Search results for: time domain passivity control

Authors: Aamir Shahzad, Hubert Roth

Abstract:

This paper is presenting the bilateral telecontrol of AutoMerlin Mobile Robot having communication delay. Passivity Observers has been designed to monitor the net energy at both ports of a two port network and if any or both ports become active making net energy negative, then the passivity controllers dissipate the proper energy to make the overall system passive in the presence of time delay. The environment force is modeled and sent back to human operator so that s/he can feel it and has additional information about the environment in the vicinity of mobile robot. The experimental results have been presented to show the performance and stability of bilateral controller. The results show the whenever the passivity observers observe active behavior then the passivity controller come into action to neutralize the active behavior to make overall system passive.

Keywords: bilateral control, human operator, haptic device, communication network, time domain passivity control, passivity observer, passivity controller, time delay, mobile robot, environment force

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Authors: H. Y. Jung, Jing Wang, J. H. Park, Hao Shen

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This brief addresses the passivity problem for neural networks with time-varying delays. The aim is focus on establishing the passivity condition of the considered neural networks.

Keywords: neural networks, passivity analysis, time-varying delays, linear matrix inequality

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Authors: Jenn-Yih Chen, Bean-Yin Lee, Yuan-Chuan Hsu, Jui-Cheng Lin, Kuang-Chyi Lee

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In this paper, a sliding mode control method based on the passivity approach is proposed to control the position of surface-mounted permanent magnet synchronous motors (PMSMs). Firstly, the dynamics of a PMSM was proved to be strictly passive. The position controller with an adaptive law was used to estimate the load torque to eliminate the chattering effects associated with the conventional sliding mode controller. The stability analysis of the overall position control system was carried out by adopting the passivity theorem instead of Lyapunov-type arguments. Finally, experimental results were provided to show that the good position tracking can be obtained, and exhibit robustness in the variations of the motor parameters and load torque disturbances.

Keywords: adaptive law, passivity theorem, permanent magnet synchronous motor, sliding mode control

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Authors: Sheila R. Pai, Rekha D. Kini, Amrutha Mary

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Objective: To assess and compare the cardiac autonomic activity after mental stress among the wards of normal and hypertensive parents. Methods: The study included 67 subjects, 30 of them had a parental history of hypertension and rest 37 had normotensive parents. Subjects were divided into control group (wards of normotensive parents) and Study group (wards of hypertensive parents). The height, weight were noted, and Body Mass Index (BMI) was also calculated. The mental stress test was carried out. Blood pressure (BP) and electro cardiogram (ECG) was recorded during normal breathing and after mental stress test. Heart rate variability (HRV) analysis was done by time domain method HRV was recorded and analyzed by the time-domain method. Analysis of HRV in the time-domain was done using the software version 1.1 AIIMS, New Delhi. The data obtained was analyzed using student’s t-test followed by Mann-Whitney U-test and P < 0.05 was considered significant. Results: There was no significant difference in systolic blood pressure and diastolic blood pressure (DBP) between study group and control group following mental stress. In the time domain analysis, the mean value of pNN50 and RMSSD of the study group was not significantly different from the control group after the mental stress test. Conclusion: The study thus concluded that there was no significant difference in HRV between study group and control group following mental stress.

Keywords: heart rate variability, time domain analysis, mental stress, hypertensive

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Authors: Li Feng

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In IEEE 802.11 networks, it is well known that the traditional time-domain contention often leads to low channel utilization. The first frequency-domain contention scheme, the time to frequency (T2F), has recently been proposed to improve the channel utilization and has attracted a great deal of attention. In this paper, we survey the latest research progress on the weighed frequency-domain contention. We present the basic ideas, work principles of these related schemes and point out their differences. This paper is very useful for further study on frequency-domain contention.

Keywords: 802.11, wireless LANs, frequency-domain contention, T2F

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Authors: Sang-Hoon Park, Yeji Ho, Gwang-Moon Eom

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Fast and accurate detection of Freezing of Gait (FOG) is desirable for appropriate application of cueing which has been shown to ameliorate FOG. Utilization of frequency spectrum of leg acceleration to derive the freeze index requires much calculation and it would lead to delayed cueing. We hypothesized that FOG can be reasonably detected from the time domain amplitude of foot acceleration. A time instant was recognized as FOG if the mean amplitude of the acceleration in the time window surrounding the time instant was in the specific FOG range. Parameters required in the FOG detection was optimized by simulated annealing. The suggested time domain methods showed performances comparable to those of frequency domain methods.

Keywords: freezing of gait, detection, Parkinson's disease, time-domain method

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Authors: Azeddine Ghodbane, David Bensoussan, Maher Hammami

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An innovative approach for controlling unstable and invertible systems has demonstrated superior performance compared to conventional controllers. It has been successfully applied to a levitation system and drone control. Simulations have yielded satisfactory performances when applied to a satellite antenna controller. This design method, based on sensitivity analysis, has also been extended to handle multivariable unstable and invertible systems that exhibit dominant diagonal characteristics at high frequencies, enabling decentralized control. Furthermore, this control method has been expanded to the realm of adaptive control. In this study, we introduce an alternative adaptive architecture that enhances both time and frequency performance, helpfully mitigating the effects of disturbances from the input plant and external disturbances affecting the output. To facilitate superior performance in both the time and frequency domains, we have developed user-friendly interactive design methods using the GeoGebra platform.

Keywords: control theory, decentralized control, sensitivity theory, input-output stability theory, robust multivariable feedback control design

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Authors: Shagufta Tabassum

Abstract:

The study of dielectric properties in a binary mixture of liquids is very useful to understand the liquid structure, molecular interaction, dynamics, and kinematics of the mixture. Time-domain reflectometry (TDR) is a powerful tool for studying the cooperation and molecular dynamics of the H-bonded system. In this paper, we discuss the basic calibration and normalization procedure for time-domain reflectometry measurements. Our approach is to explain the different types of error occur during TDR measurements and how these errors can be eliminated or minimized.

Keywords: time domain reflectometry measurement techinque, cable and connector loss, oscilloscope loss, and normalization technique

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Authors: Aziz Sezgin

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We consider the problem of stabilization of an unstable heat equation in a 2-D, 3-D and generally n-D domain by deriving a generalized backstepping boundary control design methodology. To stabilize the systems, we design boundary backstepping controllers inspired by the 1-D unstable heat equation stabilization procedure. We assume that one side of the boundary is hinged and the other side is controlled for each direction of the domain. Thus, controllers act on two boundaries for 2-D domain, three boundaries for 3-D domain and ”n” boundaries for n-D domain. The main idea of the design is to derive ”n” controllers for each of the dimensions by using ”n” kernel functions. Thus, we obtain ”n” controllers for the ”n” dimensional case. We use a transformation to change the system into an exponentially stable ”n” dimensional heat equation. The transformation used in this paper is a generalized Volterra/Fredholm type with ”n” kernel functions for n-D domain instead of the one kernel function of 1-D design.

Keywords: backstepping, boundary control, 2-D, 3-D, n-D heat equation, distributed parameter systems

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Authors: Shagufta Tabassum, V. P. Pawar, jr., G. N. Shinde

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The study of dielectric relaxation properties of polar liquids in the binary mixture has been carried out at 10, 15, 20 and 25 ºC temperatures for 11 different concentrations using time domain reflectometry technique. The dielectric properties of a solute-solvent mixture of polar liquids in the frequency range of 10 MHz to 30 GHz gives the information regarding formation of monomers and multimers and also an interaction between the molecules of the liquid mixture under study. The dielectric parameters have been obtained by the least squares fit method using the Debye equation characterized by a single relaxation time without relaxation time distribution.

Keywords: excess properties, relaxation time, static dielectric constant, and time domain reflectometry technique

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Authors: Stefano Frassinelli, Alessandro Niccolai, Riccardo E. Zich

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Diving is an important Olympic sport. In this sport, the effective performance of the athlete is related to his capability to interact correctly with the springboard. In fact, the elevation of the jump and the correctness of the dive are influenced by the vibrations of the board. In this paper, the vibrations of the springboard will be analyzed by means of typical tools for vibration analysis: Firstly, a modal analysis will be done on two different models of the springboard, then, these two model and another one will be analyzed with a time analysis, done integrating the equations of motion od deformable bodies. All these analyses will be compared with experimental data measured on a real springboard by means of a 6-axis accelerometer; these measurements are aimed to assess the models proposed. The acquired data will be analyzed both in frequency domain and in time domain.

Keywords: springboard analysis, modal analysis, time domain analysis, vibrations

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Authors: Shao-Ku Kao

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This paper presents an active rectifier with time-domain delay compensation to enhance the efficiency. A delay calibration circuit is designed to convert delay time to voltage and adaptive control on/off delay in variable input voltage. This circuit is designed in 0.18 mm CMOS process. The input voltage range is from 2 V to 3.6 V with the output voltage from 1.8 V to 3.4 V. The efficiency can maintain more than 85% when the load from 50 Ω ~ 1500 Ω for 3.6 V input voltage. The maximum efficiency is 92.4 % at output power to be 38.6 mW for 3.6 V input voltage.

Keywords: wireless power transfer, active diode, delay compensation, time to voltage converter, PCE

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Authors: Winfred Okoe Addy, Jean Jacques Dominique Beraud

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Access control systems (ACs) are some of the most important components in safety areas. Inaccuracies of regulatory frameworks make personal policies and remedies more appropriate than standard models or protocols. This problem is exacerbated by the increasing complexity of software, such as integrated Big Data (BD) software for controlling large volumes of encrypted data and resources embedded in a dedicated BD production system. This paper proposes a general access control strategy system for the diffusion of Big Data domains since it is crucial to secure the data provided to data consumers (DC). We presented a general access control circulation strategy for the Big Data domain by describing the benefit of using designated access control for BD units and performance and taking into consideration the need for BD and AC system. We then presented a generic of Big Data access control system to improve the dissemination of Big Data.

Keywords: access control, security, Big Data, domain

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Authors: Xiaoqing Wang, Jianjian Zong, Li Li, Yanxing Zheng, Jinrong Tong, Mao Zhan

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With the rapid development of network and communication technology, a great deal of data has been generated in different domains of a network. These data show a trend of increasing scale and more complex structure. Therefore, an effective and flexible cross-domain data-sharing system is needed. The Cross-domain Data Sharing System(CDSS) in a net-centric environment is composed of three sub-systems. The data distribution sub-system provides data exchange service through publish-subscribe technology that supports asynchronism and multi-to-multi communication, which adapts to the needs of the dynamic and large-scale distributed computing environment. The access control sub-system adopts Attribute-Based Access Control(ABAC) technology to uniformly model various data attributes such as subject, object, permission and environment, which effectively monitors the activities of users accessing resources and ensures that legitimate users get effective access control rights within a legal time. The cross-domain access security negotiation subsystem automatically determines the access rights between different security domains in the process of interactive disclosure of digital certificates and access control policies through trust policy management and negotiation algorithms, which provides an effective means for cross-domain trust relationship establishment and access control in a distributed environment. The CDSS’s asynchronous,multi-to-multi and loosely-coupled communication features can adapt well to data exchange and sharing in dynamic, distributed and large-scale network environments. Next, we will give CDSS new features to support the mobile computing environment.

Keywords: data sharing, cross-domain, data exchange, publish-subscribe

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Authors: Reza Rezaeipour Honarmandzad

Abstract:

This paper introduces an aircraft cable fault detection and location method in light of TFDR keeping in mind the end goal to recognize the intermittent faults adequately and to adapt to the serial and after-connector issues being hard to be distinguished in time domain reflection. In this strategy, the correlation function of reflected and reference signal is used to recognize and find the airplane fault as per the qualities of reflected and reference signal in time-frequency domain, so the hit rate of distinguishing and finding intermittent faults can be enhanced adequately. In the work process, the reflected signal is interfered by the noise and false caution happens frequently, so the threshold de-noising technique in light of wavelet decomposition is used to diminish the noise interference and lessen the shortcoming alert rate. At that point the time-frequency cross connection capacity of the reference signal and the reflected signal based on Wigner-Ville appropriation is figured so as to find the issue position. Finally, LabVIEW is connected to execute operation and control interface, the primary capacity of which is to connect and control MATLAB and LABSQL. Using the solid computing capacity and the bottomless capacity library of MATLAB, the signal processing turn to be effortlessly acknowledged, in addition LabVIEW help the framework to be more dependable and upgraded effectively.

Keywords: aircraft cable, fault location, TFDR, LabVIEW

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Authors: So-Young Ju, Sung-Mi Jo, Eui-Rim Jeong

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In this paper, based on the conventional single carrier frequency domain equalization (SC-FDE) structure, we propose a new SC-FDE structure to cope with narrowband jammer. In the conventional SC-FDE structure, channel estimation is performed in the time domain. When a narrowband jammer exists, time-domain channel estimation is very difficult due to high power jamming interference, which degrades receiver performance. To relieve from this problem, a new SC-FDE frame is proposed to enable channel estimation under narrow band jamming environments. In this paper, we proposed a modified SC-FDE structure that can perform channel estimation in the frequency domain and verified the performance via computer simulation.

Keywords: channel estimation, jammer, pilot, SC-FDE

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Authors: Henni Mansour Abdelwaheb

Abstract:

This study discusses the design of a bounded position/force feedback controller developed to ensure position and force tracking for bilateral teleoperation arms operating with variable delay, and actuator saturation. Also, an adaptive robust Radial Basis Function (RBF) neural network is used to estimate the environment torque. The parameters of the environment torque are then sent from the slave site to the master site as a non-power signal to avoid passivity problems. Moreover, a nonlinear function is applied to each controller term as a smooth saturation function, providing a bounded control signal and preserving the system’s actuators. Lastly, the Lyapunov approach demonstrates the global stability of the controlled system, and numerical experiment results further confirm the validity of the presented strategy.

Keywords: teleoperation manipulators system, time-varying delay, actuator saturation, adaptive robust rbf neural network approximation, uncertainties

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Authors: Donggun Lee, Q-Han Park

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Due to its coarse grid, the Pseudo-Spectral Time Domain (PSTD) method has advantages against the Finite Difference Time Domain (FDTD) method in terms of memory requirement and operation time. However, since the efficiency of parallelization is much lower than that of FDTD, PSTD is not a useful method for a large-scale electromagnetic simulation in a parallel platform. In this paper, we propose the parallelization technique of the hybrid PSTD-FDTD (HPF) method which simultaneously possesses the efficient parallelizability of FDTD and the quick speed and low memory requirement of PSTD. Parallelization cost of the HPF method is exactly the same as the parallel FDTD, but still, it occupies much less memory space and has faster operation speed than the parallel FDTD. Experiments in distributed memory systems have shown that the parallel HPF method saves up to 96% of the operation time and reduces 84% of the memory requirement. Also, by combining the OpenMP library to the MPI library, we further reduced the operation time of the parallel HPF method by 50%.

Keywords: FDTD, hybrid, MPI, OpenMP, PSTD, parallelization

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Authors: Xiaofei Hu, Zhiyu Cai, Weian Yao

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V-notch problem under dynamic loading condition is considered in this paper. In the time domain, the precise time domain expanding algorithm is employed, in which a self-adaptive technique is carried out to improve computing accuracy. By expanding variables in each time interval, the recursive finite element formulas are derived. In the space domain, a Symplectic Analytical Singular Element (SASE) for V-notch problem is constructed addressing the stress singularity of the notch tip. Combining with the conventional finite elements, the proposed SASE can be used to solve the dynamic stress intensity factors (DSIFs) in a simple way. Numerical results show that the proposed SASE for V-notch problem subjected to dynamic loading condition is effective and efficient.

Keywords: V-notch, dynamic stress intensity factor, finite element method, precise time domain expanding algorithm

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Authors: Bunakiye R. Japheth, Ogude U. Cyril

Abstract:

Since the process of transforming user requirements to modeling constructs are not very well supported by domain-specific frameworks, it became necessary to integrate domain requirements with the specific architectures to achieve an integrated customizable solutions space via artifact orientation. Domain-specific modeling language specifications of model-driven engineering technologies focus more on requirements within a particular domain, which can be tailored to aid the domain expert in expressing domain concepts effectively. Modeling processes through domain-specific language formalisms are highly volatile due to dependencies on domain concepts or used process models. A capable solution is given by artifact orientation that stresses on the results rather than expressing a strict dependence on complicated platforms for model creation and development. Based on this premise, domain-specific methods for producing artifacts without having to take into account the complexity and variability of platforms for model definitions can be integrated to support customizable development. In this paper, we discuss methods for the integration capabilities and necessities within a common structure and semantics that contribute a metamodel for artifact-orientation, which leads to a reusable software layer with concrete syntax capable of determining design intents from domain expert. These concepts forming the language formalism are established from models explained within the oil and gas pipelines industry.

Keywords: control process, metrics of engineering, structured abstraction, semantic model

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Authors: Alan C. Lin, Tsong Der Lin

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This study proposes a deviation control method to add interpolation points to numerical control (NC) codes of five-axis machining in order to achieve the required machining accuracy. Specific research issues include: (1) converting machining data between the CL (cutter location) domain and the NC domain, (2) calculating the deviation between the deviated path and the linear path, (3) finding interpolation points, and (4) determining tool orientations for the interpolation points. System implementation with practical examples will also be included to highlight the applicability of the proposed methodology.

Keywords: CAD/CAM, cutter path, five-axis machining, numerical control

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Authors: Khaing Yadana Swe, Lillie Dewan

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At present, the cascade PID control is widely used to control the super-heating temperature (main steam temperature). As the main steam temperature has the characteristics of large inertia, large time-delay, and time varying, etc., conventional PID control strategy can not achieve good control performance. In order to overcome the bad performance and deficiencies of main steam temperature control system, Model Free Adaptive Control (MFAC) P cascade control system is proposed in this paper. By substituting MFAC in PID of the main control loop of the main steam temperature control, it can overcome time delays, non-linearity, disturbance and time variation.

Keywords: model-free adaptive control, cascade control, adaptive control, PID

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Authors: E. Sener, O. Isik, E. Eroglu, U. Sahin

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The main idea is to solve the system of Maxwell’s equations in accordance with the causality principle to get the energy quantities via Airy functions in a hollow rectangular waveguide. We used the evolutionary approach to electromagnetics that is an analytical time-domain method. The boundary-value problem for the system of Maxwell’s equations is reformulated in transverse and longitudinal coordinates. A self-adjoint operator is obtained and the complete set of Eigen vectors of the operator initiates an orthonormal basis of the solution space. Hence, the sought electromagnetic field can be presented in terms of this basis. Within the presentation, the scalar coefficients are governed by Klein-Gordon equation. Ultimately, in this study, time-domain waveguide problem is solved analytically in accordance with the causality principle. Moreover, the graphical results are visualized for the case when the energy and surplus of the energy for the time-domain waveguide modes are represented via airy functions.

Keywords: airy functions, Klein-Gordon Equation, Maxwell’s equations, Surplus of energy, wave boundary operators

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Authors: Loubna Tani, Nabih Elouzzani

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Crosstalk among interconnects and printed-circuit board (PCB) traces is a major limiting factor of signal quality in high-speed digital and communication equipments especially when fast data buses are involved. Such a bus is considered as a planar multiconductor transmission line. This paper will demonstrate how the finite difference time domain (FDTD) method provides an exact solution of the transmission-line equations to analyze the near end and the far end crosstalk. In addition, this study makes it possible to analyze the rise time effect on the near and far end voltages of the victim conductor. The paper also discusses a statistical analysis, based upon a set of several simulations. Such analysis leads to a better understanding of the phenomenon and yields useful information.

Keywords: multiconductor transmission line, crosstalk, finite difference time domain (FDTD), printed-circuit board (PCB), rise time, statistical analysis

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Authors: Hyery Kang, Dong-Yeun Koh, Yun-Ho Ahn, Huen Lee

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Determination of the behavior of clathrate hydrate with inhibitor in the THz region will provide useful information about hydrate plug control in the upstream of the oil and gas industry. In this study, terahertz time-domain spectroscopy (THz-TDS) revealed the inhibition of the THF clathrate hydrate system with dosage of polyvinylpyrrolidone (PVP) with three different molecular weights. Distinct footprints of phase transition in the THz region (0.4–2.2 THz) were analyzed and absorption coefficients and real part of refractive indices are obtained in the temperature range of 253 K to 288 K. Along with the optical properties, ring breathing and stretching modes for different molecular weights of PVP in THF hydrate are analyzed by Raman spectroscopy.

Keywords: clathrate hydrate, terahertz spectroscopy, tetrahydrofuran, inhibitor

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Authors: Ahmad Forouzantabar, Mohammad Azadi

Abstract:

This paper presents sliding mode controller for bilateral teleoperation systems with robotic master and slave under constant communication delays. We extend the passivity-based coordination architecture to enhance position and force tracking in the presence of offset in initial conditions, environmental contacts and unknown parameters such as friction coefficient. To address these difficulties, a nonlinear sliding mode controller is designed to approximate the nonlinear dynamics of master and slave robots and improve both position and force tracking. Using the Lyapunov theory, the boundedness of master- slave tracking errors and the stability of the teleoperation system are also guaranteed. Numerical simulations show that proposed controller position and force tracking performances are superior to that of conventional coordination controller tracking performances.

Keywords: Lyapunov stability, teleoperation system, time delay, sliding mode controller

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Authors: E. Eroglu, S. Semsit, E. Sener, U.S. Sener

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In Electromagnetics, there are three canonical boundary value problem with given initial conditions for the electromagnetic field sought, namely: Cavity Problem, Waveguide Problem, and External Problem. The Cavity Problem and Waveguide Problem were rigorously studied and new results were arised at original works in the past decades. In based on studies of an analytical time domain method Evolutionary Approach to Electromagnetics (EAE), electromagnetic field strength vectors produced by a time dependent source function are sought. The fields are took place in L2 Hilbert space. The source function that performs signal transferring, energy and surplus of energy has been demonstrated with all clarity. Depth of the method and ease of applications are emerged needs of gathering obtained results. Main discussion is about perfect electric conductor and hollow waveguide. Even if well studied time-domain modes problems are mentioned, specifically, the modes which have a hollow (i.e., medium-free) cross-section domain are considered.

Keywords: evolutionary approach to electromagnetics, time-domain waveguide mode, Neumann problem, Dirichlet boundary value problem, Klein-Gordon

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Authors: Ömer Aktaş, Olga A. Suvorova, Oleg Tretyakov

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The boundary value problem on non-canonical and arbitrary shaped contour is solved with a numerically effective method called Analytical Regularization Method (ARM) to calculate propagation parameters. As a result of regularization, the equation of first kind is reduced to the infinite system of the linear algebraic equations of the second kind in the space of L2. This equation can be solved numerically for desired accuracy by using truncation method. The parameters as cut-off wavenumber and cut-off frequency are used in waveguide evolutionary equations of electromagnetic theory in time-domain to illustrate the real-valued TM fields with lossy and lossless media.

Keywords: analytical regularization method, electromagnetic theory evolutionary equations of time-domain, TM Field

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Authors: Hao-Su Liu, Jun-Qing Lei

Abstract:

This study introduces the theory of modified particle swarm optimizer and its application in time-domain expressions for bridge self-excited aerodynamic forces. Based on the indicial function expression and the rational function expression in time-domain expression for bridge self-excited aerodynamic forces, the characteristics of the two methods, i.e. the modified particle swarm optimizer and conventional search method, are compared in flutter derivatives’ fitting process. Theoretical analysis and numerical results indicate that adopting whether the indicial function expression or the rational function expression, the fitting flutter derivatives obtained by modified particle swarm optimizer have better goodness of fit with ones obtained from experiment. As to the flutter derivatives which have higher nonlinearity, the self-excited aerodynamic forces, using the flutter derivatives obtained through modified particle swarm optimizer fitting process, are much closer to the ones simulated by the experimental. The modified particle swarm optimizer was used to recognize the parameters of time-domain expressions for flutter derivatives of an actual long-span highway-railway truss bridge with double decks at the wind attack angle of 0°, -3° and +3°. It was found that this method could solve the bounded problems of attenuation coefficient effectively in conventional search method, and had the ability of searching in unboundedly area. Accordingly, this study provides a method for engineering industry to frequently and efficiently obtain the time-domain expressions for bridge self-excited aerodynamic forces.

Keywords: time-domain expressions, bridge self-excited aerodynamic forces, modified particle swarm optimizer, long-span highway-railway truss bridge

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Authors: Z. Bouchama, N. Essounbouli, A. Hamzaoui, M. N. Harmas

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A new robust finite time synergetic controller is presented based on recently developed synergetic control methodology and a terminal attractor technique. A Fast Terminal Synergetic Control (FTSC) is proposed for controlling DC-DC buck converter. Unlike Synergetic Control (SC) and sliding mode control, the proposed control scheme has the characteristics of finite time convergence and chattering free phenomena. Simulation of stabilization and reference tracking for buck converter systems illustrates the approach effectiveness while stability is assured in the Lyapunov sense and converse Lyapunov results involving scalar differential inequalities are given for finite-time stability.

Keywords: dc-dc buck converter, synergetic control, finite time convergence, terminal synergetic control, fast terminal synergetic control, Lyapunov

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