共查询到20条相似文献,搜索用时 15 毫秒
1.
《Communications in Nonlinear Science & Numerical Simulation》2008,13(7):1246-1255
This paper presents the control and synchronization of chaos by designing linear feedback controllers. The linear feedback control problem for nonlinear systems has been formulated under optimal control theory viewpoint. Asymptotic stability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution of the Hamilton–Jacobi–Bellman equation thus guaranteeing both stability and optimality. The formulated theorem expresses explicitly the form of minimized functional and gives the sufficient conditions that allow using the linear feedback control for nonlinear system. The numerical simulations were provided in order to show the effectiveness of this method for the control of the chaotic Rössler system and synchronization of the hyperchaotic Rössler system. 相似文献
2.
D. H. Chyung 《Journal of Optimization Theory and Applications》1973,12(3):242-247
The minimum-time rendezvous problem of three linear controlled systems is studied, and the existence and necessary conditions for a solution are derived.This research was supported by NSF Grant No. GK-31628. 相似文献
3.
Normal correlation coefficient of non-normal variables using piece-wise linear approximation 总被引:1,自引:0,他引:1
The correlation coefficient of non-normal variables is expressed as a function of the correlation coefficient of normal variables
using piece-wise linear approximation of each univariate transform of normal to anything, and the second order moments of
a multiply truncated bivariate normal distribution. For the inverse problem, an algorithm iterates this analytic function
in order to assign a normal correlation coefficient to two non-normal variables. The algorithm is applied for the generation
of randomized bivariate samples with given correlation coefficient and marginal distributions and used in a randomization
test for bivariate nonlinearity. The test correctly does not reject the null hypothesis of linear correlation if the nonlinearity
is plausible and due to the sample transform alone. 相似文献
4.
5.
Fatima El Guezar Hassane Bouzahir Danièle Fournier-Prunaret 《Nonlinear Analysis: Hybrid Systems》2011,5(4):626-638
Many switched circuits are made of linear components switched by a simple logic unit. In this paper, we use a generic planar Piece-wise Affine Hybrid System (PWAHS) to model this kind of circuit. Usually, simulations are run by analytical methods (adapted to a specific simple model) or by numerical simulations that can miss some events’ occurrences. We propose a generic planar method to simulate PWAHSs with periodic and state dependent events. Using analytical expressions, our approach can reach arbitrary accuracy in event detections without any loss. As a result, we have implemented our method in Scilab and Matlab toolboxes. 相似文献
6.
In this paper stabilizing unstable periodic orbits (UPO) in a chaotic fractional order system is studied. Firstly, a technique for finding unstable periodic orbits in chaotic fractional order systems is stated. Then by applying this technique to the fractional van der Pol and fractional Duffing systems as two demonstrative examples, their unstable periodic orbits are found. After that, a method is presented for stabilization of the discovered UPOs based on the theories of stability of linear integer order and fractional order systems. Finally, based on the proposed idea a linear feedback controller is applied to the systems and simulations are done for demonstration of controller performance. 相似文献
7.
V. G. Zadorozhniy 《Computational Mathematics and Mathematical Physics》2013,53(4):486-502
For three-dimensional vortex motion, a linear mathematical model with random coefficients is considered, and formulas for the first two moment functions of solutions are derived. The conditions are found under which a linear chaotic resonance occurs; i.e., the mean angular velocity of the motion increases. The results show that the energy of the vortex increases because of the chaotic motions present in the flow. 相似文献
8.
In this paper, we study the existence, continuation and bifurcation from infinity of2π-periodic solutions of autonomous Newtonian systems. We underline that the resonant case is considered. To prove the results, we apply the degree for S1-equivariant gradient maps defined by Rybicki (1994) in [15] and the angle condition introduced by Bartsch and Li (1997) in [16]. 相似文献
9.
Some impulsive synchronization criterions for coupled chaotic systems via unidirectional linear error feedback approach 总被引:5,自引:0,他引:5
Based on stability theory of impulsive differential equation and new comparison theory of impulsive differential system, we study the chaos impulsive synchronization of two coupled chaotic systems using the unidirectional linear error feedback scheme. Some generic conditions of chaos impulsive synchronization of two coupled chaotic systems are derived, and to apply the conditions to typical chaotic system––the original Chua’s circuit. The example illustrates the effectiveness of the proposed result. 相似文献
10.
Modelling the nonlinear processes of the plasmospara viticola infection on wine yards is proposed for forecasting and then for control purposes, through piece-wise affine identification of hybrid dynamical systems form data. 相似文献
11.
《Chaos, solitons, and fractals》2001,12(2):205-218
We review our recent efforts to understand why chaotic dynamics is rarely observed in natural populations. The study of two-model ecosystems considered in this paper suggests that chaos exists in narrow parameter ranges. This dynamical behaviour is caused by the crisis-induced sudden death of chaotic attractors. The computed bifurcation diagrams and basin boundary calculations reinforce our earlier conclusion [Chaos, Solitons & Fractals 8 (12) (1997) 1933; Int J Bifurc Chaos 8 (6) (1998) 1325] that the reason why chaos is rarely observed in natural populations is hidden within the mathematical structure of the ecological interactions and not with the problem associated with the data (insufficient length, precision, noise, etc.) and its analysis. We also argue that crisis-limited chaotic dynamics can be commonly found in model terrestrial ecosystems. 相似文献
12.
In this paper, a new projective lag synchronization is proposed, where a driven chaotic system synchronizes the past state of the driver up to a scaling factor α. An active control method is employed to design a controller to achieve the global synchronization of two identical chaotic systems. Based on Lyapunov stability theorem, a sufficient condition is then given for the asymptotical stability of the null solution of an error dynamics. The effectiveness of the proposed schemes is verified via numerical simulations. 相似文献
13.
By a topological dynamical system, we mean a pair (X,f), where X is a compactum and f is a continuous self-map on X. A system is said to be null if its topological sequence entropies are zero along all strictly increasing sequences of natural numbers. We show that there exists a null system which is distributionally chaotic. This system admits open distributionally scrambled sets, and its collection of all maximal distributionally scrambled sets has the same cardinality as the collection of all subsets of the phase space. Finally such system can even exist on continua. 相似文献
14.
In this paper, we consider characteristic polynomials of n-dimensional systems that determine a segment of polynomials. One parameter is used to characterize this segment of polynomials in order to determine the maximal interval of dissipativity and unstability. Then we apply this result to the generation of a family of attractors based on a class of unstable dissipative systems (UDS) of type affine linear systems. This class of systems is comprised of switched linear systems yielding strange attractors. A family of these chaotic switched systems is determined by the maximal interval of perturbation of the matrix that governs the dynamics for still having scroll attractors. 相似文献
15.
This paper investigates global complete synchronization of two identical power systems and global robust synchronization of two power systems with parameter mismatch and external disturbance, both under the master–slave linear state-error feedback control. Some criteria for achieving the synchronization via a single-variable linear coupling are derived and formulated in simple algebraic inequalities. These algebraic criteria are further optimized so as to improve their performances. The effectiveness of the new algebraic criteria is illustrated by the numerical examples. 相似文献
16.
Lixiang Li Yixian Yang Haipeng Peng Xiangdong Wang 《Chaos, solitons, and fractals》2006,28(5):1204-1211
Through the construction of a suitable fitness function, the problem of parameters estimation of the chaotic system is converted to that of parameters optimization. In this paper, an optimization method, called CAS (chaotic ant swarm), is developed to solve the problem of searching for the optimal. Finally numerical simulations are provided to show the effectiveness and feasibility of the developed method. 相似文献
17.
《Chaos, solitons, and fractals》2006,27(3):822-835
This paper deals with the problem of control and synchronization of coupled second-order oscillators showing a chaotic behavior. A classical feedback controller is first used to stabilize the system at its equilibrium. An adaptive observer is then designed to synchronize the states of the master and slave oscillators using a single scalar signal corresponding to an observable state variable of the driving oscillator. An interesting feature of the proposed approach is that it can be used for chaos control as well as synchronization purposes. Numerical simulations results confirming the analytical predictions are shown and pspice simulations are also performed to confirm the efficiency of the proposed control scheme. 相似文献
18.
《Chaos, solitons, and fractals》2006,27(2):569-573
A diode resonator chaotic circuit is presented. Multisim is used to simulate the circuit and show the presence of chaos. Time series analysis performed by the method proposed by Grasberger and Procaccia. The correlation and minimum embedding dimension ν and mmin, respectively, were calculated. Also the corresponding Kolmogorov entropy was calculated. 相似文献
19.
《Chaos, solitons, and fractals》2007,31(3):712-717
In this paper, the problem of controlling chaotic systems is studied. A control law is introduced for a chaotic system to follow a desired reference system. The control strategy is developed within the general framework of the nonlinear model-reference control systems. Lyapunov stability is used to ensure the global stability of the error dynamics represents the difference between the desired and chaotic systems. 相似文献
20.
Jianbing Hu Yan Han Lingdong Zhao 《Communications in Nonlinear Science & Numerical Simulation》2010,15(1):115-123
This work presents a direct approach to design stabilizing controller based on a special matrix structure to synchronize chaotic systems and extends the approach to synchronize fractional chaotic systems. With this method, chaos synchronization is implemented in Lorenz chaotic systems with known parameters and the same to Lorenz chaotic systems with unknown parameters. Especially, fractional Lorenz chaotic system with unknown parameters is synchronized by fractional Chen chaotic system too. Numerical simulations confirm the effectiveness of the method proposed. 相似文献