Outer synchronization of general colored networks with different-dimensional node via sliding mode control

2018 ◽  
Vol 32 (31) ◽  
pp. 1850342 ◽  
Author(s):  
Shuang Liu ◽  
Qingyun Wang
Keyword(s):  
Lyapunov Stability ◽  
Stability Theory ◽  
Control Method ◽  
Sliding Mode ◽  
Lyapunov Stability Theory ◽  
Sliding Mode Controller ◽  
Network Systems ◽  
Colored Complex ◽  
System Parameters ◽  
Linear Subsystem

In this paper, a separated sliding mode strategy is proposed for the synchronization of network systems. To break the predicament caused by the inhomogeneity of nodes coupling in complex network, a colored network with different node systems and edges is given. According to the nonlinear subsystem of the colored complex networks, a separated sliding mode controller is designed, while for the linear subsystem, some appropriate system parameters are established to implement synchronization. Then, based on the Lyapunov stability theory, the performance of the sliding mode controller is appraised through the synchronization for the colored networks consisting of different-dimensional systems and nonidentical interactions. In the end, two simulation illustrations are employed to demonstrate the presented control method.

Design and Analysis of Non-linear Controller for a Standalone PV System using Lyapunov Stability Theory

2021 ◽  
pp. 1-22
Author(s):  
Narendra Kumar ◽  
Aman Sharma
Keyword(s):  
Lyapunov Stability ◽  
Stability Theory ◽  
Sliding Mode ◽  
Equilibrium Points ◽  
Lyapunov Stability Theory ◽  
Maximum Power ◽  
Hill Climbing ◽  
Sliding Mode Controller ◽  
Nonlinear Controller ◽  
Pv System

Abstract This paper presents Lyapunov Stability Theory based Nonlinear Controller Design for a Standalone PV System. The comparative analysis of different nonlinear controllers is also carried out . Due to the nonlinear characteristics of photovoltaic systems, conventional Hill-Climbing methods like Perturbate and Observe and Incremental Conductance do not show reliable tracking of Maximum Power under various uncertainties. Therefore, these methods require nonlinear tools to meet the control objectives and design specifications. Out of various nonlinear controlling techniques, the one presented in this paper is the Sliding Mode Approach for Maximum Power Point Tracking (MPPT). In context of Lyapunov Stability Theory, sliding mode approach uses a switching manifold. In this approach, the system trajectories are made to follow the sliding surface and to remain there forever to ensure the stability of equilibrium points. Two types of Sliding Mode controllers have been simulated namely Conventional - Sliding Mode Controller (CSMC) and Terminal - Sliding Mode Controller (TSMC). The results are analyzed and compared scientifically on various performance parameters including, duty cycle ratio, ideal and PV output power and time taken for error convergence, under varying dynamic conditions. All the control algorithms are developed in MATLAB/Simulink.

ANTI-SYNCHRONIZATION OF UNIFIED HYPERCHAOTIC SYSTEMS

2014 ◽  
Vol 28 (05) ◽  
pp. 1450014
Author(s):  
PI LI ◽  
XING-YUAN WANG ◽  
PENG SUN ◽  
CHAO LUO ◽  
XIU-KUN WANG
Keyword(s):  
Adaptive Control ◽  
Active Control ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Control Methods ◽  
System Parameters ◽  
Hyperchaotic Systems ◽  
Active Control Method

In this paper, active control and adaptive control methods are applied, respectively. Adaptive control method is implemented when system parameters are unknown and active control method is applied when system parameters are known. Based on the Lyapunov stability theory, the controllers are designed to realize anti-synchronization, meanwhile, the update laws of parameters are proposed. The theoretical proof is given. And two groups of examples are shown to verify the effectiveness of the proposed schemes.

Sliding Mode Observer and Controller Design for Nonlinear Supersonic Missile

2013 ◽  
Vol 718-720 ◽  
pp. 1228-1233
Author(s):  
Hong Chao Zhao ◽  
Xian Jun Shi ◽  
Ting Wang
Keyword(s):  
Lyapunov Stability ◽  
Controller Design ◽  
Sliding Mode ◽  
Equations Of Motion ◽  
Lyapunov Stability Theory ◽  
Sliding Mode Observer ◽  
Sliding Mode Controller ◽  
Output Redefinition ◽  
Simulation Results ◽  
Nonlinear Equations Of Motion

The nonlinear equations of motion were constructed for a supersonic anti-warship missile. In order to estimate the unknown angle-of-attack, a sliding mode observer was designed. The convergence capability of the sliding mode observer was analyzed according to the Lyapunov stability theory. A sliding mode controller was designed to drive the missile normal overload output to track its command, based on the output-redefinition approach. In order to confirm the performance of the designed sliding mode observer and controller, a simulation example was carried out for nonlinear missile model. The simulation results show the fast convergence capability of the designed sliding mode observer and controller.

scholarly journals On Full-State Hybrid Projective Synchronization of General Discrete Chaotic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Adel Ouannas
Keyword(s):  
Lyapunov Stability ◽  
Discrete Time ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Full State ◽  
Hybrid Projective Synchronization ◽  
Nonlinear Control Method

The problems of full-state hybrid projective synchronization (FSHPS) and inverse full-state hybrid projective synchronization (IFSHPS) for general discrete chaotic systems are investigated in 2D. Based on nonlinear control method and Lyapunov stability theory, new controllers are designed to study FSHPS and IFSHPS, respectively, for 2D arbitrary chaotic systems in discrete-time. Numerical example and simulations are used to validate the main results of this paper.

Continuous dynamic sliding mode control of converter-fed DC motor system with high order mismatched disturbance compensation

2020 ◽  
Vol 42 (14) ◽  
pp. 2812-2821 ◽  
Author(s):  
Arshad Rauf ◽  
Shihua Li ◽  
Rafal Madonski ◽  
Jun Yang
Keyword(s):  
High Performance ◽  
Control Method ◽  
Sliding Mode ◽  
Lyapunov Stability Theory ◽  
High Order ◽  
Engineering Practice ◽  
Sliding Mode Controller ◽  
Multiple Sources ◽  
Continuous Dynamic ◽  
Dynamic Sliding Mode

The combination of DC-DC buck power converters with DC motors for generating the so-called smooth start of drives has many advantages in engineering practice. Achieving high performance of such systems is, however, limited by the influence of disturbances/uncertainties of multiple sources. Some of the disturbances are mismatched, which makes them even more difficult to handle. Furthermore, the relatively high order of system dynamics makes the control design challenging. In this paper, a control structure with continuous dynamic sliding mode controller with a finite-time disturbance observer is proposed to address these practical issues. First, a special state transformation is applied, aggregating the acting disturbances/uncertainties in a sole perturbing term of the system expressed in new coordinates. Then, the observer estimates in real time the information about the lumped disturbances based on already available input/output signals and the obtained estimated signals (and their high order time-derivatives) are used to construct a sliding surface. Finally, the sliding mode controller is applied to achieve high performance of the resultant plant dynamics and to robustify the governing scheme against modelling discrepancies. The stability of the closed-loop system is proved here using Lyapunov stability theory and the efficiency of the proposed control method is validated through a multi-criteria numerical simulation.

Robust Finite-Time Stabilization of Fractional-Order Chaotic Systems based on Fractional Lyapunov Stability Theory

2012 ◽  
Vol 7 (2) ◽  
Author(s):  
Mohammad Pourmahmood Aghababa
Keyword(s):  
Fractional Order ◽  
Lyapunov Stability ◽  
Finite Time ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Convergence Time ◽  
Control Approach ◽  
Finite Time Stability

This paper concerns the problem of stabilization of uncertain fractional-order chaotic systems in finite time. On the basis of fractional Lyapunov stability theory, a robust finite-time fractional controller is introduced to control chaos of fractional-order chaotic systems in the presence of system uncertainties. The finite-time stability of the closed-loop system is analytically proved. An estimation of the convergence time is also given. Some numerical simulations are provided to illustrate the usefulness and applicability of the proposed robust finite-time control approach. It is worth noting that the proposed fractional control method is applicable for stabilizing a broad range of uncertain fractional-order nonlinear systems in a given finite time.

scholarly journals Hybrid Chaos Synchronization of Four–Scroll Systems via Active Control

2014 ◽  
Vol 65 (2) ◽  
pp. 97-103 ◽  
Author(s):  
Rajagopal Karthikeyan ◽  
Vaidyanathan Sundarapandian
Keyword(s):  
Numerical Simulations ◽  
Active Control ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Hybrid Synchronization ◽  
Active Control Method

Abstract This paper investigates the hybrid chaos synchronization of identical Wang four-scroll systems (Wang, 2009), identical Liu-Chen four-scroll systems (Liu and Chen, 2004) and non-identical Wang and Liu-Chen four-scroll systems. Active control method is the method adopted to achieve the hybrid chaos synchronization of the four-scroll chaotic systems addressed in this paper and our synchronization results are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the active control method is effective and convenient to hybrid synchronize identical and different Wang and Liu-Chen four-scroll chaotic systems. Numerical simulations are also shown to illustrate and validate the hybrid synchronization results derived in this paper.

Control of a class of fractional-order systems with mismatched disturbances via fractional-order sliding mode controller

2020 ◽  
Vol 42 (13) ◽  
pp. 2423-2439
Author(s):  
Shabnam Pashaei ◽  
Mohammad Ali Badamchizadeh
Keyword(s):  
Fractional Order ◽  
Control Method ◽  
Sliding Mode ◽  
Estimation Error ◽  
Design Procedure ◽  
Lyapunov Stability Theory ◽  
Fast Response ◽  
Sliding Mode Controller ◽  
Fractional Order Systems ◽  
Mismatched Disturbances

This paper presents a new fractional-order sliding mode controller (FOSMC) for disturbance rejection and stabilization of a class of fractional-order systems with mismatched disturbances. To design this control strategy, firstly, a fractional-order extended disturbance observer (FOEDO) is proposed to estimate the matched and mismatched disturbances and their derivatives. Then, according to the design procedure of the sliding mode controller and based on the designed FOEDO, a proper sliding mode surface is proposed. Subsequently, the proposed FOSMC is designed to guarantee that the system states reach the sliding surface and stay on it forever. The stability of the controlled fractional-order systems is proved via fractional-order Lyapunov stability theory. The numerical examples are used to illustrate the effectiveness of the proposed fractional-order controller. The simulation results of the proposed FOSMC are compared with the results of some other researchers’ works to show the superiority of the proposed control method. The new approach displays some attractive features such as fast response, the chattering reduction, robust stability, less disturbance estimation error, the mismatched disturbance, noise rejection, and better control performance.

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