Modeling of complex-valued Wiener systems using B-spline neural network

In this brief, a new complex-valued B-spline neural network is introduced in order to model the complex-valued Wiener system using observational input/output data. The complex-valued nonlinear static function in the Wiener system is represented using the tensor product from two univariate Bspline neural networks, using the real and imaginary parts of the system input. Following the use of a simple least squares parameter initialization scheme, the Gauss–Newton algorithm is applied for the parameter estimation, which incorporates the De Boor algorithm, including both the B-spline curve and the first-order derivatives recursion. Numerical examples, including a nonlinear high-power amplifier model in communication systems, are used to demonstrate the efficacy of the proposed approaches

B-spline neural networks based PID controller for Hammerstein systems

A new PID tuning and controller approach is introduced for Hammerstein systems based on input/output data. A B-spline neural network is used to model the nonlinear static function in the Hammerstein system. The control signal is composed of a PID controller together with a correction term. In order to update the control signal, the multi-step ahead predictions of the Hammerstein system based on the B-spline neural networks and the associated Jacobians matrix are calculated using the De Boor algorithms including both the functional and derivative recursions. A numerical example is utilized to demonstrate the efficacy of the proposed approaches

Modelling and inverting complex-valued Wiener systems

We develop a complex-valued (CV) B-spline neural network approach for efficient identification and inversion of CV Wiener systems. The CV nonlinear static function in the Wiener system is represented using the tensor product of two univariate B-spline neural networks. With the aid of a least squares parameter initialisation, the Gauss-Newton algorithm effectively estimates the model parameters that include the CV linear dynamic model coefficients and B-spline neural network weights. The identification algorithm naturally incorporates the efficient De Boor algorithm with both the B-spline curve and first order derivative recursions. An accurate inverse of the CV Wiener system is then obtained, in which the inverse of the CV nonlinear static function of the Wiener system is calculated efficiently using the Gaussian-Newton algorithm based on the estimated B-spline neural network model, with the aid of the De Boor recursions. The effectiveness of our approach for identification and inversion of CV Wiener systems is demonstrated using the application of digital predistorter design for high power amplifiers with memor

Single-carrier frequency-domain equalization with hybrid decision feedback equalizer for Hammerstein channels containing nonlinear transmit amplifier

We propose a nonlinear hybrid decision feedback equalizer (NHDFE) for single-carrier (SC) block transmission systems with nonlinear transmit high power amplifier (HPA), which significantly outperforms our previous nonlinear SC frequency-domain equalization (NFDE) design. To obtain the coefficients of the channel impulse response (CIR) as well as to estimate the nonlinear mapping and the inverse nonlinear mapping of the HPA, we adopt a complex-valued (CV) B-spline neural network approach. Specifically, we use a CV B-spline neural network to model the nonlinear HPA, and we develop an efficient alternating least squares scheme for estimating the parameters of the Hammerstein channel, including both the CIR coefficients and the parameters of the CV B-spline model. We also adopt another CV B-spline neural network to model the inversion of the nonlinear HPA, and the parameters of this inverting B-spline model can be estimated using the least squares algorithm based on the pseudo training data obtained as a natural byproduct of the Hammerstein channel identification. The effectiveness of our NHDFE design is demonstrated in a simulation study, which shows that the NHDFE achieves a signal-to-noise ratio gain of 4dB over the NFDE at the bit error rate level of 10−4

Motion Planning of Uncertain Ordinary Differential Equation Systems

This work presents a novel motion planning framework, rooted in nonlinear programming theory, that treats uncertain fully and under-actuated dynamical systems described by ordinary differential equations. Uncertainty in multibody dynamical systems comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it, and poor robustness and suboptimal performance result if it’s not accounted for in a given design. In this work uncertainties are modeled using Generalized Polynomial Chaos and are solved quantitatively using a least-square collocation method. The computational efficiency of this approach enables the inclusion of uncertainty statistics in the nonlinear programming optimization process. As such, the proposed framework allows the user to pose, and answer, new design questions related to uncertain dynamical systems. Specifically, the new framework is explained in the context of forward, inverse, and hybrid dynamics formulations. The forward dynamics formulation, applicable to both fully and under-actuated systems, prescribes deterministic actuator inputs which yield uncertain state trajectories. The inverse dynamics formulation is the dual to the forward dynamic, and is only applicable to fully-actuated systems; deterministic state trajectories are prescribed and yield uncertain actuator inputs. The inverse dynamics formulation is more computationally efficient as it requires only algebraic evaluations and completely avoids numerical integration. Finally, the hybrid dynamics formulation is applicable to under-actuated systems where it leverages the benefits of inverse dynamics for actuated joints and forward dynamics for unactuated joints; it prescribes actuated state and unactuated input trajectories which yield uncertain unactuated states and actuated inputs. The benefits of the ability to quantify uncertainty when planning the motion of multibody dynamic systems are illustrated through several case-studies. The resulting designs determine optimal motion plans—subject to deterministic and statistical constraints—for all possible systems within the probability space

Network topology identification based on measured data

We consider the problem of modeling of systems and learning of models from a limited number of measurements. We also contribute to the development of inference algorithms that require high-dimensional data processing. As an inspiring example, a growing interest in biology is to determine dependencies among genes. Such problem, known as gene regulatory network inference, often leads to identifying of large networks through relatively small gene expression data. The main purpose of the thesis is to develop models and learning methods for data based applications. In particular, we first build a dynamical model for gene-gene interactions to learn the topology of gene regulatory networks from gene expression data. Our proposed model is applicable to such complex gene regulatory networks that contain loops and non-linear dependencies between genes. We seek to use dynamical gene expression data when a system is perturbed. Ideally, such dynamical changes result from local genetic or chemical perturbations of systems in steady state that can be captured in a time-dependent manner. We present a low-complexity inference method that can be adapted to incorporate other information measured across a biological system. The performance of our method is examined employing both simulated and real datasets. This work can potentially inform biological discovery relating to interactions of genes in disease-relevant networks, synthetic networks, and networks immediate to drug response. Along with the main objective of the thesis, we next seek to estimate high-dimensional covariance matrices based on a few partial observations. Notably, covariance matrices can be utilized to form networks or improve network inference. We assume that the true covariance matrix can be modeled as a sum of Kronecker products of two lower dimensional matrices. To estimate covariance, we propose a convex optimization approach computationally affordable in high-dimensional setting and applicable to missing data. Regardless of whether the process producing missing values is random or not, our novel scheme can be used without employing any imputation methods. We characterize the symmetry and positive definiteness of the estimated covariance and further shed light on its square error performance. The effect of missing values on the estimation error is mathematically presented and numerical results are illustrated to validate our method. In addition to the modeling and learning, we improve inference algorithms that involve high-dimensional data processing. Specifically, we attempt to reduce the complexity of the linear minimum mean-square error (LMMSE) estimation when observation vectors have high-dimensionality and contain missing entries. In this context, the standard LMMSE estimator must be re-computed whenever missing values take place at different positions. Instead, we propose a method to first construct the LMMSE estimator based on complete data statistics. We then apply this estimator to the data vector with missing values replaced by zeros. We finally establish a low-complexity update according to missing data patterns to modify our estimation and preserve the LMMSE optimality

Glitch Estimation and Removal Using Adaptive Spline Fitting and Wavelet Shrinkage on the Gravitational Wave Data

The false alarm rate and reduced sensitivity of searches for astrophysical signals are caused by transient signals of earthly origin, or glitches, in gravitational wave strain data from groundbased detectors. The greater number of observable astrophysical signals will increase the likelihood of glitch overlaps and exacerbate their negative impact for future detectors with higher sensitivities. The wide morphological diversity and unpredictable waveforms of glitches, and with the vast majority of cases lacking supplemental data present the main obstacles to their mitigation. Thus, nonparametric glitch mitigation techniques are required, which should operate for a wide range of glitches and, in the case of overlaps, have little impact on astrophysical signals. The arrangement of free knots is improved to estimate both smooth and non-smooth curves, and wavelet-based shrinkage is added for specific types of glitches in our method for glitch estimation and removal utilizing adaptive spline curve fitting. The effectiveness of the technique is evaluated for seven different kinds of LIGO detector glitch types. In the specific instance of a loud glitch in data from LIGO, Livingston that coincides with the event GW170817, the glitch is evaluated and eliminated without adversely altering the gravitational wave signal. For injected signals overlapped with other kinds of glitches, similar results are observed