Parham Ghorbanian

Stabilization of sets with application to multi-vehicle coordinated motion

In this paper, we develop stability and control design framework for time-varying and time-invariant sets of nonlinear dynamical systems using vector Lyapunov functions. Several Lyapunov functions arise naturally in multi-agent systems, where each agent can be associated with a generalized energy function which further becomes a component of a vector Lyapunov function. We apply the developed control framework to the problem of multi-vehicle coordinated motion to design distributed controllers for individual vehicles moving in a specified formation. The main idea of our approach is that a moving formation of vehicles can be characterized by a time-varying set in the state space, and hence, the problem of distributed control design for multi-vehicle coordinated motion is equivalent to the design of stabilizing controllers for time-varying sets of nonlinear dynamical systems. The control framework is shown to ensure global exponential stabilization of multi-vehicle formations. Finally, we implement the feedback stabilizing controllers for time-invariant sets to achieve global exponential stabilization of static formations of multiple vehicles.

An improved procedure for detection of heart arrhythmias with novel pre-processing techniques

The objective of this study is to develop an algorithm to detect and classify six types of electrocardiogram (ECG) signal beats including normal beats (N), atrial pre-mature beats (A), right bundle branch block beats (R), left bundle branch block beats (L), paced beats (P), and pre-mature ventricular contraction beats (PVC or V) using a neural network classifier. In order to prepare an appropriate input vector for the neural classifier several pre-processing stages have been applied. Initially, a signal filtering method is used to remove the ECG signal baseline wandering. Continuous wavelet transform is then applied in order to extract features of the ECG signal. Next, principal component analysis is used to reduce the size of the data. A well-known neural network architecture called the multi-layered perceptron neural network is then utilized as the final classifier to classify each ECG beat as one of six groups of signals under study. Finally, the MIT-BIH database is used to evaluate the proposed algorithm, resulting in 99.5% sensitivity, 99.66% positive predictive accuracy and 99.17% total accuracy.

Discrete wavelet transform EEG features of Alzheimer'S disease in activated states

In this study, electroencephalogram (EEG) signals obtained by a single-electrode device from 24 subjects - 10 with Alzheimers disease (AD) and 14 age-matched Controls (CN) - were analyzed using Discrete Wavelet Transform (DWT). The focus of the study is to determine the discriminating EEG features of AD patients while subjected to cognitive and auditory tasks, since AD is characterized by progressive impairments in cognition and memory. At each recording block, DWT extracts EEG features corresponding to major brain frequency bands. T-test and Kruskal-Wallis methods were used to determine the statistically significant features of EEG signals from AD patients compared to Controls. A decision tree algorithm was then used to identify the dominant features for AD patients. It was determined that the mean value of the low-δ (1 - 2 Hz) frequency band during the Paced Auditory Serial Addition Test with 2.0 (s) interval and the mean value of the δ frequency band (12 - 30 Hz) during 6 Hz auditory stimulation have higher mean values in AD patients than Controls. Due to artifacts, the less reliable low-δ features were removed and it was determined that the mean value of β frequency band during 6 Hz auditory stimulation followed by the standard deviation of θ (4 - 8 Hz) frequency band of one card learning cognitive task are higher for AD patients compared to Controls and thus the most dominant discriminating features of the disease.

Power based analysis of single-electrode human EEG recordings using continuous wavelet transform

The purpose of this paper is to demonstrate the capabilities of continuous wavelet transform (CWT) in analyzing electroencephalogram (EEG) signals produced through a single-electrode recording device. Further, CWT is used to evaluate standard fast Fourier transform (FFT) analysis results. Sequential resting eyes-closed (EC) and eyes-open (EO) EEG signals, recorded from individuals during a one year period (N = 25), are analyzed. The absolute and relative geometric mean powers of the EEG δ, θ, α, and β-bands are calculated using FFT and CWT analysis. A sliding Blackman window based FFT analysis shows a statistically significant α and β-band dominant peaks for EC compared to EO recordings. These results confirm well-known results reported in the literature, which validates the EEG recording device. CWT analysis using Morlet mother function results are consistent with those of FFT analysis and revealed additional differences where a second range of statistically significant dominant scales are clearly observed in the δ-band for EO compared with EC, which has not been reported in the literature. However, the difference between EO and EC power spectra in the β range is less significant in the wavelet analysis.

Identification of sympathetic and parasympathetic nerves function in cardiovascular regulation using ANFIS approximation

OBJECTIVE In this paper a new nonlinear system identification approach is developed for dynamical quantification of cardiovascular regulation. This approach is specifically focused on the identification of the heart rate (HR) baroreflex mechanism. The principal objective of this paper is to improve the model accuracy in the estimation of HR by proposing a modified nonlinear model. METHODS AND MATERIAL The proposed HR baroreflex model is based on inherent features of the autonomic nervous system for which we develop an adaptive neuro-fuzzy inference system (ANFIS) structure. This method allows incorporation of physiological understandings about the sympathetic and parasympathetic nerves through the selection of appropriate membership functions in the ANFIS structure. The required data for system modeling are collected from the publicly available PhysioNet database. RESULTS The results agree with the natural characteristics and physiological understanding of the cardiovascular regulatory system, such as delay in the parasympathetic function, durability in the function of sympathetic nerves and the correlation between the HR and the ABP signals. They also show significant improvements in HR prediction in terms of the normalized root mean square error (NRMSE) in comparison with other reported methods. We achieved to 0.191 in mean NRMSE in prediction of HR in this paper which is about 20% better than the best reported result in other researches. CONCLUSION We have shown that for cardiovascular system regulation, our proposed nonlinear model is more accurate than other recently developed methods. Accurate HR baroreflex modeling enables clinicians to have more reliable information for their patients.

A phenomenological model of EEG based on the dynamics of a stochastic Duffing-van der Pol oscillator network

Abstract In this work, we propose a novel phenomenological model of the EEG signal based on the dynamics of a coupled Duffing-van der Pol oscillator network. An optimization scheme is adopted to match data generated from the model with clinically obtained EEG data from subjects under resting eyes-open (EO) and eyes-closed (EC) conditions. It is shown that a coupled system of two Duffing-van der Pol oscillators with optimized parameters yields signals with characteristics that match those of the EEG in both the EO and EC cases. The results, which are reinforced using statistical analysis, show that the EEG recordings under EC and EO resting conditions are clearly distinct realizations of the same underlying model occurring due to parameter variations with qualitatively different nonlinear dynamic characteristics. In addition, the interplay between noise and nonlinearity is addressed and it is shown that, for appropriately chosen values of noise intensity in the model, very good agreement exists between the model output and the EEG in terms of the power spectrum as well as Shannon entropy. In summary, the results establish that an appropriately tuned stochastic coupled nonlinear oscillator network such as the Duffing-van der Pol system could provide a useful framework for modeling and analysis of the EEG signal. In turn, design of algorithms based on the framework has the potential to positively impact the development of novel diagnostic strategies for brain injuries and disorders.

STOCHASTIC DYNAMIC MODELING OF THE HUMAN BRAIN EEG SIGNAL

The occurrence and risk of recurrence of brain related injuries and diseases are difficult to characterize due to various factors including inter-individual variability. A useful approach is to analyze the brain electroencephalogram (EEG) for differences in brain frequency bands in the signals obtained from potentially injured and healthy normal subjects. However, significant shortcomings include: (1) contrary to empirical evidence, current spectral signal analysis based methods often assume that the EEG signal is linear and stationary; (2) nonlinear time series analysis methods are mostly numerical and do not possess any predictive features. In this work, we develop models based on stochastic differential equations that can output signals with similar frequency and magnitude characteristics of the brain EEG. Initially, a coupled linear oscillator model with a large number of degrees of freedom is developed and shown to capture the characteristics of the EEG signal in the major brain frequency bands. Then, a nonlinear stochastic model based on the Duffing oscillator with far fewer degrees of freedom is developed and shown to produce outputs that can closely match the EEG signal. It is shown that such a compact nonlinear model can provide better insight into EEG dynamics through only few parameters, which is a step towards developing a framework with predictive capabilities for addressing brain injuries.Copyright

Continuous Wavelet Transform EEG Features of Alzheimer’s Disease

In this study, we applied the continuous wavelet transform (CWT) to determine electroencephalogram (EEG) discriminating features of Alzheimer’s Disease (AD) patients compared to control subjects. The EEG was recorded from 24 subjects including 10 AD and 14 age-matched control during six sequential resting eyes-closed (EC) and eyes-open (EO) states followed by cognitive tasks and auditory stimulation. We computed the absolute and relative geometric mean powers of Morlet wavelet coefficients at different scale ranges corresponding to the major brain frequency bands. Kruskal-Wallis statistical testing method was then employed to determine the statistically significant features of the cohort geometric means. The results show that there are many discriminating features of AD patients at several different brain major frequency bands, particularly during the second and third EC and EO states. Since many features were identified, a decision tree algorithm was employed to classify the most significant one(s). The algorithm found the absolute power of θ frequency band during the second EO state to be higher for all AD patients when compared to control subjects and identified it as the most significant discriminating feature.Copyright

Obstacle avoidance in multi-vehicle coordinated motion via stabilization of time-varying sets

In this paper, we review the recent results on stability and control for time-varying sets of nonlinear time-varying dynamical systems and utilize them for the problem of multi-vehicle coordinated motion in the context of obstacle avoidance where obstacles are approximated and enclosed by elliptic shapes. Specifically, we design distributed controllers for individual vehicles moving in a specified formation in the presence of such obstacles. The obstacle avoidance algorithm that we propose is based on transitional trajectories which are denned by a set of ordinary differential equations that exhibit a stable elliptical limit cycle. The control framework is implemented on the system of double integrators and is shown to globally exponentially stabilize moving formation of the agents in pursuit of a leader while ensuring obstacle avoidance.

On the stability of sliding mode control for a class of underactuated nonlinear systems

A system is considered underactuated if the number of the actuator inputs is less than the number of degrees of freedom for the system. Sliding mode control for underactuated systems has been shown to be an effective way to achieve system stabilization. It involves exponentially stable sliding surfaces so that when the closed-loop system trajectory reaches the surface it moves along the surface while converging to the origin. In this paper, we present a general framework that provides sufficient conditions for asymptotic stabilization by a sliding mode controller for a class of underactuated nonlinear systems with two degrees of freedom. We show that, with the sliding mode controller presented, the closed-loop system trajectories reach the sliding surface in finite time. Furthermore, we develop a constructive methodology to determine exponential stability of the reduced-order closed-loop system while on the sliding surface thus ensuring asymptotic stability of the overall closed-loop system and provide a way to determine an estimate of the domain of attraction. Finally, we implement this framework on the example of an inverted pendulum.