The discovery of chaos in the sixties of last century was a breakthrough in concept,revealing the truth that some disorder behavior,called chaos,could happen even in a deterministic nonlinear system under barely deter...The discovery of chaos in the sixties of last century was a breakthrough in concept,revealing the truth that some disorder behavior,called chaos,could happen even in a deterministic nonlinear system under barely deterministic disturbance.After a series of serious studies,people begin to acknowledge that chaos is a specific type of steady state motion other than the conventional periodic and quasi-periodic ones,featuring a sensitive dependence on initial conditions,resulting from the intrinsic randomness of a nonlinear system itself.In fact,chaos is a collective phenomenon consisting of massive individual chaotic responses,corresponding to different initial conditions in phase space.Any two adjacent individual chaotic responses repel each other,thus causing not only the sensitive dependence on initial conditions but also the existence of at least one positive top Lyapunov exponent(TLE) for chaos.Meanwhile,all the sample responses share one common invariant set on the Poincaré map,called chaotic attractor,which every sample response visits from time to time ergodically.So far,the existence of at least one positive TLE is a commonly acknowledged remarkable feature of chaos.We know that there are various forms of uncertainties in the real world.In theoretical studies,people often use stochastic models to describe these uncertainties,such as random variables or random processes.Systems with random variables as their parameters or with random processes as their excitations are often called stochastic systems.No doubt,chaotic phenomena also exist in stochastic systems,which we call stochastic chaos to distinguish it from deterministic chaos in the deterministic system.Stochastic chaos reflects not only the intrinsic randomness of the nonlinear system but also the external random effects of the random parameter or the random excitation.Hence,stochastic chaos is also a collective massive phenomenon,corresponding not only to different initial conditions but also to different samples of the random parameter or the random excitation.Thus,the unique common feature of deterministic chaos and stochastic chaos is that they all have at least one positive top Lyapunov exponent for their chaotic motion.For analysis of random phenomena,one used to look for the PDFs(Probability Density Functions) of the ensemble random responses.However,it is a pity that PDF information is not favorable to studying repellency of the neighboring chaotic responses nor to calculating the related TLE,so we would rather study stochastic chaos through its sample responses.Moreover,since any sample of stochastic chaos is a deterministic one,we need not supplement any additional definition on stochastic chaos,just mentioning that every sample of stochastic chaos should be deterministic chaos.We are mainly concerned with the following two basic kinds of nonlinear stochastic systems,i.e.one with random variables as its parameters and one with ergodical random processes as its excitations.To solve the stochastic chaos problems of these two kinds of systems,we first transform the original stochastic system into their equivalent deterministic ones.Namely,we can transform the former stochastic system into an equivalent deterministic system in the sense of mean square approximation with respect to the random parameter space by the orthogonal polynomial approximation,and transform the latter one simply through replacing its ergodical random excitations by their representative deterministic samples.Having transformed the original stochastic chaos problem into the deterministic chaos problem of equivalent systems,we can use all the available effective methods for further chaos analysis.In this paper,we aim to review the state of art of studying stochastic chaos with its control and synchronization by the above-mentioned strategy.展开更多
This paper reports that the performance of permanent magnet synchronous motor （PMSM） degrades due to chaos when its systemic parameters fall into a certain area. To control the undesirable chaos in PMSM, a nonlinear...This paper reports that the performance of permanent magnet synchronous motor （PMSM） degrades due to chaos when its systemic parameters fall into a certain area. To control the undesirable chaos in PMSM, a nonlinear controller, which is simple and easy to be constructed, is presented to achieve finite-time chaos control based on the finite-time stability theory. Computer simulation results show that the proposed controller is very effective. The obtained results may help to maintain the industrial servo driven system＇s security operation.展开更多
In this paper, a new chaotic system is introduced. The proposed system is a conventional power network that demonstrates a chaotic behavior under special operating conditions. Some features such as Lyapunov exponents ...In this paper, a new chaotic system is introduced. The proposed system is a conventional power network that demonstrates a chaotic behavior under special operating conditions. Some features such as Lyapunov exponents and a strange attractor show the chaotic behavior of the system, which decreases the system performance. Two different controllers are proposed to control the chaotic system. The first one is a nonlinear conventional controller that is simple and easy to construct, but the second one is developed based on the finite time control theory and optimized for faster control. A MATLAB-based simulation verifies the results.展开更多
Multi-switching synchronizatio of multiple different orders unknown chaotisystems confines hacking in the digital transmission process.Similarly,the suppression of undesirable chattering increases synchronization perf...Multi-switching synchronizatio of multiple different orders unknown chaotisystems confines hacking in the digital transmission process.Similarly,the suppression of undesirable chattering increases synchronization performance.This paper proposes a new robust synchronization contro technique and discusses the MSS of multiple different orders UC systems.This controller accomplishe quick convergence reduces the transient oscillations,an the rate of convergence decreases in the vicinity of the origin that causes the suppression of chattering.Analysis based on the Lyapunov direct method assures this convergence behavior with any positive values of the feedback gains.This work also provides parameters updated law that estimates the true values of unknown parameters.Numerical examples of five UC systems different orders are simulated.The computer based graphical results validate the efficiency and performance of the proposed RASC technique and the synchronization strategy when compare to peer works.In the simulation,the proposed synchronization strategy successfully recovers an encrypted received image on a communication channel.The article suggests some future research problems to extend the use of the proposed work.展开更多
基金Project supported by National Natural Science Foundation of China (10872165)Northwestern Polytechnical University (CX200712)
文摘The discovery of chaos in the sixties of last century was a breakthrough in concept,revealing the truth that some disorder behavior,called chaos,could happen even in a deterministic nonlinear system under barely deterministic disturbance.After a series of serious studies,people begin to acknowledge that chaos is a specific type of steady state motion other than the conventional periodic and quasi-periodic ones,featuring a sensitive dependence on initial conditions,resulting from the intrinsic randomness of a nonlinear system itself.In fact,chaos is a collective phenomenon consisting of massive individual chaotic responses,corresponding to different initial conditions in phase space.Any two adjacent individual chaotic responses repel each other,thus causing not only the sensitive dependence on initial conditions but also the existence of at least one positive top Lyapunov exponent(TLE) for chaos.Meanwhile,all the sample responses share one common invariant set on the Poincaré map,called chaotic attractor,which every sample response visits from time to time ergodically.So far,the existence of at least one positive TLE is a commonly acknowledged remarkable feature of chaos.We know that there are various forms of uncertainties in the real world.In theoretical studies,people often use stochastic models to describe these uncertainties,such as random variables or random processes.Systems with random variables as their parameters or with random processes as their excitations are often called stochastic systems.No doubt,chaotic phenomena also exist in stochastic systems,which we call stochastic chaos to distinguish it from deterministic chaos in the deterministic system.Stochastic chaos reflects not only the intrinsic randomness of the nonlinear system but also the external random effects of the random parameter or the random excitation.Hence,stochastic chaos is also a collective massive phenomenon,corresponding not only to different initial conditions but also to different samples of the random parameter or the random excitation.Thus,the unique common feature of deterministic chaos and stochastic chaos is that they all have at least one positive top Lyapunov exponent for their chaotic motion.For analysis of random phenomena,one used to look for the PDFs(Probability Density Functions) of the ensemble random responses.However,it is a pity that PDF information is not favorable to studying repellency of the neighboring chaotic responses nor to calculating the related TLE,so we would rather study stochastic chaos through its sample responses.Moreover,since any sample of stochastic chaos is a deterministic one,we need not supplement any additional definition on stochastic chaos,just mentioning that every sample of stochastic chaos should be deterministic chaos.We are mainly concerned with the following two basic kinds of nonlinear stochastic systems,i.e.one with random variables as its parameters and one with ergodical random processes as its excitations.To solve the stochastic chaos problems of these two kinds of systems,we first transform the original stochastic system into their equivalent deterministic ones.Namely,we can transform the former stochastic system into an equivalent deterministic system in the sense of mean square approximation with respect to the random parameter space by the orthogonal polynomial approximation,and transform the latter one simply through replacing its ergodical random excitations by their representative deterministic samples.Having transformed the original stochastic chaos problem into the deterministic chaos problem of equivalent systems,we can use all the available effective methods for further chaos analysis.In this paper,we aim to review the state of art of studying stochastic chaos with its control and synchronization by the above-mentioned strategy.
基金Project supported by the Hi-Tech Research and Development Program of China (863) (Grant No 2007AA05Z229)National Natural Science Foundation of China (Grant Nos 50877028, 60774069 and 10862001)Science Foundation of Guangdong Province (Grant No 8251064101000014)
文摘This paper reports that the performance of permanent magnet synchronous motor （PMSM） degrades due to chaos when its systemic parameters fall into a certain area. To control the undesirable chaos in PMSM, a nonlinear controller, which is simple and easy to be constructed, is presented to achieve finite-time chaos control based on the finite-time stability theory. Computer simulation results show that the proposed controller is very effective. The obtained results may help to maintain the industrial servo driven system＇s security operation.
文摘In this paper, a new chaotic system is introduced. The proposed system is a conventional power network that demonstrates a chaotic behavior under special operating conditions. Some features such as Lyapunov exponents and a strange attractor show the chaotic behavior of the system, which decreases the system performance. Two different controllers are proposed to control the chaotic system. The first one is a nonlinear conventional controller that is simple and easy to construct, but the second one is developed based on the finite time control theory and optimized for faster control. A MATLAB-based simulation verifies the results.
基金partially supported by the College of Applied Sciences Nizwa,Ministry of the Higher Educations,Sultanate of Oman。
文摘Multi-switching synchronizatio of multiple different orders unknown chaotisystems confines hacking in the digital transmission process.Similarly,the suppression of undesirable chattering increases synchronization performance.This paper proposes a new robust synchronization contro technique and discusses the MSS of multiple different orders UC systems.This controller accomplishe quick convergence reduces the transient oscillations,an the rate of convergence decreases in the vicinity of the origin that causes the suppression of chattering.Analysis based on the Lyapunov direct method assures this convergence behavior with any positive values of the feedback gains.This work also provides parameters updated law that estimates the true values of unknown parameters.Numerical examples of five UC systems different orders are simulated.The computer based graphical results validate the efficiency and performance of the proposed RASC technique and the synchronization strategy when compare to peer works.In the simulation,the proposed synchronization strategy successfully recovers an encrypted received image on a communication channel.The article suggests some future research problems to extend the use of the proposed work.
文摘基于 L yapunov稳定性理论 ,提出一种具有不匹配参数混沌系统的同步控制方法。即使在有较大参数误差的情况下 ,只要选择合适的反馈控制律和参数自适应律 ,也能保证同步系统的全局稳定性。与已有的结果相比 ,该方法能克服较大参数误差对同步的影响。 L orenz系统和 Chen系统的数值仿真验证了该方法的有效性。
