A Nonlinear Adaptive Resilient Observer Design for a Class of Lipschitz Systems Using LMI

This paper presents the H ∞ static output feedback control of nonlinear fractional-order systems. Based on the extended bounded real lemma, the H ∞ control is formulated and sufficient conditions are derived in terms of linear matrix inequalities (LMIs) formulation by using the fractional Lyapunov direct method where the fractional-order α belongs to 0 < α < 1. The control approach is finally applied to the regulation of the glucose level in diabetes type 1 treatment. Therefore, it is attempted to incorporate fractional-order into the mathematical minimal model of glucose-insulin system dynamics and it is still an interesting challenge to show, how the order of a fractional differential system affects the dynamics of the system in the presence of meal disturbance. Numerical simulations are carried out to illustrate our proposed results and show that the nonlinear fractional-order glucose-insulin systems are, at least, as stable as their integer-order counterpart in the presence of exogenous glucose infusion or meal disturbance.

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“…Lemma 2 [37]: Let X and Y be real vectors of the same dimension. Then, for any scalar ε > 0, the following inequality holds…”

Section: Fractional Derivativementioning

confidence: 99%

Static output feedback ℋ ∞ control for a fractional-order glucose-insulin system

Ndoye

Voos

Darouach

et al. 2015

Int. J. Control Autom. Syst.

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“…Lipschitz observer is a common non-linear system state observer and still has a good observation performance for strongly non-linear systems with noise disturbances. Specific design process of Lipschitz observer is characterized as follows (Rajamani 1998;Zemouche and Boutayeb 2013;Pourgholi and Majd 2011).…”

Section: Fast Loop Controller Designmentioning

confidence: 99%

“…L is obtained by transforming Riccati equation into the linear matrix inequality (LMI) problem (Pourgholi and Majd 2011).…”

Section: Lipschitz Adaptive Observer Designmentioning

confidence: 99%

The Control of Asymmetric Rolling Missiles Based on Improved Trajectory Linearization Control Method

Sun¹,

Yu²,

Zhang³

2016

J.Aerosp. Technol. Manag.

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According to motion characteristic of an asymmetric rolling missile with damage fin, a three-channel controlled model is established. The controller which is used to realize non-linear tracking and decoupling control of the roll and angle motion is introduced based on an improved trajector y linearization control method. The improved method is composed of the classic trajectory linearization control method and a compensation control law. The classic trajectory linearization control method is implemented in the time-scale separation principle. The Lipschitz non-linear state observer systematically obtained by solving the linear matrix inequality approach is provided to estimate state variables and unknown parameters, and then the compensation control law utilizing the estimated unknown parameters improves the TLC method. Simulation experiments show that the adaptive decoupling control ensure tracking performance, and the robustness and accuracy of missile attitude control are ensured under the condition of the system parameters uncertainty, random observation noise and external disturbance caused by damage fin.

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“…To prove the theorem the following lemmas are used: Lemma 1: [31] Let X and Y be real vectors of the same dimension. Then, for any scalar ε > 0, the following inequality holds:…”

Section: Moreover the State T(t) Is Bounded By T(t)mentioning

confidence: 99%

Feedback control for distributed heat transfer mechanisms in direct-contact membrane distillation system

Eleiwi

Ndoye

Laleg‐Kirati

2015

2015 IEEE Conference on Control Applications (CCA)

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Abstract-In this paper, the problem of stabilization and production rate reference tracking for a Direct-Contact Membrane Distillation (DCMD) system is addressed. Sufficient conditions for the asymptotic and exponential stabilization for DCMD system are presented using the Gronwall-Bellman lemma and Linear Matrix Inequalities (LMIs) approaches, respectively. A nonlinear observer is then proposed to estimate the temperature distribution among the DCMD domain. This contributes to propose a reference production rate control design for the DCMD process via observer-based output control approach. Finally, numerical simulations are given to show the effectiveness of the proposed methods.

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A Nonlinear Adaptive Resilient Observer Design for a Class of Lipschitz Systems Using LMI

Cited by 29 publications

References 18 publications

Static output feedback ℋ ∞ control for a fractional-order glucose-insulin system

Static output feedback ℋ ∞ control for a fractional-order glucose-insulin system

The Control of Asymmetric Rolling Missiles Based on Improved Trajectory Linearization Control Method

Feedback control for distributed heat transfer mechanisms in direct-contact membrane distillation system

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