Coping with Chaos: Analysis of Chaotic Data and Exploitation by Edward Ott, Tim Sauer, James A. Yorke

By Edward Ott, Tim Sauer, James A. Yorke

Brings jointly contemporary advances within the interpretive and functional purposes of chaos, which carry nice promise for huge applicability in the course of the actual sciences and engineering. DLC: Chaotic habit in platforms.

Show description

Read or Download Coping with Chaos: Analysis of Chaotic Data and Exploitation of Chaotic Systems PDF

Similar system theory books

Linearization Models for Complex Dynamical Systems: Topics in Univalent Functions, Functional Equations and Semigroup Theory

Linearization types for discrete and non-stop time dynamical structures are the using forces for contemporary geometric functionality idea and composition operator concept on functionality areas. This e-book makes a speciality of a scientific survey and specific remedy of linearization versions for one-parameter semigroups, Schröder’s and Abel’s useful equations, and diverse periods of univalent capabilities which function intertwining mappings for nonlinear and linear semigroups.

Mathematical Modelling: A Way of Life - ICTMA 11

Mathematical modelling is frequently spoken of as a life-style, bearing on conduct of brain and to dependence at the strength of arithmetic to explain, clarify, are expecting and regulate actual phenomena. This booklet goals to inspire lecturers to supply possibilities for college kids to version numerous actual phenomena competently matched to scholars’ mathematical backgrounds and pursuits from early levels of mathematical schooling.

Dissipative Systems Analysis and Control: Theory and Applications

This moment variation of Dissipative platforms research and regulate has been considerably reorganized to house new fabric and improve its pedagogical beneficial properties. It examines linear and nonlinear platforms with examples of either in every one bankruptcy. additionally incorporated are a few infinite-dimensional and nonsmooth examples.

Extra resources for Coping with Chaos: Analysis of Chaotic Data and Exploitation of Chaotic Systems

Sample text

8. 2 Applications 27 Fig. 9. Time evolution of ψ α (k) and its estimate (real in solid line and estimated in dashed line) Fig. 10. 3 Conclusions This chapter has presented the application of HONN to solve the tracking problem for a class of MIMO discrete-time nonlinear systems, using the backstepping technique. The training of the neural network is performed online using an extended Kalman filter. The boundness of the tracking error is established on the basis of the Lyapunov approach. The HONN training with the learning algorithm based in EKF presents good performance even in presence of larger bounded disturbances such as load torque variations and change on the plant parameters (resistance change).

Recently, other kind of observer has emerged: neural observers [3, 5, 6, 9, 10], for unknown plant dynamics. N. 1) can be rewritten as x(k) = x1 (k) . . xi (k) . . xn (k) , d(k) = d1 (k) . . di (k) . . dn (k) , i = 1, · · · , n, xi (k + 1) = Fi (x(k), u(k)) + di (k), y(k) = Cx(k). 2), we propose a Luenberger neural observer (RHONO) with the following structure: x(k) = x1 (k) . . xi (k) . . 8). 5) where xi is the ith plant state, zi is a bounded approximation error, which can be reduced by increasing the number of the adjustable weights [8].

2) where xi (i = 1, 2, . . , n) is the state of the ith neuron, Li is the respective number of higher-order connections, {I1 , I2 , . . , ILi } is a collection of nonordered subsets of {1, 2, . . , n + m}, n is the state dimension, m is the number of external inputs, wi (i = 1, 2, . . 8). 1) by the following discrete-time RHONN series–parallel representation [5]: xi (k + 1) = wi∗ zi (x(k), u(k)) + zi , i = 1, . . 3) where xi is the ith plant state, zi is a bounded approximation error, which can be reduced by increasing the number of the adjustable weights [5].

Download PDF sample

Rated 4.64 of 5 – based on 43 votes