 / (m_{0} + Δ m) l^{2}} u

.…”

Section: System Formulation and Problem Statementmentioning

confidence: 99%

“…Example D : ((A3) other condition with extended structure of perturbed nonlinearity): The inverted pendulum system dynamics 13,26 is considered with uncertain mass

Δ m

{\dot{x}}_{1} = x_{2}

{\dot{x}}_{2} = {1 / (m_{0} + Δ m) l^{2}} u + (g / l) \sin x_{1}

where x 1 represents the pendulum angular displacement, x 2 is the angular velocity, u is the control input, l = 7 is the length, m 0 = 5 is the nominal mass, g = 9.8 is the acceleration of gravity, and

| Δ m | \leq 0.2

. With a prefeedback

u = m_{0} l^{2} {v - (g / l) \sin x_{1}}

, we have

\begin{align} {\overset{x}{true}}_{1} & = x_{2}, \\ {\overset{x}{true}}_{2} & = v prefix- \frac{normalΔ m}{m_{0} + normalΔ m} v + \frac{normalΔ m}{m_{0} + normalΔ m} \frac{g}{l} \sin x_{1}, \\ y & = x_{1} . \end{align}

…”

Section: Illustrative Examplesmentioning

confidence: 99%

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Global exponential stabilization for a class of nonlinear systems by output feedback control with three gain‐scaling factors

Choi

2020

Intl J Robust & Nonlinear

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SummaryIn this article, we consider a problem of global exponential stabilization for a class of nonlinear systems with the perturbed nonlinearity by output feedback. We provide a newly designed observer‐based output feedback controller with three gain‐scaling factors to deal with extended structure of nonlinearity and larger growth rate of nonlinearity over the existing results. Utilizing three gain‐scaling factors, we have more flexibility in selecting control parameters. Moreover, we present two procedures for selecting gain‐scaling parameters which are associated with stabilizing the system and improving the convergence rate of the system states and observer errors, respectively. Via numerical and practical examples, we illustrate the improved features of the proposed control scheme over the existing schemes.

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“…The digital controller can estimate the plant's state and the unknown disturbances only based on intermittently measurement outputs, and then, generates the required PI control signals. Second, a new kind of summation‐based triggering condition [30] is proposed, which aims to provide a positive minimum inter‐event time uniformly for a family of controllers parameterised by the verification periods. It is shown that the uniform positive minimum inter‐event time can be guaranteed for the proposed triggering conditions if the signals in the threshold parts can include all of those involved in the dynamics of the corresponding measurement errors.…”

Section: Introductionmentioning

confidence: 99%

Set‐point output tracking problem for linear plants via periodic event‐triggered control

Hao

2020

IET Control Theory & Applications

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Decentralized summation‐based triggering mechanism for Lipschitz nonlinear systems

Cited by 10 publications

References 31 publications

Robust observer‐based output feedback controller for nonlinear systems with uncertain triangular and nontriangular nonlinearities and diagonal terms

Robust observer‐based output feedback controller for nonlinear systems with uncertain triangular and nontriangular nonlinearities and diagonal terms

Global exponential stabilization for a class of nonlinear systems by output feedback control with three gain‐scaling factors

Set‐point output tracking problem for linear plants via periodic event‐triggered control

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