scholarly journals Generalized conformable operators: Application to the design of nonlinear observers

2021 ◽  
Vol 6 (11) ◽  
pp. 12952-12975
Author(s):  
Fidel Meléndez-Vázquez ◽  
◽  
Guillermo Fernández-Anaya ◽  
Aldo Jonathan Muñóz-Vázquez ◽  
Eduardo Gamaliel Hernández-Martínez ◽  
...  
Keyword(s):  
Differential Operator ◽  
Nonlinear Systems ◽  
Exponential Stability ◽  
Numerical Simulations ◽  
Stability Function ◽  
Nonlinear Observers ◽  
Conformable Derivatives ◽  
Generalized Differential ◽  
The Stability ◽  
Comparison Of The Results

<abstract><p>In this work, a pair of observers are proposed for a class of nonlinear systems whose dynamics involve a generalized differential operator that encompasses the conformable derivatives. A generalized conformable exponential stability function, based on this derivative, is introduced in order to prove some Lyapunov-like theorems. These theorems help to verify the stability of the observers proposed, which is exponential in a generalized sense. The performance of the observation scheme is evaluated by means of numerical simulations. Moreover, a comparison of the results obtained with integer, fractional, and generalized conformable derivatives is made.</p></abstract>

scholarly journals General conformable estimators with finite-time stability

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Fidel Meléndez-Vázquez ◽  
Guillermo Fernández-Anaya ◽  
Eduardo G. Hernández-Martínez
Keyword(s):  
Dynamical Systems ◽  
Finite Time ◽  
Nonlinear Dynamical Systems ◽  
Time Stability ◽  
Conformable Derivative ◽  
Stability Function ◽  
Nonlinear Dynamical ◽  
Finite Time Stability ◽  
Conformable Derivatives ◽  
The Stability

Abstract In this paper, some estimators are proposed for nonlinear dynamical systems with the general conformable derivative. In order to analyze the stability of these estimators, some Lyapunov-like theorems are presented, taking into account finite-time stability. Thus, to prove these theorems, a stability function is defined based on the general conformable operator, which implies exponential stability. The performance of the estimators is assessed by means of numerical simulations. Furthermore, a comparison is made between the results obtained with the integer, fractional, and general conformable derivatives.

scholarly journals Observer-based adaptive neural network backstepping sliding mode control for switched fractional order uncertain nonlinear systems with unmeasured states

2021 ◽  
pp. 002029402110211
Author(s):  
Tao Chen ◽  
Damin Cao ◽  
Jiaxin Yuan ◽  
Hui Yang
Keyword(s):  
Neural Network ◽  
Nonlinear Systems ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Tracking Error ◽  
Adaptive Neural Network ◽  
Dynamic Surface ◽  
Mode Control ◽  
The Stability

This paper proposes an observer-based adaptive neural network backstepping sliding mode controller to ensure the stability of switched fractional order strict-feedback nonlinear systems in the presence of arbitrary switchings and unmeasured states. To avoid “explosion of complexity” and obtain fractional derivatives for virtual control functions continuously, the fractional order dynamic surface control (DSC) technology is introduced into the controller. An observer is used for states estimation of the fractional order systems. The sliding mode control technology is introduced to enhance robustness. The unknown nonlinear functions and uncertain disturbances are approximated by the radial basis function neural networks (RBFNNs). The stability of system is ensured by the constructed Lyapunov functions. The fractional adaptive laws are proposed to update uncertain parameters. The proposed controller can ensure convergence of the tracking error and all the states remain bounded in the closed-loop systems. Lastly, the feasibility of the proposed control method is proved by giving two examples.

On the kinetics of Hadamard-type fractional differential systems

2020 ◽  
Vol 23 (2) ◽  
pp. 553-570 ◽  
Author(s):  
Li Ma
Keyword(s):  
Differential Operator ◽  
Numerical Simulations ◽  
Type Inequality ◽  
The Other ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Kinetics Of ◽  
Theoretical Results

AbstractThis paper is devoted to the investigation of the kinetics of Hadamard-type fractional differential systems (HTFDSs) in two aspects. On one hand, the nonexistence of non-trivial periodic solutions for general HTFDSs, which are considered in some functional spaces, is proved and the corresponding eigenfunction of Hadamard-type fractional differential operator is also discussed. On the other hand, by the generalized Gronwall-type inequality, we estimate the bound of the Lyapunov exponents for HTFDSs. In addition, numerical simulations are addressed to verify the obtained theoretical results.

MASTER STABILITY FUNCTIONS FOR SYNCHRONIZED COUPLED SYSTEMS

1999 ◽  
Vol 09 (12) ◽  
pp. 2315-2320 ◽  
Author(s):  
LOUIS M. PECORA ◽  
THOMAS L. CARROLL
Keyword(s):  
Simple Form ◽  
Coupled Systems ◽  
Stability Function ◽  
Coupled Oscillator ◽  
Synchronous State ◽  
Master Stability Function ◽  
Stability Functions ◽  
The Stability

We show that many coupled oscillator array configurations considered in the literature can be put into a simple form so that determining the stability of the synchronous state can be done by a master stability function which solves, once and for all, the problem of synchronous stability for many couplings of that oscillator.

scholarly journals Fast-Scale Instability and Stabilization by Adaptive Slope Compensation of a PV-Fed Differential Boost Inverter

2021 ◽  
Vol 11 (5) ◽  
pp. 2106
Author(s):  
Abdelali El Aroudi ◽  
Mohamed Debbat ◽  
Mohammed Al-Numay ◽  
Abdelmajid Abouloiafa
Keyword(s):  
Numerical Simulations ◽  
Full Range ◽  
Weather Conditions ◽  
Current Loop ◽  
Point Tracking ◽  
Bifurcation Phenomena ◽  
Slope Compensation ◽  
Power Point ◽  
The Stability ◽  
Detailed Circuit

Numerical simulations reveal that a single-stage differential boost AC module supplied from a PV module under an Maximum Power Point Tracking (MPPT) control at the input DC port and with current synchronization at the AC grid port might exhibit bifurcation phenomena under some weather conditions leading to subharmonic oscillation at the fast-switching scale. This paper will use discrete-time approach to characterize such behavior and to identify the onset of fast-scale instability. Slope compensation is used in the inner current loop to improve the stability of the system. The compensation slope values needed to guarantee stability for the full range of operating duty cycle and leading to an optimal deadbeat response are determined. The validity of the followed procedures is finally validated by a numerical simulations performed on a detailed circuit-level switched model of the AC module.

scholarly journals Earth-size planet formation in the habitable zone of circumbinary stars

2020 ◽  
Vol 494 (1) ◽  
pp. 1045-1057 ◽  
Author(s):  
G O Barbosa ◽  
O C Winter ◽  
A Amarante ◽  
A Izidoro ◽  
R C Domingos ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Planet Formation ◽  
Terrestrial Planet ◽  
Close Binary ◽  
Habitable Zone ◽  
Density Profiles ◽  
Habitable Planets ◽  
Habitable Zones ◽  
Test Particles ◽  
The Stability

ABSTRACT This work investigates the possibility of close binary (CB) star systems having Earth-size planets within their habitable zones (HZs). First, we selected all known CB systems with confirmed planets (totaling 22 systems) to calculate the boundaries of their respective HZs. However, only eight systems had all the data necessary for the computation of HZ. Then, we numerically explored the stability within HZs for each one of the eight systems using test particles. From the results, we selected five systems that have stable regions inside HZs, namely Kepler-34,35,38,413, and 453. For these five cases of systems with stable regions in HZ, we perform a series of numerical simulations for planet formation considering discs composed of planetary embryos and planetesimals, with two distinct density profiles, in addition to the stars and host planets of each system. We found that in the case of the Kepler-34 and 453 systems, no Earth-size planet is formed within HZs. Although planets with Earth-like masses were formed in Kepler-453, they were outside HZ. In contrast, for the Kepler-35 and 38 systems, the results showed that potentially habitable planets are formed in all simulations. In the case of the Kepler-413system, in just one simulation, a terrestrial planet was formed within HZ.

scholarly journals Optimal profile for concave slopes under static and seismic conditions

2016 ◽  
Vol 53 (9) ◽  
pp. 1522-1532 ◽  
Author(s):  
Farshid Vahedifard ◽  
Shahriar Shahrokhabadi ◽  
Dov Leshchinsky
Keyword(s):  
Limit Equilibrium ◽  
Stable Configuration ◽  
Preliminary Evaluation ◽  
Construction Technology ◽  
Stability Of Slopes ◽  
Optimal Profile ◽  
Stabilized Soil ◽  
The Stability ◽  
Comparison Of The Results ◽  
The Impact

This study presents a methodology to determine the stability and optimal profile for slopes with concave cross section under static and seismic conditions. Concave profiles are observed in some natural slopes suggesting that such geometry is a more stable configuration. In this study, the profile of a concave slope was idealized by a circular arc defined by a single variable, the mid-chord offset (MCO). The proposed concave profile formulation was incorporated into a limit equilibrium–based log spiral slope stability method. Stability charts are presented to show the stability number, MCO, and mode of failure for homogeneous slopes corresponding to the most stable configuration under static and pseudostatic conditions. It is shown that concave profiles can significantly improve the stability of slopes. Under seismic conditions, the impact of concavity is most pronounced. Good agreement was demonstrated upon comparison of the results from the proposed method against those attended from a rigorous upper bound limit analysis. The proposed methodology, along with recent advances in construction technology, can be employed to use concave profiles in trenches, open mine excavations, earth retaining systems, and naturally cemented and stabilized soil slopes. The results presented provide a useful tool for preliminary evaluation for adopting such concave profiles in practice.

scholarly journals Actuator Saturated Fuzzy Controller Design for Interval Type-2 Takagi-Sugeno Fuzzy Models with Multiplicative Noises

Processes ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 823
Author(s):  
Wen-Jer Chang ◽  
Yu-Wei Lin ◽  
Yann-Horng Lin ◽  
Chin-Lin Pen ◽  
Ming-Hsuan Tsai
Keyword(s):  
Nonlinear Systems ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Actuator Saturation ◽  
Design Method ◽  
Fuzzy Model ◽  
The Stability ◽  
Interval Type ◽  
Takagi Sugeno

In many practical systems, stochastic behaviors usually occur and need to be considered in the controller design. To ensure the system performance under the effect of stochastic behaviors, the controller may become bigger even beyond the capacity of practical applications. Therefore, the actuator saturation problem also must be considered in the controller design. The type-2 Takagi-Sugeno (T-S) fuzzy model can describe the parameter uncertainties more completely than the type-1 T-S fuzzy model for a class of nonlinear systems. A fuzzy controller design method is proposed in this paper based on the Interval Type-2 (IT2) T-S fuzzy model for stochastic nonlinear systems subject to actuator saturation. The stability analysis and some corresponding sufficient conditions for the IT2 T-S fuzzy model are developed using Lyapunov theory. Via transferring the stability and control problem into Linear Matrix Inequality (LMI) problem, the proposed fuzzy control problem can be solved by the convex optimization algorithm. Finally, a nonlinear ship steering system is considered in the simulations to verify the feasibility and efficiency of the proposed fuzzy controller design method.

Mathematical Model Establishment and Analysis on the Pipe Deformation under External Pressure with the Ovality

2013 ◽  
Vol 760-762 ◽  
pp. 2263-2266
Author(s):  
Kang Yong ◽  
Wei Chen
Keyword(s):  
Mathematical Model ◽  
Theoretical Analysis ◽  
Yield Strength ◽  
Residual Stresses ◽  
Numerical Simulations ◽  
Significant Influence ◽  
External Pressure ◽  
Pipe Diameter ◽  
Axial Loads ◽  
The Stability

Beside the residual stresses and axial loads, other factors of pipe like ovality, moment could also bring a significant influence on pipe deformation under external pressure. The Standard of API-5C3 has discussed the influences of deformation caused by yield strength of pipe, pipe diameter and pipe thickness, but the factor of ovality degree is not included. Experiments and numerical simulations show that with the increasing of pipe ovality degree, the anti-deformation capability under external pressure will become lower, and ovality affecting the stability of pipe shape under external pressure is significant. So it could be a path to find out the mechanics relationship between ovality and pipe deformation under external pressure by the methods of numerical simulations and theoretical analysis.

Exponential stability and periodicity of memristor-based recurrent neural networks with time-varying delays

2017 ◽  
Vol 10 (02) ◽  
pp. 1750027 ◽  
Author(s):  
Wei Zhang ◽  
Chuandong Li ◽  
Tingwen Huang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Functional Approach ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Matrix Inequalities ◽  
Inclusion Theory ◽  
The Stability

In this paper, the stability and periodicity of memristor-based neural networks with time-varying delays are studied. Based on linear matrix inequalities, differential inclusion theory and by constructing proper Lyapunov functional approach and using linear matrix inequality, some sufficient conditions are obtained for the global exponential stability and periodic solutions of memristor-based neural networks. Finally, two illustrative examples are given to demonstrate the results.

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