Fast recursive filters for simulating nonlinear dynamic systems

A fast and accurate computational scheme for simulating nonlinear dynamic systems is presented. The scheme assumes that the system can be represented by a combination of components of only two different types: first-order low-pass filters and static nonlinearities. The parameters of these filters and nonlinearities may depend on system variables, and the topology of the system may be complex, including feedback. Several examples taken from neuroscience are given: phototransduction, photopigment bleaching, and spike generation according to the Hodgkin-Huxley equations. The scheme uses two slightly different forms of autoregressive filters, with an implicit delay of zero for feedforward control and an implicit delay of half a sample distance for feedback control. On a fairly complex model of the macaque retinal horizontal cell it computes, for a given level of accuracy, 1-2 orders of magnitude faster than 4th-order Runge-Kutta. The computational scheme has minimal memory requirements, and is also suited for computation on a stream processor, such as a GPU (Graphical Processing Unit).Comment: 20 pages, 8 figures, 1 table. A comparison with 4th-order Runge-Kutta integration shows that the new algorithm is 1-2 orders of magnitude faster. The paper is in press now at Neural Computatio

Control of flexible joint robotic manipulator using tuning functions design

The goal of this thesis is to design the controller for a single arm manipulator having a flexible joint for the tracking problem in two different cases. A controller is designed for a deterministic case wherein the plant parameters are assumed to be known while another is designed for an adaptive case where all the plant parameters are assumed to be unknown. In general the tracking problem is; given a smooth reference trajectory, the end effector has to track the reference while maintaining the stability. It is assumed that only the output of the manipulator, which is the link angle, is available for measurement. Also without loss of generality, the fast dynamics, that is the dynamics of the driver side of the system are neglected for the sake of simplicity; In the first case, the design procedure adopted is called observer backstepping. Since the states of the system are unavailable for measurement, an observer is designed that estimates the system states. These estimates are fed to the controller which in turn produces the control input to the system; The second case employs a design procedure called tuning functions design. In this case, since the plant parameters are unknown, the observer designed in case one cannot be used for determining the state estimates. For this purpose, parameter update laws and filters are designed for estimation of plant parameters. The filters employed are k-filters. The k-filters and the parameter update laws are given as input to the controller, which generates the control input to the system; For both cases, the mathematical models are simulated using Matlab/Simulink, and the results are verified

Linear MMSE-Optimal Turbo Equalization Using Context Trees

Formulations of the turbo equalization approach to iterative equalization and decoding vary greatly when channel knowledge is either partially or completely unknown. Maximum aposteriori probability (MAP) and minimum mean square error (MMSE) approaches leverage channel knowledge to make explicit use of soft information (priors over the transmitted data bits) in a manner that is distinctly nonlinear, appearing either in a trellis formulation (MAP) or inside an inverted matrix (MMSE). To date, nearly all adaptive turbo equalization methods either estimate the channel or use a direct adaptation equalizer in which estimates of the transmitted data are formed from an expressly linear function of the received data and soft information, with this latter formulation being most common. We study a class of direct adaptation turbo equalizers that are both adaptive and nonlinear functions of the soft information from the decoder. We introduce piecewise linear models based on context trees that can adaptively approximate the nonlinear dependence of the equalizer on the soft information such that it can choose both the partition regions as well as the locally linear equalizer coefficients in each region independently, with computational complexity that remains of the order of a traditional direct adaptive linear equalizer. This approach is guaranteed to asymptotically achieve the performance of the best piecewise linear equalizer and we quantify the MSE performance of the resulting algorithm and the convergence of its MSE to that of the linear minimum MSE estimator as the depth of the context tree and the data length increase.Comment: Submitted to the IEEE Transactions on Signal Processin

Stereophonic acoustic echo cancellation employing selective-tap adaptive algorithms

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