Search results for: Implicit Lyapunov control

Authors: Xiaoyan Dou, Yongkun Li

Abstract:

In this paper, we consider a food-limited population model with delay and feedback control. By applying the comparison theorem of the differential equation and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the permanence and existence of a unique globally attractive positive almost periodic solution of the system are obtained.

Keywords: Almost periodic solution, food-limited population, feedback control, permanence.

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Authors: Gwanghee Heo, Geonhyeok Bang, Chunggil Kim, Chinok Lee

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This paper attempts to develop a wireless feedback control system as a primary step eventually toward a bio-inspired structure system where inanimate structure behaves like a life form autonomously. It is a standalone wireless control system which is supposed to measure externally caused structural responses, analyze structural state from acquired data, and take its own action on the basis of the analysis with an embedded logic. For an experimental examination of its effectiveness, we applied it on a model of two-span bridge and performed a wireless control test. Experimental tests have been conducted for comparison on both the wireless and the wired system under the conditions of Un-control, Passive-off, Passive-on, and Lyapunov control algorithm. By proving the congruence of the test result of the wireless feedback control system with the wired control system, its control performance was proven to be effective. Besides, it was found to be economical in energy consumption and also autonomous by means of a command algorithm embedded into it, which proves its basic capacity as a bio-inspired system.

Keywords: Structural vibration control, wireless system, MR damper, feedback control, embedded system.

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Authors: Bhanu Gupta, Sanjay K. Srivastava

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In this paper, we shall present sufficient conditions for the ψ-exponential stability of a class of nonlinear impulsive differential equations. We use the Lyapunov method with functions that are not necessarily differentiable. In the last section, we give some examples to support our theoretical results.

Keywords: Exponential stability, globally exponential stability, impulsive differential equations, Lyapunov function, ψ-stability.

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Authors: B. S. Raghavendra, D. Narayana Dutt

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Many recent electrophysiological studies have revealed the importance of investigating meditation state in order to achieve an increased understanding of autonomous control of cardiovascular functions. In this paper, we characterize heart rate variability (HRV) time series acquired during meditation using nonlinear dynamical parameters. We have computed minimum embedding dimension (MED), correlation dimension (CD), largest Lyapunov exponent (LLE), and nonlinearity scores (NLS) from HRV time series of eight Chi and four Kundalini meditation practitioners. The pre-meditation state has been used as a baseline (control) state to compare the estimated parameters. The chaotic nature of HRV during both pre-meditation and meditation is confirmed by MED. The meditation state showed a significant decrease in the value of CD and increase in the value of LLE of HRV, in comparison with premeditation state, indicating a less complex and less predictable nature of HRV. In addition, it was shown that the HRV of meditation state is having highest NLS than pre-meditation state. The study indicated highly nonlinear dynamic nature of cardiac states as revealed by HRV during meditation state, rather considering it as a quiescent state.

Keywords: Correlation dimension, Embedding dimension, Heartrate variability, Largest Lyapunov exponent, Meditation, Nonlinearity score.

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Authors: Li Xu, Shouming Zhong

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The reachable set bounding estimation for distributed delay systems with disturbances is a new problem. In this paper,we consider this problem subject to not only time varying delay and polytopic uncertainties but also distributed delay systems which is not studied fully untill now. we can obtain improved non-ellipsoidal reachable set estimation for neural networks with time-varying delay by the maximal Lyapunov-Krasovskii fuctional which is constructed as the pointwise maximum of a family of Lyapunov-Krasovskii fuctionals corresponds to vertexes of uncertain polytope.On the other hand,matrix inequalities containing only one scalar and Matlabs LMI Toolbox is utilized to give a non-ellipsoidal description of the reachable set.finally,numerical examples are given to illustrate the existing results.

Keywords: Reachable set, Distributed delay, Lyapunov-Krasovskii function, Polytopic uncertainties.

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Authors: Amer S. Al-Yahmadi, T.C. Hsia

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This paper seeks to develop simple yet practical and efficient control scheme that enables cooperating arms to handle a flexible beam. Specifically the problem studied herein is that of two arms rigidly grasping a flexible beam and such capable of generating forces/moments in such away as to move a flexible beam along a predefined trajectory. The paper develops a sliding mode control law that provides robustness against model imperfection and uncertainty. It also provides an implicit stability proof. Simulation results for two three joint arms moving a flexible beam, are presented to validate the theoretical results.

Keywords: Sliding mode control, cooperative manipulators.

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Authors: Kazem Ghanbari, Yousef Gholami

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This paper deals with study about fractional order impulsive Hamiltonian systems and fractional impulsive Sturm-Liouville type problems derived from these systems. The main purpose of this paper devotes to obtain so called Lyapunov type inequalities for mentioned problems. Also, in view point on applicability of obtained inequalities, some qualitative properties such as stability, disconjugacy, nonexistence and oscillatory behaviour of fractional Hamiltonian systems and fractional Sturm-Liouville type problems under impulsive conditions will be derived. At the end, we want to point out that for studying fractional order Hamiltonian systems, we will apply recently introduced fractional Conformable operators.

Keywords: Fractional derivatives and integrals, Hamiltonian system, Lyapunov type inequalities, stability, disconjugacy.

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Authors: Sukir Maryanto, Didik R. Santosa, Iyan Mulyana, Muhammad Hendrasto

Abstract:

Successive event of explosion earthquake and harmonic tremor recorded at Semeru volcano were analyzed to investigate the dynamical system regarding to their eruptive mechanism. The eruptive activity at Semeru volcano East Java, Indonesia is intermittent emission of ash and bombs with Strombolian style which occurred at interval of 15 to 45 minutes. The explosive eruptions accompanied by explosion earthquakes and followed by volcanic tremor which generated by continuous emission of volcanic ash. The spectral and Lyapunov exponent of successive event of explosion and harmonic tremor were analyzed. Peak frequencies of explosion earthquakes range 1.2 to 1.9 Hz and those of the harmonic tremor have peak frequency range 1.5 — 2.2 Hz. The phase space is reconstructed and evaluated based on the Lyapunov exponents. Harmonic tremors have smaller Lyapunov exponent than explosion earthquakes. It can be considerably as correlated complexity of the mechanism from the variance of spectral and fractal dimension and can be concluded that the successive event of harmonic tremor and explosions are chaotic.

Keywords: Semeru volcano, explosion earthquakes, harmonic tremor, lyapunov exponent, chaotic.

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Authors: Fudziah Ismail

Abstract:

In this paper a new embedded Singly Diagonally Implicit Runge-Kutta Nystrom fourth order in fifth order method for solving special second order initial value problems is derived. A standard set of test problems are tested upon and comparisons on the numerical results are made when the same set of test problems are reduced to first order systems and solved using the existing embedded diagonally implicit Runge-Kutta method. The results suggests the superiority of the new method.

Keywords: Runge-Kutta Nystrom, Special second orderproblems.

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Authors: Abolhassan Razminia, Mohammad-Ali Sadrnia

Abstract:

Chua’s circuit is one of the most important electronic devices that are used for Chaos and Bifurcation studies. A central role of secure communication is devoted to it. Since the adaptive control is used vastly in the linear systems control, here we introduce a new trend of application of adaptive method in the chaos controlling field. In this paper, we try to derive a new adaptive control scheme for Chua’s circuit controlling because control of chaos is often very important in practical operations. The novelty of this approach is for sake of its robustness against the external perturbations which is simulated as an additive noise in all measured states and can be generalized to other chaotic systems. Our approach is based on Lyapunov analysis and the adaptation law is considered for the feedback gain. Because of this, we have named it NAFT (Nonlinear Adaptive Feedback Technique). At last, simulations show the capability of the presented technique for Chua’s circuit.

Keywords: Chaos, adaptive control, nonlinear control, Chua's circuit.

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Authors: Wookyong Kwon, Sangmoon Lee

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In this paper, a sampled-data model predictive tracking control method is presented for mobile robots which is modeled as constrained continuous-time linear parameter varying (LPV) systems. The presented sampled-data predictive controller is designed by linear matrix inequality approach. Based on the input delay approach, a controller design condition is derived by constructing a new Lyapunov function. Finally, a numerical example is given to demonstrate the effectiveness of the presented method.

Keywords: Model predictive control, sampled-data control, linear parameter varying systems, LPV.

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Authors: Gülnihal Meral

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In this study, the density dependent nonlinear reactiondiffusion equation, which arises in the insect dispersal models, is solved using the combined application of differential quadrature method(DQM) and implicit Euler method. The polynomial based DQM is used to discretize the spatial derivatives of the problem. The resulting time-dependent nonlinear system of ordinary differential equations(ODE-s) is solved by using implicit Euler method. The computations are carried out for a Cauchy problem defined by a onedimensional density dependent nonlinear reaction-diffusion equation which has an exact solution. The DQM solution is found to be in a very good agreement with the exact solution in terms of maximum absolute error. The DQM solution exhibits superior accuracy at large time levels tending to steady-state. Furthermore, using an implicit method in the solution procedure leads to stable solutions and larger time steps could be used.

Keywords: Density Dependent Nonlinear Reaction-Diffusion Equation, Differential Quadrature Method, Implicit Euler Method.

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Authors: N. M. Nusi, M. Othman, M. Suleiman, F. Ismail, N. Alias

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In this paper, an alternating implicit block method for solving two dimensional scalar wave equation is presented. The new method consist of two stages for each time step implemented in alternating directions which are very simple in computation. To increase the speed of computation, a group of adjacent points is computed simultaneously. It is shown that the presented method increase the maximum time step size and more accurate than the conventional finite difference time domain (FDTD) method and other existing method of natural ordering.

Keywords: FDTD, Scalar wave equation, alternating direction implicit (ADI), alternating group explicit (AGE), asymmetric approximation.

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Authors: Norsinnira Zainul Azlan, Hiroshi Yamaura

Abstract:

This paper presents a new adaptive impedance control strategy, based on Function Approximation Technique (FAT) to compensate for unknown non-flat environment shape or time-varying environment location. The target impedance in the force controllable direction is modified by incorporating adaptive compensators and the uncertainties are represented by FAT, allowing the update law to be derived easily. The force error feedback is utilized in the estimation and the accurate knowledge of the environment parameters are not required by the algorithm. It is shown mathematically that the stability of the controller is guaranteed based on Lyapunov theory. Simulation results presented to demonstrate the validity of the proposed controller.

Keywords: Adaptive impedance control, Function Approximation Technique (FAT), impedance control, unknown environment position.

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Authors: Miaomiao Yang, Shouming Zhong

Abstract:

This paper studies the problem of asymptotically stability for neural networks with time-varying delays.By establishing a suitable Lyapunov-Krasovskii function and several novel sufficient conditions are obtained to guarantee the asymptotically stability of the considered system. Finally,two numerical examples are given to illustrate the effectiveness of the proposed main results.

Keywords: Neural networks, Lyapunov-Krasovskii, Time-varying delays, Linear matrix inequality.

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Authors: Norsinnira Zainul Azlan, Hiroshi Yamaura

Abstract:

This study is concerned with a new adaptive impedance control strategy to compensate for unknown time-varying environment stiffness and position. The uncertainties are expressed by Function Approximation Technique (FAT), which allows the update laws to be derived easily using Lyapunov stability theory. Computer simulation results are presented to validate the effectiveness of the proposed strategy.

Keywords: Adaptive Impedance Control, Function Approximation Technique (FAT), unknown time-varying environment position and stiffness.

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Authors: Cemil Tunc

Abstract:

In this paper, we study the instability of the zero solution to a nonlinear differential equation with variable delay. By using the Lyapunov functional approach, some sufficient conditions for instability of the zero solution are obtained.

Keywords: Instability, Lyapunov-Krasovskii functional, delay differential equation, fifth order.

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Authors: Bibhya Sharma, Jito Vanualailai, Ravindra Rai

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This research paper designs a unique motion planner of multiple platoons of nonholonomic car-like robots as a feasible solution to the lane changing/merging maneuvers. The decentralized planner with a leaderless approach and a path-guidance principle derived from the Lyapunov-based control scheme generates collision free avoidance and safe merging maneuvers from multiple lanes to a single lane by deploying a split/merge strategy. The fixed obstacles are the markings and boundaries of the road lanes, while the moving obstacles are the robots themselves. Real and virtual road lane markings and the boundaries of road lanes are incorporated into a workspace to achieve the desired formation and configuration of the robots. Convergence of the robots to goal configurations and the repulsion of the robots from specified obstacles are achieved by suitable attractive and repulsive potential field functions, respectively. The results can be viewed as a significant contribution to the avoidance algorithm of the intelligent vehicle systems (IVS). Computer simulations highlight the effectiveness of the split/merge strategy and the acceleration-based controllers.

Keywords: Lane merging, Lyapunov-based control scheme, path-guidance principle, split/merge strategy.

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Authors: Sanjay K.Srivastava, Bhanu Gupta

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In this paper some results on strict stability heve beeb extended for fuzzy differential equations with impulse effect using Lyapunov functions and Razumikhin technique.

Keywords: Fuzzy differential equations, Impulsive differential equations, Strict stability, Lyapunov function, Razumikhin technique.

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Authors: Adnene Arbi, Chaouki Aouiti, Abderrahmane Touati

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In this paper, we consider the global exponential stability of the equilibrium point of Hopfield neural networks with delays and impulsive perturbation. Some new exponential stability criteria of the system are derived by using the Lyapunov functional method and the linear matrix inequality approach for estimating the upper bound of the derivative of Lyapunov functional. Finally, we illustrate two numerical examples showing the effectiveness of our theoretical results.

Keywords: Hopfield Neural Networks, Exponential stability.

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Authors: Hongji Tang, Yanbo Gao, Yue Yu

Abstract:

This paper presents a new nonlinear integral-type sliding surface for synchronizing two different chaotic systems with parametric uncertainty. On the basis of Lyapunov theorem and average dwelling time method, we obtain the control gains of controllers which are derived to achieve chaos synchronization. In order to reduce the gains, the error system is modeled as a switching system. We obtain the sufficient condition drawn for the robust stability of the error dynamics by stability analysis. Then we apply it to guide the design of the controllers. Finally, numerical examples are used to show the robustness and effectiveness of the proposed control strategy.

Keywords: Chaos synchronization, Nonlinear sliding surface, Control gains, Sliding mode control.

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Authors: Bibhya Sharma, Jito Vanualailai, Jai Raj

Abstract:

In this paper, we propose a solution to the motion planning and control problem for a swarm of three-dimensional boids. The swarm exhibit collective emergent behaviors within the vicinity of the workspace. The capability of biological systems to autonomously maneuver, track and pursue evasive targets in a cluttered environment is vastly superior to any engineered system. It is considered an emergent behavior arising from simple rules that are followed by individuals and may not involve any central coordination. A generalized, yet scalable algorithm for attraction to the centroid and inter-individual swarm avoidance is proposed. We present a set of new continuous time-invariant velocity control laws, formulated via the Lyapunov-based control scheme for target attraction and collision avoidance. The controllers provide a collision-free trajectory. The control laws proposed in this paper also ensures practical stability of the system. The effectiveness of the control laws is demonstrated via computer simulations.

Keywords: Swarm, Practical stability, Motion planning.

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Authors: Chenxi Yang, Zhouhong Li

Abstract:

This paper is concerned with an epidemic model with delay. By using the comparison theorem of the differential equation and constructing a suitable Lyapunov functional, Some sufficient conditions which guarantee the permeance and existence of a unique globally attractive positive almost periodic solution of the model are obtain. Finally, an example is employed to illustrate our result.

Keywords: Permanence, Almost periodic solution, Epidemic model, Delay, Feedback control.

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Authors: Jinsiang Shaw, Ray Pan, Yin-Chieh Chang

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In this paper, an magnetorheological (MR) mount with fuzzy sliding mode controller (FSMC) is studied for vibration suppression when the system is subject to base excitations. In recent years, magnetorheological fluids are becoming a popular material in the field of the semi-active control. However, the dynamic equation of an MR mount is highly nonlinear and it is difficult to identify. FSMC provides a simple method to achieve vibration attenuation of the nonlinear system with uncertain disturbances. This method is capable of handling the chattering problem of sliding mode control effectively and the fuzzy control rules are obtained by using the Lyapunov stability theory. The numerical simulations using one-dimension and two-dimension FSMC show effectiveness of the proposed controller for vibration suppression. Further, the well-known skyhook control scheme and an adaptive sliding mode controller are also included in the simulation for comparison with the proposed FSMC.

Keywords: adaptive sliding mode controller, fuzzy sliding modecontroller, magnetorheological mount, skyhook control.

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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: Jafar Abbaszadeh Chekan, Kaveh Merat, Hassan Zohoor

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In this study the regional stability of a rotor system which is supported on rolling bearings with radial clearance is studied. The rotor is assumed to be rigid. Due to radial clearance of bearings and dynamic configuration of system, each rolling elements of bearings has the possibility to be in contact with both of the races (under compression) or lose its contact. As a result, this change in dynamic of the system makes it to be known as switching system which is a type of Hybrid systems. In this investigation by adopting Multiple Lyapunov Function theorem and using Hamiltonian function as a candidate Lyapunov function, the stability of the system is studied. The purpose of this study is to inspect the regional stability of rotor-roller bearing and rotor-ball bearing systems.

Keywords: Stability analysis, Rotor-rolling bearing systems, Switching systems, Multiple Lyapunov Function Method

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Authors: Ginhsuan Li, Chiuyun Hung, Desheng Chen, Yiwen Wang

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Application-Specific Instruction (ASI ) set Processors (ASIP) have become an important design choice for embedded systems due to runtime flexibility, which cannot be provided by custom ASIC solutions. One major bottleneck in maximizing ASIP performance is the limitation on the data bandwidth between the General Purpose Register File (GPRF) and ASIs. This paper presents the Implicit Registers (IRs) to provide the desirable data bandwidth. An ASI Input/Output model is proposed to formulate the overheads of the additional data transfer between the GPRF and IRs, therefore, an IRs allocation algorithm is used to achieve the better performance by minimizing the number of extra data transfer instructions. The experiment results show an up to 3.33x speedup compared to the results without using IRs.

Keywords: Application-Specific Instruction-set Processors, data bandwidth, configurable processor, implicit register.

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Authors: Ardeshir Karami Mohammadi

Abstract:

A Variable Structure Model Reference Adaptive Controller using state variables is proposed for a class of multi input-multi output systems. Adaptation law is of variable structure type and switching functions is designed based on stability requirements. Global exponential stability is proved based on Lyapunov criterion. Transient behavior is analyzed using sliding mode control and shows perfect model following at a finite time.

Keywords: Adaptive control, Model reference, Variablestructure, MIMO system.

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Authors: Adnene Arbi, Chaouki Aouiti, Abderrahmane Touati

Abstract:

In this paper, we consider the uniform asymptotic stability, global asymptotic stability and global exponential stability of the equilibrium point of discrete Hopfield neural networks with delays. Some new stability criteria for system are derived by using the Lyapunov functional method and the linear matrix inequality approach, for estimating the upper bound of Lyapunov functional derivative.

Keywords: Hopfield neural networks, uniform asymptotic stability, global asymptotic stability, exponential stability.

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Authors: S. H. Lee, M. J. Park, O. M. Kwon

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In this paper, reliable consensus of multi-agent systems with sampled-data is investigated. By using a suitable Lyapunov-Krasovskii functional and some techniques such as Wirtinger Inequality, Schur Complement and Kronecker Product, the results of such system are obtained by solving a set of Linear Matrix Inequalities (LMIs). One numerical example is included to show the effectiveness of the proposed criteria.

Keywords: Multi-agent, Linear Matrix Inequalities (LMIs), Kronecker Product, Sampled-Data, Lyapunov method.

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