Search results for: Lyapunov Stability.
1241 A New Stability Analysis and Stabilization of Discrete-Time Switched Linear Systems Using Vector Norms Approach
Authors: Marwen Kermani, Anis Sakly, Faouzi M'sahli
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In this paper, we aim to investigate a new stability analysis for discrete-time switched linear systems based on the comparison, the overvaluing principle, the application of Borne-Gentina criterion and the Kotelyanski conditions. This stability conditions issued from vector norms correspond to a vector Lyapunov function. In fact, the switched system to be controlled will be represented in the Companion form. A comparison system relative to a regular vector norm is used in order to get the simple arrow form of the state matrix that yields to a suitable use of Borne-Gentina criterion for the establishment of sufficient conditions for global asymptotic stability. This proposed approach could be a constructive solution to the state and static output feedback stabilization problems.
Keywords: Discrete-time switched linear systems, Global asymptotic stability, Vector norms, Borne-Gentina criterion, Arrow form state matrix, Arbitrary switching, State feedback controller, Static output feedback controller.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16271240 Reachable Set Bounding Estimation for Distributed Delay Systems with Disturbances
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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18471239 Anti-periodic Solutions for Cohen-Grossberg Shunting Inhibitory Neural Networks with Delays
Authors: Yongkun Li, Tianwei Zhang, Shufa Bai
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By using the method of coincidence degree theory and constructing suitable Lyapunov functional, several sufficient conditions are established for the existence and global exponential stability of anti-periodic solutions for Cohen-Grossberg shunting inhibitory neural networks with delays. An example is given to illustrate our feasible results.
Keywords: Anti-periodic solution, coincidence degree, global exponential stability, Cohen-Grossberg shunting inhibitory cellular neural networks.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14941238 Periodic Solutions of Recurrent Neural Networks with Distributed Delays and Impulses on Time Scales
Authors: Yaping Ren, Yongkun Li
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In this paper, by using the continuation theorem of coincidence degree theory, M-matrix theory and constructing some suitable Lyapunov functions, some sufficient conditions are obtained for the existence and global exponential stability of periodic solutions of recurrent neural networks with distributed delays and impulses on time scales. Without assuming the boundedness of the activation functions gj, hj , these results are less restrictive than those given in the earlier references.
Keywords: Recurrent neural networks, global exponential stability, periodic solutions, distributed delays, impulses, time scales.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15791237 Stability Analysis in a Fractional Order Delayed Predator-Prey Model
Authors: Changjin Xu, Peiluan Li
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In this paper, we study the stability of a fractional order delayed predator-prey model. By using the Laplace transform, we introduce a characteristic equation for the above system. It is shown that if all roots of the characteristic equation have negative parts, then the equilibrium of the above fractional order predator-prey system is Lyapunov globally asymptotical stable. An example is given to show the effectiveness of the approach presented in this paper.
Keywords: Fractional predator-prey model, laplace transform, characteristic equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 24901236 Preliminary Chaos Analyses of Explosion Earthquakes Followed by Harmonic Tremors at Semeru Volcano, East Java, Indonesia
Authors: Sukir Maryanto, Didik R. Santosa, Iyan Mulyana, Muhammad Hendrasto
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15671235 Synchronization Between Two Chaotic Systems: Numerical and Circuit Simulation
Authors: J. H. Park, T. H. Lee, S. M. Lee, H. Y. Jung
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In this paper, a generalized synchronization scheme, which is called function synchronization, for chaotic systems is studied. Based on Lyapunov method and active control method, we design the synchronization controller for the system such that the error dynamics between master and slave chaotic systems is asymptotically stable. For verification of our theory, computer and circuit simulations for a specific chaotic system is conducted.
Keywords: Chaotic systems, synchronization, Lyapunov method, simulation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16711234 Stability Analysis of Linear Fractional Order Neutral System with Multiple Delays by Algebraic Approach
Authors: Lianglin Xiong, Yun Zhao, Tao Jiang
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In this paper, we study the stability of n-dimensional linear fractional neutral differential equation with time delays. By using the Laplace transform, we introduce a characteristic equation for the above system with multiple time delays. We discover that if all roots of the characteristic equation have negative parts, then the equilibrium of the above linear system with fractional order is Lyapunov globally asymptotical stable if the equilibrium exist that is almost the same as that of classical differential equations. An example is provided to show the effectiveness of the approach presented in this paper.
Keywords: Fractional neutral differential equation, Laplace transform, characteristic equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 22891233 Modeling and Stability Analysis of Delayed Game Network
Authors: Zixin Liu, Jian Yu, Daoyun Xu
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This paper aims to establish a delayed dynamical relationship between payoffs of players in a zero-sum game. By introducing Markovian chain and time delay in the network model, a delayed game network model with sector bounds and slope bounds restriction nonlinear function is first proposed. As a result, a direct dynamical relationship between payoffs of players in a zero-sum game can be illustrated through a delayed singular system. Combined with Finsler-s Lemma and Lyapunov stable theory, a sufficient condition guaranteeing the unique existence and stability of zero-sum game-s Nash equilibrium is derived. One numerical example is presented to illustrate the validity of the main result.
Keywords: Game networks, zero-sum game, delayed singular system, nonlinear perturbation, time delay.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14331232 Formation Control of Mobile Robots
Authors: Krishna S. Raghuwaiya, Shonal Singh, Jito Vanualailai
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In this paper, we study the formation control problem for car-like mobile robots. A team of nonholonomic mobile robots navigate in a terrain with obstacles, while maintaining a desired formation, using a leader-following strategy. A set of artificial potential field functions is proposed using the direct Lyapunov method for the avoidance of obstacles and attraction to their designated targets. The effectiveness of the proposed control laws to verify the feasibility of the model is demonstrated through computer simulationsKeywords: Control, Formation, Lyapunov, Nonholonomic
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20651231 Instability of a Nonlinear Differential Equation of Fifth Order with Variable Delay
Authors: Cemil Tunc
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14451230 Nonlinear Integral-Type Sliding Surface for Synchronization of Chaotic Systems with Unknown Parameters
Authors: Hongji Tang, Yanbo Gao, Yue Yu
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20171229 Trajectory Control of a Robotic Manipulator Utilizing an Adaptive Fuzzy Sliding Mode
Authors: T. C. Kuo
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In this paper, a novel adaptive fuzzy sliding mode control method is proposed for the robust tracking control of robotic manipulators. The proposed controller possesses the advantages of adaptive control, fuzzy control, and sliding mode control. First, system stability and robustness are guaranteed based on the sliding mode control. Further, fuzzy rules are developed incorporating with adaptation law to alleviate the input chattering effectively. Stability of the control system is proven by using the Lyapunov method. An application to a three-degree-of-freedom robotic manipulator is carried out. Accurate trajectory tracking as well as robustness is achieved. Input chattering is greatly eliminated.Keywords: Fuzzy control, sliding mode control, roboticmanipulator, adaptive control.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19351228 Posture Stabilization of Kinematic Model of Differential Drive Robots via Lyapunov-Based Control Design
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In this paper, the problem of posture stabilization for a kinematic model of differential drive robots is studied. A more complex model of the kinematics of differential drive robots is used for the design of stabilizing control. This model is formulated in terms of the physical parameters of the system such as the radius of the wheels, and velocity of the wheels are the control inputs of it. In this paper, the framework of Lyapunov-based control design has been used to solve posture stabilization problem for the comprehensive model of differential drive robots. The results of the simulations show that the devised controller successfully solves the posture regulation problem. Finally, robustness and performance of the controller have been studied under system parameter uncertainty.Keywords: Differential drive robots, nonlinear control, Lyapunov-based control design, posture regulation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17871227 Multi-Agent Coverage Control with Bounded Gain Forgetting Composite Adaptive Controller
Authors: Mert Turanli, Hakan Temeltas
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In this paper, we present an adaptive controller for decentralized coordination problem of multiple non-holonomic agents. The performance of the presented Multi-Agent Bounded Gain Forgetting (BGF) Composite Adaptive controller is compared against the tracking error criterion with a Feedback Linearization controller. By using the method, the sensor nodes move and reconfigure themselves in a coordinated way in response to a sensed environment. The multi-agent coordination is achieved through Centroidal Voronoi Tessellations and Coverage Control. Also, a consensus protocol is used for synchronization of the parameter vectors. The two controllers are given with their Lyapunov stability analysis and their stability is verified with simulation results. The simulations are carried out in MATLAB and ROS environments. Better performance is obtained with BGF Adaptive Controller.
Keywords: Adaptive control, Centroidal Voronoi Tessellations, composite adaptation, coordination.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 10291226 Trajectory Tracking Using Artificial Potential Fields
Authors: Krishna S. Raghuwaiya, Shonal Singh, Jito Vanualailai
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In this paper, the trajectory tracking problem for carlike mobile robots have been studied. The system comprises of a leader and a follower robot. The purpose is to control the follower so that the leader-s trajectory is tracked with arbitrary desired clearance to avoid inter-robot collision while navigating in a terrain with obstacles. A set of artificial potential field functions is proposed using the Direct Method of Lyapunov for the avoidance of obstacles and attraction to their designated targets. Simulation results prove the efficiency of our control technique.
Keywords: Control, Trajectory Tracking, Lyapunov.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 22501225 Stability Analysis of a Tricore
Authors: C. M. De Marco Muscat-Fenech, A.M. Grech La Rosa
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The application of stability theory has led to detailed studies of different types of vessels; however, the shortage of information relating to multihull vessels demanded further investigation. This study shows that the position of the hulls has a very influential effect on both the transverse and longitudinal stability of the tricore. HSC stability code is applied for the optimisation of the hull configurations. Such optimization criteria would undoubtedly aid the performance of the vessel for both commercial or leisure purposes
Keywords: Stability, Multihull, Tricore
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 28941224 Reliable Consensus Problem for Multi-Agent Systems with Sampled-Data
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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17341223 Leader-following Consensus Criterion for Multi-agent Systems with Probabilistic Self-delay
Authors: M.J. Park, K.H. Kim, O.M. Kwon
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This paper proposes a delay-dependent leader-following consensus condition of multi-agent systems with both communication delay and probabilistic self-delay. The proposed methods employ a suitable piecewise Lyapunov-Krasovskii functional and the average dwell time approach. New consensus criterion for the systems are established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. Numerical example showed that the proposed method is effective.
Keywords: Multi-agent systems, probabilistic self-delay, consensus, Lyapunov method, LMI.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17401222 Robust Control for Discrete-Time Sector Bounded Systems with Time-Varying Delay
Authors: Ju H. Park, S.M. Lee
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In this paper, we propose a robust controller design method for discrete-time systems with sector-bounded nonlinearities and time-varying delay. Based on the Lyapunov theory, delaydependent stabilization criteria are obtained in terms of linear matrix inequalities (LMIs) by constructing the new Lyapunov-Krasovskii functional and using some inequalities. A robust state feedback controller is designed by LMI framework and a reciprocally convex combination technique. The effectiveness of the proposed method is verified throughout a numerical example.
Keywords: Lur'e systems, Time-delay, Stabilization, LMIs.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16791221 Sensorless Backstepping Control Using an Adaptive Luenberger Observer with Three Levels NPC Inverter
Authors: A. Bennassar, A. Abbou, M. Akherraz, M. Barara
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In this paper, we propose a sensorless backstepping control of induction motor (IM) associated with three levels neutral clamped (NPC) inverter. First, the backstepping approach is designed to steer the flux and speed variables to theirs references and to compensate the uncertainties. A Lyapunov theory is used and it demonstrates that the dynamic trajectories tracking are asymptotically stable. Second, we estimate the rotor flux and speed by using the adaptive Luenberger observer (ALO). Simulation results are provided to illustrate the performance of the proposed approach in high and low speeds and load torque disturbance.
Keywords: Sensorless backstepping, IM, Three levels NPC inverter, Lyapunov theory, ALO.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21891220 Exponential Passivity Criteria for BAM Neural Networks with Time-Varying Delays
Authors: Qingqing Wang, Baocheng Chen, Shouming Zhong
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In this paper,the exponential passivity criteria for BAM neural networks with time-varying delays is studied.By constructing new Lyapunov-Krasovskii functional and dividing the delay interval into multiple segments,a novel sufficient condition is established to guarantee the exponential stability of the considered system.Finally,a numerical example is provided to illustrate the usefulness of the proposed main results
Keywords: BAM neural networks, Exponential passivity, LMI approach, Time-varying delays.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18971219 Motion Planning and Control of a Swarm of Boids in a 3-Dimensional Space
Authors: Bibhya Sharma, Jito Vanualailai, Jai Raj
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19021218 Dynamics and Control of a Chaotic Electromagnetic System
Authors: Shun-Chang Chang
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In this paper, different nonlinear dynamics analysis techniques are employed to unveil the rich nonlinear phenomena of the electromagnetic system. In particular, bifurcation diagrams, time responses, phase portraits, Poincare maps, power spectrum analysis, and the construction of basins of attraction are all powerful and effective tools for nonlinear dynamics problems. We also employ the method of Lyapunov exponents to show the occurrence of chaotic motion and to verify those numerical simulation results. Finally, two cases of a chaotic electromagnetic system being effectively controlled by a reference signal or being synchronized to another nonlinear electromagnetic system are presented.
Keywords: bifurcation, Poincare map, Lyapunov exponent, chaotic motion.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15891217 Implementation of an Associative Memory Using a Restricted Hopfield Network
Authors: Tet H. Yeap
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An analog restricted Hopfield Network is presented in this paper. It consists of two layers of nodes, visible and hidden nodes, connected by directional weighted paths forming a bipartite graph with no intralayer connection. An energy or Lyapunov function was derived to show that the proposed network will converge to stable states. By introducing hidden nodes, the proposed network can be trained to store patterns and has increased memory capacity. Training to be an associative memory, simulation results show that the associative memory performs better than a classical Hopfield network by being able to perform better memory recall when the input is noisy.Keywords: Associative memory, Hopfield network, Lyapunov function, Restricted Hopfield network.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4741216 Performance of the Strong Stability Method in the Univariate Classical Risk Model
Authors: Safia Hocine, Zina Benouaret, Djamil A¨ıssani
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In this paper, we study the performance of the strong stability method of the univariate classical risk model. We interest to the stability bounds established using two approaches. The first based on the strong stability method developed for a general Markov chains. The second approach based on the regenerative processes theory . By adopting an algorithmic procedure, we study the performance of the stability method in the case of exponential distribution claim amounts. After presenting numerically and graphically the stability bounds, an interpretation and comparison of the results have been done.Keywords: Markov Chain, regenerative processes, risk models, ruin probability, strong stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 11311215 Static Analysis and Pseudostatic Slope Stability
Authors: Meftah Ali
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This article aims to analyze the static stability and pseudostatic slope by using different methods such as: Bishop method, Junbu, Ordinary, Morgenstern-price and GLE. The two dimensional modeling of slope stability under various loading as: the earthquake effect, the water level and road mobile charges. The results show that the slope is stable in the static case without water, but in other cases, the slope lost its stability and give unstable. The calculation of safety factor is to evaluate the stability of the slope using the limit equilibrium method despite the difference between the results obtained by these methods that do not rely on the same assumptions. In the end, the results of this study illuminate well the influence of the action of water, moving loads and the earthquake on the stability of the slope.Keywords: Slope stability, pseudo static, safety factor, limit equilibrium.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 33441214 Effects of Tap Changing Transformer and Shunt Capacitor on Voltage Stability Enhancement of Transmission Networks
Authors: Pyone Lai Swe, Wanna Swe, Kyaw Myo Lin
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Voltage stability has become an important issue to many power systems around the world due to the weak systems and long line on power system networks. In this paper, MATLAB load flow program is applied to obtain the weak points in the system combined with finding the voltage stability limit. The maximum permissible loading of a system, within the voltage stability limit, is usually determined. The methods for varying tap ratio (using tap changing transformer) and applying different values of shunt capacitor injection to improve the voltage stability within the limit are also provided.
Keywords: Load flow, Voltage stability, Tap changingtransformer, Shunt capacitor injection, Voltage stability limit
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 59641213 Influence of Adaptation Gain and Reference Model Parameters on System Performance for Model Reference Adaptive Control
Authors: Jan Erik Stellet
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This article presents a detailed analysis and comparative performance evaluation of model reference adaptive control systems. In contrast to classical control theory, adaptive control methods allow to deal with time-variant processes. Inspired by the works [1] and [2], two methods based on the MIT rule and Lyapunov rule are applied to a linear first order system. The system is simulated and it is investigated how changes to the adaptation gain affect the system performance. Furthermore, variations in the reference model parameters, that is changing the desired closed-loop behaviour are examinded.Keywords: Adaptive control systems, Adaptation gain, MIT rule, Lyapunov rule, Model reference adaptive control.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 22141212 A C1-Conforming Finite Element Method for Nonlinear Fourth-Order Hyperbolic Equation
Authors: Yang Liu, Hong Li, Siriguleng He, Wei Gao, Zhichao Fang
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In this paper, the C1-conforming finite element method is analyzed for a class of nonlinear fourth-order hyperbolic partial differential equation. Some a priori bounds are derived using Lyapunov functional, and existence, uniqueness and regularity for the weak solutions are proved. Optimal error estimates are derived for both semidiscrete and fully discrete schemes.
Keywords: Nonlinear fourth-order hyperbolic equation, Lyapunov functional, existence, uniqueness and regularity, conforming finite element method, optimal error estimates.
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