• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.4 s.247
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• pp.435-441
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• 2006

The anterior cruciate ligament(ACL) is an important stabilizer of knee joint. The ACL injury of knee is common and a serious ACL injury leads to ligament reconstruction surgery. Gait analysis is essential to identify knee condition of patients who display abnormal gait. The purpose of this study is to evaluate and classify knee condition of ACL deficient patients using a nonlinear dynamic method. The nonlinear method focuses on understanding how variations in the gait pattern change over time. The experiments were carried out for 17 subjects(l2 healthy subjects and five subjects with unilateral deficiency) walking on a motorized treadmill for 100 seconds. Three dimensional kinematics of the lower extremity were collected by using four cameras and KWON 3D motion analysis system. The largest Lyapunov exponent calculated from knee joint flexion-extension time series was used to quantify knee stability. The results revealed the difference between healthy subjects and patients. The deficient knee was significantly unstable compared with the contralateral knee. This study suggests an evaluation scheme of the severity of injury and the level of recovery. The proposed Lyapunov exponent can be used in rehabilitation and diagnosis of recoverable patients.

• Proceedings of the IEEK Conference
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• 2009.05a
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• pp.37-39
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• 2009

In the research of speech recognition, locating the beginning and end of a speech utterance in a background of noise is of great importance. Since the background noise presenting to record will introduce disturbance while we just want to get the stationary parameters to represent the corresponding speech section, in particular, a major source of error in automatic recognition system of isolated words is the inaccurate detection of beginning and ending boundaries of test and reference templates, thus we must find potent method to remove the unnecessary regions of a speech signal. The conventional methods for speech endpoint detection are based on two simple time-domain measurements - short-time energy, and short-time zero-crossing rate, which couldn't guarantee the precise results if in the low signal-to-noise ratio environments. This paper proposes a novel approach that finds the Lyapunov exponent of time-domain waveform. This proposed method has no use for obtaining the frequency-domain parameters for endpoint detection process, e.g. Mel-Scale Features, which have been introduced in other paper. Comparing with the conventional methods based on short-time energy and short-time zero-crossing rate, the novel approach based on time-domain Lyapunov Exponents(LEs) is low complexity and suitable for Digital Isolated Word Recognition System.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.5
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• pp.137-144
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• 2000

In this paper, a longitudinal control of the lead vehicle for a platoon in IVHS Regulation Layer is proposed. The backstepping method has been used for the controller design. This method has an advantage in that its stability need not be proven since the controller is designed based on the Lyapunov Function. The control object is that the lead vehicle tracks a reference velocity and maintains a safe distance between the inter-platoons while the followers are keeping the speed of the lead vehicle of a platoon. The coordinate of system is transformed to a new coordinate system for its convenience to design controller. The new coordinate system is composed of error and new error variable. The error is the difference between the safe distance and the actual distance of inter-platoons. A new error variable is the difference between the velocity of vehicle and the estimated state of a system operated by the virtual input. The Lyapunov function is obtained based on the variables of new coordinate system. In the computer simulation, several cases have been studied such as when the lead vehicle is tracking the optimal speed. or a lead vehicle of the following platoon tracks the velocity of the previous platoon while maintaining a safe distance. Also a nonlinear engine time constant case has been investigated. All the simulation results show that the designed controller satisfies the control object sufficiently.

• Journal of the Korean Society for Precision Engineering
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• v.23 no.2 s.179
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• pp.164-171
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• 2006

Anterior cruciate ligament(ACL) injury of the knee is common and a serious ACL injury leads to ligament reconstruction surgery. Gait analysis is used to identify the result of surgery. The purpose of this study is to numerically evaluate and classify knee condition of patients through the chaos analysis. Experiments were carried out for 13 subjects (8 healthy subjects, 5 ACL deficient patients) walking on a treadmill. Sagittal kinematic data of the right lower extremity were collected by using a 3D motion analysis system. The recorded gait patterns were digitized and then coordinated by KWON3D. The largest Lyapunov exponent from the measured knee angular displacement time series was calculated to quantify local stability. It was found that the Lyapunov exponent becomes larger as the knee condition becomes worse. This study suggested a method of the severity of injury and the level of recovery. The proposed method discerns difference between healthy subjects and patients.

• Korean Journal of Applied Biomechanics
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• v.33 no.1
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• pp.34-44
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• 2023

Objective: The purpose of this study was to examine the effects of increasing running speed on human stability by comparing the Lyapunov Exponent (LyE) and Coefficient of Variation (CV) methods, with the goal of identifying key variables and uncovering new insights. Method: Fourteen adult males (age: 24.7 ± 6.4 yrs, height: 176.9 ± 4.6 cm, weight: 74.7 ± 10.9 kg) participated in this study. Results: In the CV method, significant differences were observed in ankle (flexion-inversion/eversion; p < .05) and hip joint (internal-external rotation; p < .05) movements, while the center of mass (COM) variable in the coronal axis movements showed a significant difference at the p < .001 level. In the LyE method, statistical differences were observed at the p < .05 level in knee (flexion-extension), hip joint (internal-external rotation) movements, and COM across all three directions (sagittal, coronal, and transverse axis). Conclusion: Our results revealed that the stability of the human body is affected at faster running speeds. The movement of the COM and ankle joint were identified as the most critical factors influencing stability. This suggests that LyE, a nonlinear time series analysis, should be actively introduced to better understand human stabilization strategies.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.187-190
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• 1997

In the past few years, many researchers are interesting of control of mobile robot with nonholonomic constraints. And tracking problems is important as well as regulation in nonholonomic system control. Some researchers have investigated the stable tracking control law for mobile robot. But, few results showed the globally asymptotically stable control method simply. So, we address the design of globally asymptotically stable tracking control law for mobile robot with nonholonomic velocity constraints using simple method. The stabilizability of the controller is derived by Lyapunov direct method. And we analyze the system responses according to the variation of control parameters in line tracking problem. It is derived that the responses represent no overshoot property in line tracking. Examples are two-wheeled mobile robot and car-like mobile robot and the simulation results represent the effectiveness of our method.

• Journal of IKEEE
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• v.13 no.1
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• pp.11-18
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• 2009

In this paper, the stability of second order uncertain systems with regulation of PID type controllers is analyzed by using Lyapunov second method for the first time in the time domain. The property of the stability of PID regulation servo systems is revealed in sense of Lyapunov, i.e., bounded stability due to the disturbances and uncertainties. By means of the results of this stability analysis, the maximum norm bound of the error from the output without variation of the uncertainties and disturbances is determined as a function of the gains of the PID control, which make it enable to analyze the effect resulted from the variations of the disturbances and uncertainties using this norm bound for given PID gains. Using the relationship of the error from the output without variation of the uncertainties and disturbances and the PID gain with maximum bounds of the disturbances and uncertainties, the robust gain design rule is suggested so that the error from the output without the variation of the disturbances and uncertainties can be guaranteed by the prescribed specifications as the advantages of this study. The usefulness of the proposed algorithm is verified through an illustrative example.

• Ocean and Polar Research
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• v.28 no.4
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• pp.459-465
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• 2006

Ambient noise as a background noise in the ocean has been well known for its the various and irregular signal characteristics. Generally, these signals we treated as noise and they are analyzed through stochastical level if they don't include definite sinusoidal signals. This study is to see how ocean ambient noise can be analyzed by the chaotic analysis technique. The chaotic analysis is carried out with underwater ambient noise obtained in areas near the Korean Peninsula. The calculated physical parameters of time series signal are as follows: histogram, self-correlation coefficient, delay time, frequency spectrum, sonogram, return map, embedding dimension, correlation dimension, Lyapunov exponent, etc. We investigate the chaotic pattern of noises from these parameters. From the embedding dimensions of underwater noises, the assesment of underwater noise by chaotic analysis shows similar results if they don't include a definite sinusoidal signal. However, the values of Lyapunov exponent (divergence exponent) are smaller than that of random noise signal. As a result we confirm the possibility of classification of underwater noise using Lyapunov analysis.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.16 no.8
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• pp.2490-2506
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• 2022

In Mobile Edge Computing (MEC), attackers can speculate and mine sensitive user information by eavesdropping wireless channel status and offloading usage pattern, leading to user privacy leakage. To solve this problem, this paper proposes a Privacy-preserving and Energy-efficient Offloading Algorithm (PEOA) based on Lyapunov optimization. In this method, a continuous Markov process offloading model with a buffer queue strategy is built first. Then the amount of privacy of offloading usage pattern in wireless channel is defined. Finally, by introducing the Lyapunov optimization, the problem of minimum average energy consumption in continuous state transition process with privacy constraints in the infinite time domain is transformed into the minimum value problem of each timeslot, which reduces the complexity of algorithms and helps obtain the optimal solution while maintaining low energy consumption. The experimental results show that, compared with other methods, PEOA can maintain the amount of privacy accumulation in the system near zero, while sustaining low average energy consumption costs. This makes it difficult for attackers to infer sensitive user information through offloading usage patterns, thus effectively protecting user privacy and safety.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.11 no.1
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• pp.49-53
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• 2011

Path following of the mobile robot is one research hot for the mobile robot navigation. For the control system of the wheeled mobile robot(WMR) being in nonhonolomic system and the complex relations among the control parameters, it is difficult to solve the problem based on traditional mathematics model. In this paper, we presents a simple and effective way of implementing an adaptive following controller based on the PID for mobile robot path following. The method uses a non-linear model of mobile robot kinematics and thus allows an accurate prediction of the future trajectories. The proposed controller has a parallel structure that consists of PID controller with a fixed gain. The control law is constructed on the basis of Lyapunov stability theory. Computer simulation for a differentially driven nonholonomic mobile robot is carried out in the velocity and orientation tracking control of the nonholonomic WMR. The simulation results of wheel type mobile robot platform are given to show the effectiveness of the proposed algorithm.