Equilibria of Parametrized N-Player Nonlinear Games Using Inequalities and Nonsmooth Dynamics

2020 ◽  
pp. 33-53
Author(s):  
Monica G. Cojocaru ◽  
Fatima Etbaigha
Keyword(s):  
Nonsmooth Dynamics

Nonlinear Dynamics and Bifurcation Analysis of a Boost Converter for Battery Charging in Photovoltaic Applications

2014 ◽  
Vol 24 (11) ◽  
pp. 1450142 ◽  
Author(s):  
Mohammed M. Al-Hindawi ◽  
Abdullah Abusorrah ◽  
Yusuf Al-Turki ◽  
Damian Giaouris ◽  
Kuntal Mandal ◽  
...  
Keyword(s):  
Current Mode ◽  
Solar Irradiation ◽  
Nonsmooth Dynamics ◽  
Pv Systems ◽  
Current Mode Control ◽  
Mode Control ◽  
Pv Panel ◽  
Voltage Variation ◽  
Average Current ◽  
Average Current Mode Control

Photovoltaic (PV) systems with a battery back-up form an integral part of distributed generation systems and therefore have recently attracted a lot of interest. In this paper, we consider a system of charging a battery from a PV panel through a current mode controlled boost dc-dc converter. We analyze its complete nonlinear/nonsmooth dynamics, using a piecewise model of the converter and realistic nonlinear v–i characteristics of the PV panel. Through this study, it is revealed that system design without taking into account the nonsmooth dynamics of the converter combined with the nonlinear v–i characteristics of the PV panel can lead to unpredictable responses of the overall system with high current ripple and other undesirable phenomena. This analysis can lead to better designed converters that can operate under a wide variation of the solar irradiation and the battery's state of charge. We show that the v–i characteristics of the PV panel combined with the battery's output voltage variation can increase or decrease the converter's robustness, both under peak current mode control and average current mode control. We justify the observation in terms of the change in the discrete-time map caused by the nonlinear v–i characteristics of the PV panel. The theoretical results are validated experimentally.

A General Purpose Formulation for Nonsmooth Dynamics With Finite Rotations: Application to the Woodpecker Toy

2020 ◽  
Vol 16 (3) ◽  
Author(s):  
Alejandro Cosimo ◽  
Federico J. Cavalieri ◽  
Javier Galvez ◽  
Alberto Cardona ◽  
Olivier Brüls
Keyword(s):  
Finite Element ◽  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Horizontal Displacement ◽  
General Purpose ◽  
Nonsmooth Dynamics ◽  
Unilateral Constraints ◽  
Simulation Code ◽  
Frictional Contacts ◽  
Large Rotations

Abstract The aim of this work is to extend the finite element multibody dynamics approach to problems involving frictional contacts and impacts. The nonsmooth generalized-α (NSGA) scheme is adopted, which imposes bilateral and unilateral constraints both at position and velocity levels avoiding drift phenomena. This scheme can be implemented in a general purpose simulation code with limited modifications of pre-existing elements. The study of the woodpecker toy dynamics sets up a good example to show the capabilities of the NSGA scheme within the context of a general finite element framework. This example has already been studied by many authors who generally adopted a model with a minimal set of coordinates and small rotations. It is shown that good results are obtained using a general purpose finite element code for multibody dynamics, in which the equations of motion are assembled automatically and large rotations are easily taken into account. In addition, comparing results between different models of the woodpecker toy, the importance of modeling large rotations and the horizontal displacement of the woodpecker's sleeve is emphasized.

Dynamics of a Simplified van der Pol Oscillator Revisited

2007 ◽  
Author(s):  
Albert C. J. Luo ◽  
Arun Rajendran
Keyword(s):  
Bifurcation Analysis ◽  
Local Stability ◽  
Van Der Pol Oscillator ◽  
Nonsmooth Dynamics ◽  
Mapping Technique ◽  
Periodic Motions ◽  
Van Der Pol ◽  
Chaotic Motions ◽  
Mapping Structures ◽  
Stability And Bifurcation Analysis

In this paper, the dynamic characteristics of a simplified van der Pol oscillator are investigated. From the theory of nonsmooth dynamics, the structures of periodic and chaotic motions for such an oscillator are developed via the mapping technique. The periodic motions with a certain mapping structures are predicted analytically for m-cycles with n-periods. Local stability and bifurcation analysis for such motions are carried out. The (m:n)-periodic motions are illustrated. The further investigation of the stable and unstable periodic motions in such a system should be completed. The chaotic motion based on the Levinson donuts should be further discussed.

scholarly journals Exploring the Dynamics of Base-Excited Structures Impacting a Rigid Stop

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Peter J. Christopher ◽  
Barnaby Dobson ◽  
Nicholas A. Alexander
Keyword(s):  
High Performance ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Performance Measure ◽  
Nonsmooth Dynamics ◽  
Structural Parameter ◽  
Sigmoid Function ◽  
Stiffness Ratio ◽  
Complex Behaviour ◽  
Interstorey Drift

This paper explores the nonlinear dynamics of a multidegree of freedom (MDoF) structure impacting a rigid stop. The contact mechanics is simplified by continuous sigmoid function idealisation of a lossless spring. By introducing a smooth nonlinear formulation, we avoid the computational expense of event-driven, piecewise, nonsmooth dynamics. A large parametric study using high-performance computing is undertaken. The nondimensional equations of motion suggest one primary structural parameter, contact-to-storey stiffness ratio, and two excitation parameters, nondimensional ground amplitude and frequency. Bifurcation plots indicate an extremely rich and complex behaviour, particularly in the cases where at least two-floor degrees of freedom (DoFs) impact the stop and when the contact-to-storey stiffness ratio is large. When considering interstorey drift as a performance measure, period-1 impacting solutions are generally favourable when compared to an analogous nonimpacting case. This paper also discusses whether chaotic impacting can be favourable. Finally, we consider the question of whether higher modes are significantly excited, at a linear resonance, for impacting solutions to this system.

Stick–Slip Motion of the Chaplygin Sleigh With a Piecewise-Smooth Nonholonomic Constraint

2017 ◽  
Vol 12 (3) ◽  
Author(s):  
Vitaliy Fedonyuk ◽  
Phanindra Tallapragada
Keyword(s):  
Nonholonomic Constraint ◽  
Nonholonomic Constraints ◽  
Piecewise Smooth ◽  
Nonsmooth Dynamics ◽  
Chaplygin Sleigh ◽  
Stick Slip ◽  
Velocity Decay ◽  
Asymptotic Speed ◽  
Asymptotic Motion ◽  
Stick Slip Motion

The Chaplygin sleigh is a canonical problem of mechanical systems with nonholonomic constraints. Such constraints often arise due to the role of a no-slip requirement imposed by friction. In the case of the Chaplygin sleigh, it is well known that its asymptotic motion is that of pure translation along a straight line. Any perturbations in angular velocity decay and result in an increase in asymptotic speed of the sleigh. Such motion of the sleigh is under the assumption that the magnitude of friction is as high as necessary to prevent slipping. We relax this assumption by setting a maximum value to the friction. The Chaplygin sleigh is then under a piecewise-smooth nonholonomic constraint and transitions between “slip” and “stick” modes. We investigate these transitions and the resulting nonsmooth dynamics of the system. We show that the reduced state space of the system can be partitioned into sets of distinct dynamics and that the stick–slip transitions can be explained in terms of transitions of the state of the system between these sets.

scholarly journals Adaptive Critic Learning-Based Robust Control of Systems with Uncertain Dynamics

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Jun Zhao ◽  
Qingliang Zeng ◽  
Bin Guo
Keyword(s):  
Optimal Control ◽  
Robust Control ◽  
Control Problem ◽  
Control Method ◽  
System Modeling ◽  
Uncertain System ◽  
Nonsmooth Dynamics ◽  
Adaptive Critic ◽  
Uncertain Dynamics ◽  
Critic Neural Network

Model uncertainties are usually unavoidable in the control systems, which are caused by imperfect system modeling, disturbances, and nonsmooth dynamics. This paper presents a novel method to address the robust control problem for uncertain systems. The original robust control problem of the uncertain system is first transformed into an optimal control of nominal system via selecting the appropriate cost function. Then, we develop an adaptive critic leaning algorithm to learn online the optimal control solution, where only the critic neural network (NN) is used, and the actor NN widely used in the existing methods is removed. Finally, the feasibility analysis of the control algorithm is given in the paper. Simulation results are given to show the availability of the presented control method.

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