Adaptive Look-up Table Research Articles

A computationally efficient Kalman filter based estimator for updating look-up tables applied to NOx estimation in diesel engines

Nox estimation in diesel engines is an up-to-date problem but still some issues need to be solved. Raw sensor signals are not fast enough for real-time use while control-oriented models suffer from drift and aging. A control-oriented gray box model based on engine maps and calibrated off-line is used as benchmark model for Nox estimation. Calibration effort is important and engine data-dependent. This motivates the use of adaptive look-up tables. In addition to, look-up tables are often used in automotive control systems and there is a need for systematic methods that can estimate or update them on-line. For that purpose, Kalman filter (KF) based methods are explored as having the interesting property of tracking estimation error in a covariance matrix. Nevertheless, when coping with large systems, the computational burden is high, in terms of time and memory, compromising its implementation in commercial electronic control units. However look-up table estimation has a structure, that is here exploited to develop a memory and computationally efficient approximation to the KF, named Simplified Kalman filter (SKF). Convergence and robustness is evaluated in simulation and compared to both a full KF and a minimal steady-state version, that neglects the variance information. SKF is used for the online calibration of an adaptive model for Nox estimation in dynamic engine cycles. Prediction results are compared with the ones of the benchmark model and of the other methods. Furthermore, actual online estimation of Nox is solved by means of the proposed adaptive structure. Results on dynamic tests with a diesel engine and the computational study demonstrate the feasibility and capabilities of the method for an implementation in engine control units.

Comparing high performance techniques for the automatic generation of efficient solvers of cardiac cell models

In silico experiments have been used for a better understanding of the electrical activity of cardiac myocytes, usually via models based on nonlinear systems of ordinary differential equations. Many different models for cardiac myocytes are available that vary on the level of complexity, depending on how detailed the phenomena is described. Long simulations of realistic and complex models are computationally expensive. To cope with this problem, this work compares different techniques to automatically speed up the numerical solution of cardiac models: (a) adaptive time step method, (b) Partial Evaluation (PE) and Lookup Tables (LUTs), and (c) an automatic way to find and exploit code concurrency via OpenMP directives. All the techniques were implemented as part of an automatic code generator for the numerical solution of models that are described in the CellML markup language. Experimental results demonstrated that the adaptive time step simulations were up to 32 times faster than the traditional Euler that use fixed time step. Combined with parallel computing on a multicore processor the execution time was further decreased and simulations were 41 times faster. Finally, the LUTs and PE techniques resulted in a 117-fold improvement in computation time over the Euler method and 72-fold improvement when compared to the traditional Rush–Larsen method.

A novel ROM compression architecture for DDFS utilizing the parabolic approximation of equi-section division

In this paper, we propose the parabolic approximation of equi-section division (PAESD) utilizing the symmetry property and amplitude approximation of a sinusoidal waveform to design a direct digital frequency synthesizer (DDFS). The sinusoidal phase of a one-quarter period is divided into equi-sections. The proposed method utilizes the curvature equivalence to derive each parabolic curve function, and then the value of the error function between each parabolic curve function and the sinusoidal function is stored in an error-compensation ROM to reconstruct the real sinusoidal waveform. The upper/lower bound of the maximum error value stored in the error-compensation ROM is derived to determine the minimum required memory word length relative to the number of bits of the equi-sections. Thus, the minimum size of the total ROMs of the DDFS using the PAESD without error-compensation ROM is compressed to 544 bits; the total compression ratio, compared with the minimum size of the total ROMs of the DDFS using the basic look-up table (LUT), is approximately 843:1, achieved by consuming additional circuits [71 adaptive look-up tables (ALUTs), 3 digital signal processor (DSP) block 9-bit elements]. Consequently, the results show that the proposed ROM compression method can effectively achieve a better compression ratio than the state-of-the-art solutions without affecting the spectrum performance of an average spurious-free dynamic range (SFDR) of -85 dBc.

A learning algorithm concept for updating look-up tables for automotive applications

Look-up tables are commonly used in the automotive field for handling operating point variations. However, constant maps cannot cope with systems variations and ageing. Methods, such as Kalman filter or Extended Kalman filter for non-linear cases, can be used for table adaptation providing an optimal solution to the problem. But these methods are computationally intensive, making difficult to implement them on commercial engine control units. The current paper proposes a learning method for online updating of look-up tables or maps. This algorithm uses precalculated membership functions based on a standard Kalman filter observer for weighting the adaptation. The main contribution of the method is the derivation of a steady-state Kalman filter observer that lowers the calculation burden and simplifies the implementation against the standard Kalman filter implementation that requires higher computational cost. As far as table is updated online while engine runs, this allows correcting drift errors and the unit-to-unit dispersion. The method is illustrated for mapping engine variables such as λ−1 and NOx in a Diesel engine by using an adaptive look-up table, and its characteristics make it suitable for implementing in commercial engine electronic control units for online purposes.

Response of double-auction markets to instantaneous Selling–Buying signals with stochastic Bid–Ask spread

Statistical properties of order-driven double-auction markets with Bid–Ask spread are investigated through the dynamical quantities such as response function. We first attempt to utilize the so-called Madhavan–Richardson–Roomans model (MRR for short) to simulate the stochastic process of the price-change in empirical data sets (say, EUR/JPY or USD/JPY exchange rates) in which the Bid–Ask spread fluctuates in time. We find that the MRR theory apparently fails to simulate so much as the qualitative behaviour (‘non-monotonic’ behaviour) of the response function R(l) (l denotes the difference of times at which the response function is evaluated) calculated from the data. Especially, we confirm that the stochastic nature of the Bid–Ask spread causes apparent deviations from a linear relationship between the R(l) and the auto-correlation function C(l), namely, \({R(l) \propto -C(l)}\). To make the microscopic model of double-auction markets having stochastic Bid–Ask spread, we use the minority game with a finite market history length and find numerically that appropriate extension of the game shows quite similar behaviour of the response function to the empirical evidence. We also reveal that the minority game modeling with the adaptive (‘annealed’) look-up table reproduces the non-linear relationship \({R(l) \propto -f(C(l))}\) (f(x) stands for a non-linear function leading to ‘λ-shapes’) more effectively than the fixed (‘quenched’) look-up table does.

HARDWARE IMPLEMENTATION AND VERIFICATION OF FIR FILTER UTILIZING M-BIT PDA

An efficient architecture for a FPGA symmetry FIR filter is proposed that employs the M-bit parallel-distributed arithmetic (M-bit PDA). The partial product is pre-calculated and saved into the distributed ROM to eliminate a large amount of multiplications. Altera Stratix II EP2S60 is used as a target device to implement the M-bit PDA. The hardware implementation requires 936 adaptive look-up tables (ALUTs), 888 registers, 1 PLL, 40960 memory bits for the FIR filter implementation with the M-bit PDA (in this case M = 2). Additionally, the maximum clock rate for this implementation can be achieved up to 155.36 MHz. In comparison with the parallel multiplier/adder cell (MAC) and serial distributed arithmetic (SDA), the proposed architecture consumes a smaller area and operates with a higher speed due to omitting the multipliers.

Optimal Spacing of a Linearly Interpolated Complex-Gain LUT Predistorter

Modern spectrally efficient modulation techniques produce radio-frequency signals with varying envelopes. Transmitting these signals through nonlinear amplifiers results in spectral regrowth and degradation of the bit error rate. Lookup table (LUT) predistorters have been widely used to mitigate the effects of nonlinear amplifiers. This paper theoretically proves that the use of linearly interpolated LUT predistorters results in superior rejection of residual nonlinear distortions, as compared with conventional noninterpolated LUT predistorters. The refinement of LUT performance with linear interpolation results in 12-dB additional rejection for every bit of precision, as opposed to 6 dB for noninterpolated LUTs. It is also shown that linearly interpolated LUT predistorters benefit more from optimal spacing than their noninterpolated counterparts. Besides improved mapping fidelity, potential benefits also include reduced gate count and faster convergence of adaptive LUT training algorithms.

Real-time gaze control of an active head-eye system without calibration

This article describes real-time gaze control using position-based visual servoing. The main control objective of the system is to enable a gaze point to track the target so that the image feature of the target is located at each image center. The overall system consists of two parts: the vision process and the control system. The vision system extracts a predefined color feature from images. An adaptive look-up table method is proposed in order to get the 3-D position of the feature within the video frame rate under varying illumination. An uncalibrated camera raises the problem of the reconstructed 3-D positions not being correct. To solve the calibration problem in the position-based approach, we constructed an end-point closed-loop system using an active head-eye system. In the proposed control system, the reconstructed position error is used with a Jacobian matrix of the kinematic relation. The system stability is locally guaranteed, like image-based visual servoing, and the gaze position was shown to converge to the feature position. The proposed approach was successfully applied to a tracking task with a moving target in some simulations and some real experiments. The processing speed satisfies the property of real time.

Experimental evaluation of nonlinear adaptive controllers

Attractive methods for learning the dynamics and improving the control of robot manipulators during movements have been proposed for more than 10 years, but they still await applications. This article investigates practical issues for the implementation of these methods, Two nonlinear adaptive controllers, selected for their simplicity and efficiency, are tested on 2-DOF and 3-DOF manipulators. The experimental results show that the adaptive feedforward controller (AFFC) is well suited for learning the parameters of the dynamic equation, even in the presence of friction and noise. The control performance along the learning trajectory and other test trajectories are also better than when measured parameters are used. However, when the task consists of driving a repeated trajectory, the adaptive lookup table MEMory is simpler to implement. It also provides a robust and stable control, and results in even better performance.