scholarly journals Local modal participation analysis of nonlinear systems using Poincaré linearization

2019 ◽  
Vol 99 (1) ◽  
pp. 803-811 ◽  
Author(s):  
Boumediene Hamzi ◽  
Eyad H. Abed
Keyword(s):  
Nonlinear Systems ◽  
Autonomous Systems ◽  
Analytical Formula ◽  
Linear Case ◽  
Local Mode ◽  
Initial Condition ◽  
Initial State ◽  
State Participation ◽  
Symmetry Assumption ◽  
Definition Of

AbstractThe paper studies an extension to nonlinear systems of a recently proposed approach to the definition of modal participation factors. A definition is given for local mode-in-state participation factors for smooth nonlinear autonomous systems. While the definition is general, the resulting measures depend on the assumed uncertainty law governing the system initial condition, as in the linear case. The work follows Hashlamoun et al. (IEEE Trans Autom Control 54(7):1439–1449 2009) in taking a mathematical expectation (or set-theoretic average) of a modal contribution measure over an uncertain set of system initial state. Poincaré linearization is used to replace the nonlinear system with a locally equivalent linear system. It is found that under a symmetry assumption on the distribution of the initial state, the tractable calculation and analytical formula for mode-in-state participation factors found for the linear case persists to the nonlinear setting. This paper is dedicated to the memory of Professor Ali H. Nayfeh.

scholarly journals Protector control: Extension to a class of nonlinear distributed systems

2010 ◽  
Vol 20 (3) ◽  
pp. 427-443 ◽  
Author(s):  
Youssef Qaraai ◽  
Abdes Bernoussi
Keyword(s):  
Distributed Systems ◽  
Nonlinear Systems ◽  
Propagation Velocity ◽  
Delay System ◽  
Linear Case ◽  
Initial State ◽  
Finite Propagation ◽  
Control Scheme ◽  
Nonlinear Delay

Protector control: Extension to a class of nonlinear distributed systemsWe present an extension of the protector control scheme introduced for the linear case in a previous work to a class of nonlinear systems. The systems considered are assumed to have a finite propagation velocity while the initial state is subject to a spreading disturbance. We characterize such a control first by using the remediability approach to the resulting nonlinear delay system, and then by coupling families of transformations and the delay approach. To illustrate this work, we provide a simulation example.

Iterative learning control algorithm for sensor fault nonlinear systems

2020 ◽  
pp. 1-8
Author(s):  
Zimian Lan
Keyword(s):  
Nonlinear Systems ◽  
Iterative Learning Control ◽  
Control Algorithm ◽  
Tracking Error ◽  
Learning Control ◽  
Open Loop ◽  
Iterative Learning ◽  
Sensor Fault ◽  
Initial State ◽  
Control Gain

In this paper, we propose a new iterative learning control algorithm for sensor faults in nonlinear systems. The algorithm does not depend on the initial value of the system and is combined with the open-loop D-type iterative learning law. We design a period that shortens as the number of iterations increases. During this period, the controller corrects the state deviation, so that the system tracking error converges to the boundary unrelated to the initial state error, which is determined only by the system’s uncertainty and interference. Furthermore, based on the λ norm theory, the appropriate control gain is selected to suppress the tracking error caused by the sensor fault, and the uniform convergence of the control algorithm and the boundedness of the error are proved. The simulation results of the speed control of the injection molding machine system verify the effectiveness of the algorithm.

DETERMINISTIC DIFFERENTIAL GAMES UNDER PROBABILITY KNOWLEDGE OF INITIAL CONDITION

2008 ◽  
Vol 10 (01) ◽  
pp. 1-16 ◽  
Author(s):  
P. CARDALIAGUET ◽  
M. QUINCAMPOIX
Keyword(s):  
Differential Games ◽  
Differential Game ◽  
Random Distribution ◽  
Uniqueness Result ◽  
Initial Condition ◽  
Initial State ◽  
Lack Of Information ◽  
In The Beginning ◽  
Zero Sum ◽  
Future Work

We study a zero-sum differential game where the players have only an unperfect information on the state of the system. In the beginning of the game only a random distribution on the initial state is available. The main result of the paper is the existence of the value obtained through an uniqueness result for Hamilton-Jacobi-Isaacs equations stated on the space of measure in ℝn. This result is the first step for future work on differential games with lack of information.

scholarly journals Convex skeletons of complex networks

2018 ◽  
Vol 15 (145) ◽  
pp. 20180422 ◽  
Author(s):  
Lovro Šubelj
Keyword(s):  
Protein Interactions ◽  
Spanning Tree ◽  
Autonomous Systems ◽  
Shortest Paths ◽  
Induced Subgraph ◽  
Social Collaboration ◽  
Computer Scientists ◽  
High Betweenness ◽  
Network Backbone ◽  
Definition Of

A convex network can be defined as a network such that every connected induced subgraph includes all the shortest paths between its nodes. A fully convex network would therefore be a collection of cliques stitched together in a tree. In this paper, we study the largest high-convexity part of empirical networks obtained by removing the least number of edges, which we call a convex skeleton. A convex skeleton is a generalization of a network spanning tree in which each edge can be replaced by a clique of arbitrary size. We present different approaches for extracting convex skeletons and apply them to social collaboration and protein interactions networks, autonomous systems graphs and food webs. We show that the extracted convex skeletons retain the degree distribution, clustering, connectivity, distances, node position and also community structure, while making the shortest paths between the nodes largely unique. Moreover, in the Slovenian computer scientists coauthorship network, a convex skeleton retains the strongest ties between the authors, differently from a spanning tree or high-betweenness backbone and high-salience skeleton. A convex skeleton thus represents a simple definition of a network backbone with applications in coauthorship and other social collaboration networks.

An Optimization Procedure of Model’s Base Construction in Multimodel Representation of Complex Nonlinear Systems

2021 ◽  
Author(s):  
Bennasr Hichem ◽  
M’Sahli Faouzi
Keyword(s):  
Nonlinear Systems ◽  
Learning Algorithm ◽  
Batch Reactor ◽  
Optimization Procedure ◽  
Base Number ◽  
Deterministic Approach ◽  
Modeling Analysis ◽  
Complex Nonlinear Systems ◽  
Definition Of ◽  
And Control

The multimodel approach is a research subject developed for modeling, analysis and control of complex systems. This approach supposes the definition of a set of simple models forming a model’s library. The number of models and the contribution of their validities is the main issues to consider in the multimodel approach. In this chapter, a new theoretical technique has been developed for this purpose based on a combination of probabilistic approaches with different objective function. First, the number of model is constructed using neural network and fuzzy logic. Indeed, the number of models is determined using frequency-sensitive competitive learning algorithm (FSCL) and the operating clusters are identified using Fuzzy K- means algorithm. Second, the Models’ base number is reduced. Focusing on the use of both two type of validity calculation for each model and a stochastic SVD technique is used to evaluate their contribution and permits the reduction of the Models’ base number. The combination of FSCL algorithms, K-means and the SVD technique for the proposed concept is considered as a deterministic approach discussed in this chapter has the potential to be applied to complex nonlinear systems with dynamic rapid. The recommended approach is implemented, reviewed and compared to academic benchmark and semi-batch reactor, the results in Models’ base reduction is very important witch gives a good performance in modeling.

Magna-Lok rivet joint and the stiffness-equivalent FE model

2019 ◽  
Vol 91 (6) ◽  
pp. 834-842
Author(s):  
Jakub Šedek ◽  
Roman Růžek
Keyword(s):  
Complex Structure ◽  
Analytical Formula ◽  
General View ◽  
Fe Model ◽  
Equivalent Stiffness ◽  
Fe Modelling ◽  
Content Type ◽  
Particular Solution ◽  
Definition Of

Purpose The purpose of this paper is to present a methodology for the determination of the stiffness when using simplified substitutive model of the joint. The usage of detailed finite element (FE) model of the joint in complex assemblies is not convenient; therefore, the substitutive model of the joint is used in FE models. Design/methodology/approach The detailed and simplified FE model of the joint is created in ABAQUS software and the analysis as well. The results of displacements are used for the determination of the stiffness of connecting element in simplified substitutive FE model. The approach is presented based on the general view on the different regions in the joint. Findings A simple FE modelling approach for the joint including the equivalent stiffness is presented. The particular solution is performed for Magna-Lok type of the rivet. The results show the same displacement for the detailed and simplified FE models. The analytical formula for stiffness determination in the load case with minimal secondary bending is introduced. Practical implications The approach for stiffness determination is straightforward and so no stiffness “tuning” is necessary in the simplified FE model. Originality/value The new approach for definition of simple FE model of the joint is introduced. It is not necessary to model a complex structure with detailed joints. The equivalent stiffness can be determined by presented procedure for every joint without limitation of the type.

Fuzzy Cell Mapping Applied to Autonomous Systems

2001 ◽  
Author(s):  
Y. Song ◽  
D. Edwards ◽  
V. S. Manoranjan
Keyword(s):  
Nonlinear Systems ◽  
Analytical Methods ◽  
Autonomous Systems ◽  
Global Behavior ◽  
Cell Mapping ◽  
Strongly Nonlinear ◽  
Scientific Disciplines ◽  
Fuzzy Cell ◽  
Engineering Physics ◽  
Viable Method

Abstract Nonlinear systems appear in many scientific disciplines such as engineering, physics, chemistry, biology, economics, and demography. Therefore methods of analysis of nonlinear systems, which can provide a good understanding of their behavior have wide applications. Although there are several analytical methods (See Hsu [3] and references therein), determining the global behavior of strongly nonlinear systems is still a substantially difficult task. The direct approach of numerical integration is a viable method. However, such an approach is sometimes prohibitively time consuming even with the powerful present-day computers.

“Intelligent” Optimal Design

2000 ◽  
Author(s):  
Joseph Zarka
Keyword(s):  
Optimal Design ◽  
Numerical Simulations ◽  
Constitutive Modeling ◽  
Initial State ◽  
Practical Solution ◽  
Real Definition ◽  
The World ◽  
Definition Of ◽  
Real Returns

Abstract The engineers have to face very important problems in the design, the test, the survey and the maintenance of their structures. These problems did not yet get full answer even from the best people in the world. Usually in these problems (such as no satisfactory constitutive modeling of materials, no real control of the accuracy of the numerical simulations, no real definition of the initial state and/or the effective loading of the structure), there is no solution and the experts do not understand the problem in its whole. Moreover, the available data may be not statistically representative (i.e. are in limited number), fuzzy, qualitative and missing in part. We propose a practical solution the «Intelligent Optimal Design of Materials and Structures» where the actual best knowledges of the researchers/experts are intelligently mixed to the results of experiments or real returns.

Extended Finite Time Inverse Optimal Control of Nonlinear Systems

2011 ◽  
Vol 403-408 ◽  
pp. 1499-1502
Author(s):  
Xin Jun Ren ◽  
Yan Jun Shen
Keyword(s):  
Optimal Control ◽  
Nonlinear Systems ◽  
Finite Time ◽  
Lyapunov Functions ◽  
Control Law ◽  
Inverse Optimal Control ◽  
Closed Loop System ◽  
Affine Nonlinear Systems ◽  
Definition Of ◽  
The Cost

In this paper, we use the definition of control Lyapunov functions to study finite time inverse optimal control for affine nonlinear systems. Based on control Lyapunov functions, a finite time universal control formula is presented, which can ensure the closed-loop system is finite time stable. From this, less conservative conditions for the finite time inverse optimal control are derived. We design a finite time inverse optimal control law, which minimizes the cost functional. A numerical example verifies the validity of the proposed method.

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