On the estimation of a maximal Lyapunov function and domain of attraction determination via a genetic algorithm

Hamidi, Faiçal; Jerbi, Houssem

doi:10.1109/ssd.2009.4956667

Cited by 11 publications

(8 citation statements)

References 8 publications

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“…This is to determine a region of asymptotic stability in the vicinity of origin defined by the following equation [9]: 1…”

Section: A Linearization Of Carlemanmentioning

confidence: 99%

“…One of the main tools to study the stability of nonlinear systems is the theory of Lyapunov [1,9,10]. This theory asserts the existence of a positive void only at the point of balance 0 x and decreases strictly along paths.…”

Section: Introductionmentioning

confidence: 99%

“…These two properties provide stability in asymptotic system 0 x . Specifically, there is no systematic method for the construction of Lyapunov functions as a class of nonlinear systems [9]. However, the approach of Lyapunov remains the most effective way to study the stability of nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

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A Synthesis on Lyapunov Methods to the Estimation and Enlargement of Attraction Domain for Nonlinear Autonomous Systems

Hamidi

Jerbi

2009

2009 International Conference on Computational Intelligence, Modelling and Simulation

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The objective of this work is to study Lyapunov approaches for the estimation and the enlargement of Asymptotic Stability Region of nonlinear autonomous systems. These approaches have been investigated in order to develop digital algorithms based on the synthesis of a quadratic and maximum Lyapunov functions. The results on all three explored methods: McCann Method, estimation method via a Maximal Lyapunov function and the estimation method via a Quadratic Lyapunov function, showed that this variety of methods: i) is efficient for a large class of nonlinear systems, ii) has an interesting capacity of enlargement of the asymptotic stability region, and iii) is characterized by an obviousproperty of implementation for reduced and high order nonlinear systems. The efficiency and the validation of the investigated methods are tested via a simulation study. The performances of all methods are compared and discussed via the study of the well known the Van der Pol model.

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“…This is to determine a region of asymptotic stability in the vicinity of origin defined by the following equation [9]: 1…”

Section: A Linearization Of Carlemanmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Synthesis on Lyapunov Methods to the Estimation and Enlargement of Attraction Domain for Nonlinear Autonomous Systems

Hamidi

Jerbi

2009

2009 International Conference on Computational Intelligence, Modelling and Simulation

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“…Uncertainties, such as un-modeled or unknown dynamics, process parameter variations and external disturbances appear in the built models [10] and influence the performance. Consequently, the design of control systems is significantly affected when the disturbance is attenuated [11][12][13][14]. As a result, control algorithms created based on disturbance observers have been formulated to neutralize such uncertainties [15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Design of a Fuzzy Optimization Control Structure for Nonlinear Systems: A Disturbance-Rejection Method

et al. 2021

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This paper tackles the control problem of nonlinear disturbed polynomial systems using the formalism of output feedback linearization and a subsequent sliding mode control design. This aims to ensure the asymptotic stability of an unstable equilibrium point. The class of systems under investigation has an equivalent Byrnes–Isidori normal form, which reveals stable zero dynamics. For the case of modeling uncertainties and/or process dynamic disturbances, conventional feedback linearizing control strategies may fail to be efficient. To design a robust control strategy, meta-heuristic techniques are synthesized with feedback linearization and sliding mode control. The resulting control design guarantees the decoupling of the system output from disturbances and achieves the desired output trajectory tracking with asymptotically stable dynamic behavior. The effectiveness and efficiency of the designed technique were assessed based on a benchmark model of a continuous stirred tank reactor (CSTR) through numerical simulation analysis.

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“…These implementations involve a broad variety, including automotive, power grids, robotics, chemical processes, air traffic management networks and communication systems (Donkers et al, 2011;Charfeddine et al, 2011). Stability analysis and the stabilization of nonlinear switched system types represent a problem addressed within many studies (Hamidi et al, 2009;Kermani & Sakly, 2015;Pang & Zhao, 2017). In the analysis of the stability of switched systems, certain outcomes have been achieved by means of a regular Lyapunov function, several Lyapunov function sets (Hamidi et al (2011) and the idea of dwell time (Chesi & Colaneri, 2017).…”

Section: Introductionmentioning

confidence: 99%

An Enhanced Stabilizing Strategy for Switched Nonlinear Systems

Hamidi¹,

Jerbi²,

Olteanu³

et al. 2019

SIC

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This study examines a computational technique used to design a novel feedback control law based on an expansion strategy of the Attraction Domain (DA) for a class of nonlinear switched systems. It is supposed that the state space is distributed into numerous regions without any intersections and modelled by polynomial inequalities. The main concept involves the maximization of the DA for local subsystems surrounding particular operational points. It was demonstrated that the DA can be ascertained by joining a Genetic Algorithmic method (GA) as an enhanced optimisation approach with the LMI method for a specified Lyapunov function. The feedback controller can then be constructed in order to ensure a global stability by using the Multiple Lyapunov function sets via switching signals. The effectiveness of this evolved strategy is eventually confirmed via a simulation examination by means of the benchmark Van der Pol oscillator.

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On the estimation of a maximal Lyapunov function and domain of attraction determination via a genetic algorithm

Cited by 11 publications

References 8 publications

A Synthesis on Lyapunov Methods to the Estimation and Enlargement of Attraction Domain for Nonlinear Autonomous Systems

A Synthesis on Lyapunov Methods to the Estimation and Enlargement of Attraction Domain for Nonlinear Autonomous Systems

Design of a Fuzzy Optimization Control Structure for Nonlinear Systems: A Disturbance-Rejection Method

An Enhanced Stabilizing Strategy for Switched Nonlinear Systems

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