scholarly journals Chaotic Particle Swarm Optimisation for Enlarging the Domain of Attraction of Polynomial Nonlinear Systems

Electronics ◽  
2020 ◽  
Vol 9 (10) ◽  
pp. 1704
Author(s):  
Faiçal Hamidi ◽  
Messaoud Aloui ◽  
Houssem Jerbi ◽  
Mourad Kchaou ◽  
Rabeh Abbassi ◽  
...  
Keyword(s):  
Iterative Procedure ◽  
Stability Region ◽  
Linear Inequality ◽  
Time Derivative ◽  
Domain Of Attraction ◽  
Polynomial Systems ◽  
Software Environment ◽  
Novel Technique ◽  
Asymptotic Stability Region ◽  
Achievable Region

A novel technique for estimating the asymptotic stability region of nonlinear autonomous polynomial systems is established. The key idea consists of examining the optimal Lyapunov function (LF) level set that is fully included in a region satisfying the negative definiteness of its time derivative. The minor bound of the biggest achievable region, denoted as Largest Estimation Domain of Attraction (LEDA), can be calculated through a Generalised Eigenvalue Problem (GEVP) as a quasi-convex Linear Inequality Matrix (LMI) optimising approach. An iterative procedure is developed to attain the optimal volume or attraction region. Furthermore, a Chaotic Particular Swarm Optimisation (CPSO) efficient technique is suggested to compute the LF coefficients. The implementation of the established scheme was performed using the Matlab software environment. The synthesised methodology is evaluated throughout several benchmark examples and assessed with other results of peer technique in the literature.

Polynomial control design for polynomial systems: A non-iterative sum of squares approach

2018 ◽  
Vol 41 (7) ◽  
pp. 1993-2004
Author(s):  
Mohsen Rakhshan ◽  
Navid Vafamand ◽  
Mohammad Mehdi Mardani ◽  
Mohammad-Hassan Khooban ◽  
Tomislav Dragičević
Keyword(s):  
Controller Design ◽  
Time Derivative ◽  
Polynomial Systems ◽  
Sum Of Squares ◽  
Continuous Stirred Tank Reactor ◽  
Wide Range ◽  
Convex Problem ◽  
Lyapunov Matrix ◽  
Different Chaotic Systems ◽  
Real Time Simulations

This paper proposes a non-iterative state feedback design approach for polynomial systems using polynomial Lyapunov function based on the sum of squares (SOS) decomposition. The polynomial Lyapunov matrix consists of states of the system leading to the non-convex problem. A lower bound on the time derivative of the Lyapunov matrix is considered to turn the non-convex problem into a convex one; and hence, the solutions are computed through semi-definite programming methods in a non-iterative fashion. Furthermore, we show that the proposed approach can be applied to a wide range of practical and industrial systems that their controller design is challenging, such as different chaotic systems, chemical continuous stirred tank reactor, and power permanent magnet synchronous machine. Finally, software-in-the-loop (SiL) real-time simulations are presented to prove the practical application of the proposed approach.

scholarly journals Stability investigation of quadratic systems with delay

2000 ◽  
Vol 13 (1) ◽  
pp. 85-92 ◽  
Author(s):  
Vladimir Davydov ◽  
Denis Khusainov
Keyword(s):  
Asymptotic Stability ◽  
Quadratic Form ◽  
Stability Region ◽  
Zero Solution ◽  
Stability Conditions ◽  
Quadratic Systems ◽  
Systems Of Differential Equations ◽  
Asymptotic Stability Region ◽  
Lyapunov’S Second Method ◽  
Form Stability

Systems of differential equations with quadratic right-hand sides with delay are considered in the paper. Compact matrix notation form is proposed for the systems of such type. Stability investigations are performed by Lyapunov's second method with functions of quadratic form. Stability conditions of quadratic systems with delay, uniformly by argument deviation, and with delay depending on the system's parameters are derived. A guaranteed radius of the ball of asymptotic stability region for zero solution is obtained.

Large Signal Stability Analysis of a Hybrid AC/DC Microgrid With a Cascaded Control Inverter

2018 ◽  
Author(s):  
Hongru Xu ◽  
Yan Chen ◽  
Brian Keel
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Stability Region ◽  
Domain Of Attraction ◽  
Analysis Tool ◽  
Large Signal ◽  
Dc Microgrid ◽  
Stability Regions ◽  
Signal Stability ◽  
Grid Connected Inverter

The large signal stability analysis of a hybrid AC/DC microgrid based on a grid-connected inverter with cascaded control is discussed. The impacts of the connected inductor, capacitor, and the control parameters of the inverter on the DC link stability region are analyzed. To achieve these analyses, a dynamic model of the microgrid with the cascaded control inverter is first developed. A Lyapunov large-signal stability analysis tool is then applied to estimate the domain of attraction, which is the asymptotic stability region. Results show that DC side capacitor, the AC side grid filter, as well as the control gain, will have different influences on the stability regions of the DC link voltage. High fidelity simulations through PLECS are successfully applied to verify the asymptotic stability regions estimated from the Lyapunov large signal analysis method.

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