Konstantinos Tsakalis

Evaluation of time delay effects to wide-area power system stabilizer design

Centralized control using system-wide data has been suggested to enhance the dynamic performance of large interconnected power systems. Because of the distance involved in wide-area interconnections, communication delay cannot be ignored. Long time delay may be detrimental to system stability and may degrade system performance. The time delay tolerance of a centralized controller and the associated performance tradeoff is analyzed using a small gain criterion. Special attention is paid to the choice of weighting functions in a robust control design. As expected, it is found that time delay tolerance decreases when the system bandwidth increases, while the nominal system time-domain performance is concomitantly improved. Several approaches which can maintain a good system performance while increasing the time delay tolerance are suggested and compared. A modern controller design technique, like gain scheduling via linear matrix inequalities, is evaluated for the design of the supervisory power system stabilizer accounting for various time delays.

Long-term prospective on-line real-time seizure prediction

OBJECTIVE Epilepsy, one of the most common neurological disorders, constitutes a unique opportunity to study the dynamics of spatiotemporal state transitions in real, complex, nonlinear dynamical systems. In this study, we evaluate the performance of a prospective on-line real-time seizure prediction algorithm in two patients from a common database. METHODS We previously demonstrated that measures of chaos and angular frequency, estimated from electroencephalographic (EEG) signals recorded at critical sites in the cerebral cortex, progressively converge (i.e. become dynamically entrained) as the epileptic brain transits from the asymptomatic interictal state to the ictal state (seizure) (Iasemidis et al., 2001, 2002a, 2003a). This observation suggested the possibility of developing algorithms to predict seizures well ahead of their occurrences. One of the central points in those investigations was the application of optimization theory, specifically quadratic zero-one programming, for the selection of the critical cortical sites. This current study combines that observation with a dynamical entrainment detection method to prospectively predict epileptic seizures. The algorithm was tested in two patients with long-term (107.54h) and multi-seizure EEG data B and C (Lehnertz and Litt, 2004). RESULTS Analysis from the 2 test patients resulted in the prediction of up to 91.3% of the impending 23 seizures, about 89+/-15min prior to seizure onset, with an average false warning rate of one every 8.27h and an allowable prediction horizon of 3h. CONCLUSIONS The algorithm provides warning of impending seizures prospectively and in real time, that is, it constitutes an on-line and real-time seizure prediction scheme. SIGNIFICANCE These results suggest that the proposed seizure prediction algorithm could be used in novel diagnostic and therapeutic applications in epileptic patients.

Direct Heuristic Dynamic Programming for Nonlinear Tracking Control With Filtered Tracking Error

This paper makes use of the direct heuristic dynamic programming design in a nonlinear tracking control setting with filtered tracking error. A Lyapunov stability approach is used for the stability analysis of the tracking system. It is shown that the closed-loop tracking error and the approximating neural network weight estimates retain the property of uniformly ultimate boundedness under the presence of neural network approximation error and bounded unknown disturbances under certain conditions.

Information Flow and Application to Epileptogenic Focus Localization From Intracranial EEG

Transfer entropy (TE) is a recently proposed measure of the information flow between coupled linear or nonlinear systems. In this study, we suggest improvements in the selection of parameters for the estimation of TE that significantly enhance its accuracy and robustness in identifying the direction and the level of information flow between observed data series generated by coupled complex systems. We show the application of the improved TE method to long (in the order of days; approximately a total of 600 h across all patients), continuous, intracranial electroencephalograms (EEG) recorded in two different medical centers from four patients with focal temporal lobe epilepsy (TLE) for localization of their foci. All patients underwent ablative surgery of their clinically assessed foci. Based on a surrogate statistical analysis of the TE results, it is shown that the identified potential focal sites through the suggested analysis were in agreement with the clinically assessed sites of the epileptogenic focus in all patients analyzed. It is noteworthy that the analysis was conducted on the available whole-duration multielectrode EEG, that is, without any subjective prior selection of EEG segments or electrodes for analysis. The above, in conjunction with the use of surrogate data, make the results of this analysis robust. These findings suggest a critical role TE may play in epilepsy research in general, and as a tool for robust localization of the epileptogenic focus/foci in patients with focal epilepsy in particular.

Information Flow in Coupled Nonlinear Systems: Application to the Epileptic Human Brain

A recently proposed measure, namely Transfer Entropy (TE), is used to estimate the direction of information flow between coupled linear and nonlinear systems. In this study, we suggest improvements in the selection of parameters for the estimation of TE that significantly enhance its accuracy and robustness in identifying the direction of information flow and quantifying the level of interaction between observed data series from coupled systems. We demonstrate the potential usefulness of the improved method through simulation examples with coupled nonlinear chaotic systems. The statistical significance of the results is shown through the use of surrogate data. The improved TE method is then used for the study of information flow in the epileptic human brain. We illustrate the application of TE to electroencephalographic (EEG) signals for the study of localization of the epileptogenic focus and the dynamics of its interaction with other brain sites in two patients with Temporal Lobe Epilepsy (TLE).

Brain dynamical disentrainment by anti-epileptic drugs in rat and human status epilepticus

We utilize a measure of brain dynamics, namely the short-term largest Lyapunov exponent (STL/sub max/) to evaluate the efficacy of treatment in epileptic animals and humans with known antiepileptic drugs (AED) like diazepam and phenobarbital during status epilepticus (SE). This measure is estimated from analysis of electroencephalographic (EEG) recordings at multiple brain locations in both an SE patient and a cobalt/homocysteine thiolactone SE-induced animal. Techniques from optimization theory and statistics are applied to select optimal sets of brain sites, whose dynamics are then measured over time to study their entrainment/disentrainment. Results from such analysis indicate that the observed abnormal spatio-temporal dynamical entrainment in SE is reversed by AED administration (resetting of brain dynamics). These results may provide a potential use of nonlinear dynamical measures in the evaluation of the efficacy of AEDs and the development of new treatment strategies in epilepsy.

Measuring the direction and the strength of coupling in nonlinear Systems-a modeling approach in the State space

We present a novel signal processing methodology to determine the direction and the strength of coupling between coupled nonlinear systems. The methodology is based on multivariate local linear prediction in the reconstructed state spaces of the observed variables from each multivariable nonlinear system. Application of the method is illustrated with systems of coupled Rossler and Lorenz oscillators in various coupling configurations. The obtained results are compared with ones produced by the use of the directed transfer function, a model-based method in the time domain. Through a surrogate analysis, it is shown that the proposed method is more reliable than the directed transfer function in identifying the direction and strength of the involved interactions.

Performance Evaluation of Direct Heuristic Dynamic Programming using Control-Theoretic Measures

Approximate dynamic programming (ADP) has been widely studied from several important perspectives: algorithm development, learning efficiency measured by success or failure statistics, convergence rate, and learning error bounds. Given that many learning benchmarks used in ADP or reinforcement learning studies are control problems, it is important and necessary to examine the learning controllers from a control-theoretic perspective. This paper makes use of direct heuristic dynamic programming (direct HDP) and three typical benchmark examples to introduce a unique analytical framework that can be applied to other learning control paradigms and other complex control problems. The sensitivity analysis and the linear quadratic regulator (LQR) design are used in the paper for two purposes: to quantify direct HDP performances and to provide guidance toward designing better learning controllers. The use of LQR however does not limit the direct HDP to be a learning controller that addresses nonlinear dynamic system control issues. Toward this end, applications of the direct HDP for nonlinear control problems beyond sensitivity analysis and the confines of LQR have been developed and compared whenever appropriate to an LQR design.

Brain dynamics based automated epileptic seizure detection.

We developed and tested a seizure detection algorithm based on two measures of nonlinear and linear dynamics, that is, the adaptive short-term maximum Lyapunov exponent (ASTLmax) and the adaptive Teager energy (ATE). The algorithm was tested on long-term (0.5-11.7 days) continuous EEG recordings from five patients (3 with intracranial and 2 with scalp EEG) with a total of 56 seizures, producing a mean sensitivity of 91% and mean specificity of 0.14 false positives per hour. The developed seizure detection algorithm is data-adaptive, training-free, and patient-independent.

Robust control of an islanded microgrid

A variety of distributed control strategies have been applied to microgrids, including master-slave, current mode control, and droop [1], [2], [3]. Droop control has received a great deal of attention and has been implemented with rudimentary modifications in order to improve performance [4], [5]. Prior work has typically assumed that the droop coefficients are constant and relied on elementary control design [6]. Two fundamental issues that have not been addressed using these approaches, are the ability to design an inverter to operate in a microgrid without analyzing the entire microgrid and improved transient performance using dynamic controllers of order greater than one. These issues will be addressed in this paper by designing a dynamic controller using Glover McFarlane loop shaping [7].