This paper deals with the design of robust fault detection system for Takagi-Sugeno (T-S) modes with parametric uncertainties and time-varying delay. An Unknown Input Observer (UIO) is designed such that the unknown inputs are thoroughly decoupled from residual signals while they show the maximum possible sensitivity to the faults and the minimum possible sensitivity to the external disturbances. Since the system under consideration is subjected to parametric uncertainties, the H ∞ model matching approach is used to design an optimal observer. Design procedure is given in terms of Linear Matrix Inequalities (LMIs). Finally, a numerical example is presented to show the effectiveness of the proposed method.
This paper studies the behavior of singularly perturbed nonlinear differential equations with boundary-layer solutions that do not necessarily converge to an equilibrium. Using the average of the fast variable and assuming the boundary layer solutions converge to a bounded set, results on the closeness of solutions of the singularly perturbed system to the solutions of the reduced average and boundary layer systems over a finite time interval are presented. The closeness of solutions error is shown to be of order O (√{ε}), where ε is the perturbation parameter.
This paper deals with the problem of fault detection for linear uncertain time-delay systems. The proposed method for Luenberger observers is developed for unknown input observers (UIOs), and a novel procedure for the design of residual based on UIOs is presented. The design procedure is carried out based on the model matching approach which minimizes the difference between generated residuals by the optimal observer and those by the designed observer in the presence of uncertainties. The optimal observer is designed for the ideal system and works so that the fault effect is maximized while the exogenous disturbances and noise effects are minimized. This observer can give disturbance decoupling in the presence of noise and uncertainties for linear uncertain time-delay systems. The developed method is applied to a numerical example, and the simulation results show that the proposed approach is able to detect faults reliably in the presence of modeling errors, disturbances, and noise.
This paper addresses identification and robust control of vibration of a flexible plate attached to the upper side of an enclosure. The frequency domain subspace methods and minimax-linear quadratic Gaussian (LQG) control are utilized to identify the model and to control the vibration of the flexible plate, respectively. In order to identify the model of the flexible plate, several frequency domain subspace identification algorithms with Instrumental Variable idea are used. Considering the fact that the flexible plate system is stable by nature, all identified unstable models are passed through a stabilized process using an iterative algorithm with different initial values. The first three modes of the plate are selected for control purposes, and the other modes are chosen as uncertainty term. To design the weighting function for the minimax-LQG controller, Chebychev and Yule–Walker filters are utilized to consider the effect of modeling uncertainty. These weights have a great effect on robust stability and performance of the control system. Simulation results are presented to show the effectiveness of the designed controllers for the reference model. Results confirm that some indexes that show the quality of the identified models can be used as suitable measures to predict performance of the designed controller.
This paper addresses integral input-to-state stability (iISS) for a feedback interconnection of parameterised discrete-time systems involving two subsystems. Particularly, we give a construction for a smooth iISS Lyapunov function for the whole system from the sum of nonlinearly weighted Lyapunov functions of individual subsystems. Motivations for such a construction are given. We consider two main cases. The first one investigates iISS for the whole system when both subsystems are iISS. The second one gives iISS for the interconnected system when one of subsystems is allowed to be input-to-state stable. The approach is also valid for both discrete-time cascades and a feedback interconnection of iISS and static systems. Examples are given to illustrate the effectiveness of the results.
Background: Exposure to thousands of head and body impacts during a career in contact and collision sports may contribute to current or later life issues related to brain health. Wearable technology enables the measurement of impact exposure. The validation of impact detection is required for accurate exposure monitoring. In this study, we present a method of automatic identification (classification) of head and body impacts using an instrumented mouthguard, video-verified impacts, and machine-learning algorithms. Methods: Time series data were collected via the Nexus A9 mouthguard from 60 elite level men (mean age = 26.33; SD = 3.79) and four women (mean age = 25.50; SD = 5.91) from the Australian Rules Football players from eight clubs, participating in 119 games during the 2020 season. Ground truth data labeling on the captures used in this machine learning study was performed through the analysis of game footage by two expert video reviewers using SportCode and Catapult Vision. The visual labeling process occurred independently of the mouthguard time series data. True positive captures (captures where the reviewer directly observed contact between the mouthguard wearer and another player, the ball, or the ground) were defined as hits. Spectral and convolutional kernel based features were extracted from time series data. Performances of untuned classification algorithms from scikit-learn in addition to XGBoost were assessed to select the best performing baseline method for tuning. Results: Based on performance, XGBoost was selected as the classifier algorithm for tuning. A total of 13,712 video verified captures were collected and used to train and validate the classifier. True positive detection ranged from 94.67% in the Test set to 100% in the hold out set. True negatives ranged from 95.65 to 96.83% in the test and rest sets, respectively. Discussion and conclusion: This study suggests the potential for high performing impact classification models to be used for Australian Rules Football and highlights the importance of frequencies <150 Hz for the identification of these impacts.
We investigate how changes in network structure can lead to pathological oscillations similar to those observed in epileptic brain. Specifically, we conduct a bifurcation analysis of a network of two Jansen-Rit neural mass models, representing two cortical regions, to investigate different aspects of its behavior with respect to changes in the input and interconnection gains. The bifurcation diagrams, along with simulated EEG time series, exhibit diverse behaviors when varying the input, coupling strength, and network structure. We show that this simple network of neural mass models can generate various oscillatory activities, including delta wave activity, which has not been previously reported through analysis of a single Jansen-Rit neural mass model. Our analysis shows that spike-wave discharges can occur in a cortical region as a result of input changes in the other region, which may have important implications for epilepsy treatment. The bifurcation analysis is related to clinical data in two case studies.
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