共查询到20条相似文献,搜索用时 46 毫秒
1.
《Chaos, solitons, and fractals》2006,27(2):537-548
This work presents chaos control of chaotic dynamical systems by using backstepping design method. This technique is applied to achieve chaos control for each of the dynamical systems Lorenz, Chen and Lü systems. Based on Lyapunov stability theory, control laws are derived. We used the same technique to enable stabilization of chaotic motion to a steady state as well as tracking of any desired trajectory to be achieved in a systematic way. Numerical simulations are shown to verify the results. 相似文献
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In this paper, we investigate the dynamic properties of an overlapping generations’ model with capital accumulation and publicly funded inventions under three different expectations: perfect foresight, myopic expectations and adaptive expectations. We show that considering productive public expenditures in the model will increase the dimension of the dynamical system. To study the dynamic behavior of a high-dimensional dynamical system, we focus on the case when the elasticity of publicly funded invention to output is small and approximate the system by using a one-dimensional dynamical system. This approximation method provides an efficient way to rigorously prove the existence of chaos in high-dimensional dynamical systems. We show that when agents are perfectly foresighted, there exists a unique, nontrivial steady state which is a global attractor. Cycles or even chaos may occur under myopic and adaptive expectations when the inter-temporal elasticity of substitution of consumption is large enough. Furthermore, we find that the impact of fiscal policy is sensible to the expectation formation. 相似文献
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In this paper, a duopoly Stackelberg model of competition on output is formulated. The firms announce plan products sequentially in planning phase and act simultaneously in production phase. For the duopoly Stackelberg model, a nonlinear dynamical system which describes the time evolution with different strategies is analyzed. We present results on existence, stability and local bifurcations of the equilibrium points. Numerical simulations demonstrate that the system with varying model parameters may drive to chaos and the loss of stability may be caused by period doubling bifurcations. It is also shown that the state variables feedback and parameter variation method can be used to keep the system from instability and chaos. 相似文献
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In this paper, an attempt is made to propose a general definition of synchronization for finite dimensional dynamical systems. The synchronization is defined here for two coupled dynamical systems with control inputs. Output functions of such systems are introduced to describe the systems’ properties on which the synchronization problem focus. Exact synchronization, asymptotic synchronization, and approximate synchronization are, respectively, defined by comparing the output functions in the corresponding ways. The definition here can also include chaos control and anti-control. The definition here covers various synchronization investigated in the references. 相似文献
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M. Sadeghpour M. Khodabakhsh H. Salarieh 《Communications in Nonlinear Science & Numerical Simulation》2012,17(12):4731-4739
A method for controlling chaos when the mathematical model of the system is unknown is presented in this paper. The controller is designed by the pole placement algorithm which provides a linear feedback control method. For calculating the feedback gain, a neural network is used for identification of the system from which the Jacobian of the system in its fixed point can be approximated. The weights of the neural network are adjusted online by the gradient descent algorithm in which the difference between the system output and the network output is considered as the error to be decreased. The method is applied on both discrete-time and continuous-time systems. For continuous-time systems, equivalent discrete-time systems are constructed by using the Poincare map concept. Two discrete-time systems and one continuous-time system are tested as examples for simulation and the results show good functionality of the proposed method. It can be concluded that the chaos in systems with unknown dynamics may be eliminated by the presented intelligent control system based on pole placement and neural network. 相似文献
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P. Palaniyandi 《Chaos, solitons, and fractals》2009,39(2):625-658
A simple method is introduced for modelling chaotic dynamical systems from the time series, based on the concept of controlling of chaos by constant bias. In this method, a modified system is constructed by including some constants (controlling constants) into the given (original) system. The system parameters and the controlling constants are determined by solving a set of implicit nonlinear simultaneous algebraic equations which is obtained from the relation connecting original and modified systems. The method is also extended to find the form of the evolution equation of the system itself. The important advantage of the method is that it needs only a minimal number of time series data and is applicable to dynamical systems of any dimension. It also works extremely well even in the presence of noise in the time series. The method is illustrated in some specific systems of both discrete and continuous cases. 相似文献
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Jian-guo Du Tingwen Huang Zhaohan Sheng 《Nonlinear Analysis: Real World Applications》2009,10(4):2493-2501
In some economic chaotic systems, players are concerned about whether their performance is improved besides taking some methods to control chaos. In the face of chaos occurring in competition, whether one player takes controlling measures or not affects not only their own earning but also other opponents’ income. An output duopoly competing evolution model with bounded rationality is introduced in this paper. Using modern game theory, decision-making analyses about chaos control of the model are taken by taking aggregate profits as players’ payoff. It is found that the speed of players’ response to the market and whether the decisive parameters are in the stable region of the Nash equilibrium or not have a distinct influence on the results of the game. The impact of cost function’ type on results of the game is also found. The mechanism of influences is discovered by using numerical simulation. 相似文献
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In this survey, we describe the contemporary state of the theory of chaotic dynamical systems on a fairly rigorous level.
We present results related to the development of chaos in such systems and consider their basic properties. We also analyze
current methods for the stabilization of chaotic behavior and controlling the dynamics of deterministic systems. 相似文献
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We develop a model of asset pricing and hedging for interconnected financial markets with frictions – transaction costs and portfolio constraints. The model is based on a control theory for random fields on a directed graph. Market dynamics are described by using von Neumann–Gale dynamical systems first considered in connection with the modelling of economic growth [13,24]. The main results are hedging criteria stated in terms of risk-acceptable portfolios and consistent price systems, extending the classical superreplication criteria formulated in terms of equivalent martingale measures. 相似文献
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Hoda Sadeghian Kaveh Merat Hassan Salarieh Aria Alasty 《Applied Mathematical Modelling》2011,35(3):1016-1023
This paper presents a fuzzy algorithm for controlling chaos in nonlinear systems via minimum entropy approach. The proposed fuzzy logic algorithm is used to minimize the Shannon entropy of a chaotic dynamics. The fuzzy laws are determined in such a way that the entropy function descends until the chaotic trajectory of the system is replaced by a regular one. The Logistic and the Henon maps as two discrete chaotic systems, and the Duffing equation as a continuous one are used to validate the proposed scheme and show the effectiveness of the control method in chaotic dynamical systems. 相似文献
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In this work we propose an exact semidefinite relaxation for non-linear, non-convex dynamical programs under discrete constraints
in the state variables and the control variables. We outline some theoretical features of the method and workout the solutions
of a benchmark problem in cybernetics and the classical inventory problem under discrete constraints. 相似文献
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Aneel Tanwani 《PAMM》2015,15(1):31-34
We consider the problem of designing state feedback control laws for output regulation in a class of dynamical systems where state trajectories are constrained to evolve within time-varying, closed, and convex sets. The first main result states sufficient conditions for existence and uniqueness of solutions in such systems. We then design a static state feedback control law using the internal model principle, which results in a well-posed closed-loop system and solves the regulation problem. As an application, we demonstrate how control input resulting from the solution of a variational inequality results in regulating the output of the system while maintaining polyhedral state constraints. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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In this paper, an LMI-based approach is proposed for the design of static output feedback for multi-nonlinear Lur’e-Postnikov systems. The resulting control laws ensure absolute stability and, at the same time, maximize the size of the nonlinear sectors. The proposed method is computationally efficient, and can accommodate feedback laws with arbitrary information structure constraints. The effectiveness of this approach is demonstrated on a large-scale example with 100 state variables. 相似文献
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S. Benenti 《Regular and Chaotic Dynamics》2008,13(4):283-315
The basic notions of the dynamics of nonholonomic systems are revisited in order to give a general and simple method for writing
the dynamical equations for linear as well as non-linear kinematical constraints. The method is based on the representation
of the constraints by parametric equations, which are interpreted as dynamical equations, and leads to first-order differential
equations in normal form, involving the Lagrangian coordinates and auxiliary variables (the use of Lagrangian multipliers
is avoided). Various examples are illustrated.
相似文献
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S. K. Korovin I. S. Medvedev V. V. Fomichev 《Computational Mathematics and Modeling》2011,22(2):145-171
The article considers the construction of a functional observer with a given rate of convergence for the most general case:
a vector state functional of a linear dynamical system with a vector output. An upper bound is derived on the minimum dimension
of such an observer, which holds for almost all functionals. An algorithm is proposed for constructing an observer that achieves
this bound. The algorithm can be used to construct a functional observer for almost all specified spectra (i.e., with the
exception of a set of measure zero). The scalar observer method previously developed by the authors and proposed in the present
article is based on canonical form Luenberger observability for systems with vector output. 相似文献
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In this paper we investigate Martelli’s chaos of inverse limit dynamical systems and hyperspace dynamical systems which are both induced from dynamical systems on a compact metric space. We give the implication of Martelli’s chaos among those systems. More precisely, we show that inverse limit dynamical system is Martelli’s chaos if and only if so is original system, and we prove that hyperspace dynamical system is Martelli’s chaos implies original system is Martelli’s chaos if the orbit of every single point set of original system is unstable in hyperspace dynamical system. 相似文献
18.
J. C. Geromel L. F. B. Baptistella 《Journal of Optimization Theory and Applications》1981,35(2):231-249
In this paper, we propose a feasible-direction method for large-scale nonconvex programs, where the gradient projection on a linear subspace defined by the active constraints of the original problem is determined by dual decomposition. Results are extended for dynamical problems which include distributed delays and constraints both in state and control variables. The approach is compared with other feasible-direction approaches, and the method is applied to a power generation problem. Some computational results are included.This work was supported by the Conselho Nacional de Desenvolvimento Cientifico e Tecnologico, Brasilia, Brasil, and by the Fundaçao de Amparo a Pesquisa do Estado de Sao Paulo, Sao Paulo, Brazil.On leave from UNICAMP, Campinas, Brazil. 相似文献
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In this paper we present an extension of Moreau’s sweeping process for higher order systems. The dynamical framework is carefully
introduced, qualitative, dissipativity, stability, existence, regularity and uniqueness results are given. The time-discretization
of these nonsmooth systems with a time-stepping algorithm is also presented. This differential inclusion can be seen as a
mathematical formulation of complementarity dynamical systems with arbitrary dimension and arbitrary relative degree between
the complementary-slackness variables. Applications of such high-order sweeping processes can be found in dynamic optimization
under state constraints and electrical circuits with ideal diodes. 相似文献