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.

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.

Fuzzy Cell Mapping

2012 ◽  
pp. 161-174
Author(s):  
Jian-Qiao Sun ◽  
Ling Hong
Keyword(s):  
Cell Mapping ◽  
Fuzzy Cell

scholarly journals Application of the Robust Fixed Point Iteration Method in Control of the Level of Twin Tanks Liquid

Computation ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 96
Author(s):  
Hamza Khan ◽  
Hazem Issa ◽  
József K. Tar
Keyword(s):  
Numerical Simulation ◽  
Fixed Point ◽  
Nonlinear Systems ◽  
Flow Rate ◽  
Fluid Level ◽  
Process Industries ◽  
Fixed Point Iteration ◽  
Precise Control ◽  
Strongly Nonlinear ◽  
Simulation Results

Precise control of the flow rate of fluids stored in multiple tank systems is an important task in process industries. On this reason coupled tanks are considered popular paradigms in studies because they form strongly nonlinear systems that challenges the controller designers to develop various approaches. In this paper the application of a novel, Fixed Point Iteration (FPI)-based technique is reported to control the fluid level in a “lower tank” that is fed by the egress of an “upper” one. The control signal is the ingress rate at the upper tank. Numerical simulation results obtained by the use of simple sequential Julia code with Euler integration are presented to illustrate the efficiency of this approach.

A Cell Mapping Method for Nonlinear Deterministic and Stochastic Systems—Part II: Examples of Application

1986 ◽  
Vol 53 (3) ◽  
pp. 702-710 ◽  
Author(s):  
H. M. Chiu ◽  
C. S. Hsu
Keyword(s):  
Present Method ◽  
Stochastic Systems ◽  
Random Excitation ◽  
Mapping Method ◽  
Cell Mapping ◽  
Generalized Cell Mapping ◽  
Deterministic Systems ◽  
Strongly Nonlinear ◽  
Stochastic Problems ◽  
A Cell

In this second part of the two-part paper we demonstrate the viability of the compatible simple and generalized cell mapping method by applying it to various deterministic and stochastic problems. First we consider deterministic problems with non-chaotic responses. For this class of problems we show how system responses and domains of attraction can be obtained by a refining procedure of the present method. Then, we consider stochastic problems with stochasticity lying in system parameters or excitation. Next, deterministic systems with chaotic responses are considered. By the present method, finding the statistical responses of such systems under random excitation also presents no difficulties. Some of the systems studied here are well-known. New results are, however, also obtained. These are results on Duffing systems with a stochastic coefficient, the global results of a Duffing system shown in Section 4, the results on strongly nonlinear Duffing systems under random excitations reported in Section 7.2, and the strange attractor results for systems subjected to random excitations.

scholarly journals DYNAMICAL SYSTEMS ON THREE MANIFOLDS PART II: THREE-MANIFOLDS, HEEGAARD SPLITTINGS AND THREE-DIMENSIONAL SYSTEMS

2007 ◽  
Vol 17 (06) ◽  
pp. 2085-2095 ◽  
Author(s):  
YI SONG ◽  
STEPHEN P. BANKS
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Systems ◽  
Systems Theory ◽  
Topological Structure ◽  
Three Dimensional ◽  
Local System ◽  
Operating Point ◽  
Global Behavior ◽  
Heegaard Splittings

The global behavior of nonlinear systems is extremely important in control and systems theory since the usual local theories will only provide information about a system in some neighborhood of an operating point. Away from that point, the system may have totally different behavior and so the theory developed for the local system will be useless for the global one. In this paper we shall consider the analytical and topological structure of systems on two- and three-manifolds and show that it is possible to obtain systems with "arbitrarily strange" behavior, i.e. arbitrary numbers of chaotic regimes which are knotted and linked in arbitrary ways. We shall do this by considering Heegaard Splittings of these manifolds and the resulting systems defined on the boundaries.

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