Controlling chaos using time delay coordinates

“…In general the future development of the system depends on the whole history of the control. Taking two control steps into account the least squares condition reads k x n+2 (p n p n+1 )k 2 evaluation of the least squares procedure yields the result p = ;(C tr C) ;1 C tr d (8) as long as the square matrix (C tr C) is invertible. Otherwise, we have to use the Penrose pseudo inverse C + obtained by s i n g u l a r v alue decomposition (SVD) (Broomhead and Lowe, 1988) and get more generally…”

Section: Instantaneous and Delayed Controlmentioning

confidence: 99%

“…An appropriate control algorithm stabilizing a desired periodic orbit is then implemented into a feedforward network with one layer of neurons. To achieve this, we have to reformulate the control algorithm using least square control similar to Reyl et al (1993), Stollenwerk and Pasemann (1996) and delayed feedback similar to Dressler and Nitsche (1992), Stollenwerk (1995).…”

Section: Introductionmentioning

confidence: 99%

Attractor switching by neural control of chaotic neurodynamics

Pasemann

Stollenwerk

1998

Network: Computation in Neural Systems

View full text Add to dashboard Cite

Chaotic attractors of discrete-time neural networks include in nitely many unstable periodic orbits, which can be stabilized by small parameter changes in a feedback c o n trol. Here we explore the control of unstable periodic orbits in a chaotic neural network with only two neurons. Analytically a local control algorithm is derived on the basis of least squares minimization of the future deviations between actual system states and the desired orbit. This delayed control allows a consistent neural implementation, i.e. the same types of neurons are used for chaotic and controlling modules. The control signal is realized with one layer of neurons, allowing selective switching between di erent stabilized periodic orbits. For chaotic modules with noise random switching between di erent periodic orbits is observed. permanent address: MOD, Forschungszentrum J ulich, D-52425 J ulich, Germany

show abstract

“…Also, a wide choice between a rich variety of dynamical behavior is possible [3]. Based on this observation, several chaotic system control methods have been developed [1][2][3][4][5][6]33]. Small perturbation control of chaotic systems is a technique developed by Edward Ott, Celso Grebogi, and James York in 1990, known as the OGY technique [4].…”

Section: Small Perturbation Control Of Chaotic Systemsmentioning

confidence: 99%

Neural Network Based Montioring and Control of Fluidized Bed.

Bodruzzaman¹,

Essawy²

1996

View full text Add to dashboard Cite

The goal of this project was to develop chaos analysis and neural network-based modeling techniques and apply them to the pressure-drop data obtained from the Fluid Bed Combustion (FBC) system (a small scale prototype model) located at the Federal Energy Technology Center (FETC)-Morgantown. The second goal was to develop neural network-based chaos control techniques and provide a suggestive prototype for possible real-time application to the FBC system. The experimental pressure data were collected from a cold FBC experimental setup at the Morgantown Center. We have performed several analysis on these data in order to unveil their dynamical and chaotic characteristics. The phase-space attractors were constructed from the one dimensional time series data, using the time-delay embedding method, for both normal and abnormal conditions. Several identifying parameters were also computed from these attractors such as the correlation dimension, the Kolmogorov entropy, and the Lyapunov exponents. These chaotic attractor parameters can be used to discriminate between the normal and abnormal operating conditions of the FBC system. It was found that, the abnormal data has higher correlation dimension, larger Kolmogorov entropy and larger positive Lyapunov exponents as compared to the normal data. Chaotic system control using neural network based techniques were also investigated and compared to conventional chaotic system control techniques. Both types of chaotic system control techniques were applied to some typical chaotic systems such as the logistic, the Henon, and the Lorenz systems. A prototype model for real-time implementation of these techniques has been suggested to control the FBC system. These models can be implemented for real-time control in a next phase of the project after obtaining further measurements from the experimental model. After testing the control algorithms developed for the FBC model, the next step is to implement them on hardware and link them to the experimental system. In this report, the hardware implementation issues of the control algorithms are also discussed.ii 8 Figure 8 The chaotic behavior of the Lorenz system starting at (0.05,0.05,0.05).10 Figure 9 The Lorenz system state space attractor.10 Figure 10 The general training strategy for the DSI controller.11 Figure 11 The DSI control signal (u(t)), and the time behavior of the Lorenz system after applying and then removing the control at the stabilized point. 13 Figure 12 The trajectory of the Lorenz system, after applying and then removing the control action at the stabilized point. 13 Figure 13 The time behavior of the Lorenz system, controlled by the DSI to achieve a periodic orbit, starting at (1,5,10). 13 Figure 14 The trajectory for the Lorenz system, controlled by the DSI to achieve a periodic orbit, starting at (5,5,1). Executive SummaryThis research report describes the work completed under the DoE Contract # DE-FG22-94MT94015 titled "Neural Network-Based Monitoring and Control of Fluidized Bed" for the period from O...

show abstract

Controlling chaos using time delay coordinates

Cited by 263 publications

References 9 publications

The control of chaos: theory and applications

The control of chaos: theory and applications

Attractor switching by neural control of chaotic neurodynamics

Neural Network Based Montioring and Control of Fluidized Bed.

Contact Info

Product

Resources

About