Pub Date : 2014-12-01DOI: 10.1080/21642583.2013.863168
J. Chen, Hongfen Zou
The matrix exponential eA t plays a central role in linear system and control theory. This paper develops a method to compute the accurate solution for the matrix exponential eA t with the assumption that the matrix A has an eigenvalue s1=0. The examples show the effectiveness of the proposed method.
{"title":"An interesting method for the exponentials for some special matrices","authors":"J. Chen, Hongfen Zou","doi":"10.1080/21642583.2013.863168","DOIUrl":"https://doi.org/10.1080/21642583.2013.863168","url":null,"abstract":"The matrix exponential eA t plays a central role in linear system and control theory. This paper develops a method to compute the accurate solution for the matrix exponential eA t with the assumption that the matrix A has an eigenvalue s1=0. The examples show the effectiveness of the proposed method.","PeriodicalId":22127,"journal":{"name":"Systems Science & Control Engineering: An Open Access Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88334423","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-12-01DOI: 10.1080/21642583.2013.879842
Wei Wang, Guangyi Wang, Xiaoyuan Wang
The memristor is the fourth fundamental circuit element besides the resistor, inductor and capacitor. As a two-terminal nonlinear resistor, the memristor has a broad application prospect. In this paper, a negative memconductance expression of a flux-controlled memristor is derived from the relationship between voltage and current for the Hewlett-Packard memristor. By replacing Chua's diode with the active flux-controlled TiO 2 memristor, a chaotic circuit is obtained. By means of the conventional dynamic analysis method, dynamic behaviors of the chaotic circuit are investigated. Software simulation and theoretical analysis all indicate that this active memristor-based chaotic circuit has more complex behaviors. Furthermore, the integrated circuit experiment on the digital signal processor chip of this circuit was also realized.
{"title":"Research on a chaotic circuit based on an active TiO 2 memristor","authors":"Wei Wang, Guangyi Wang, Xiaoyuan Wang","doi":"10.1080/21642583.2013.879842","DOIUrl":"https://doi.org/10.1080/21642583.2013.879842","url":null,"abstract":"The memristor is the fourth fundamental circuit element besides the resistor, inductor and capacitor. As a two-terminal nonlinear resistor, the memristor has a broad application prospect. In this paper, a negative memconductance expression of a flux-controlled memristor is derived from the relationship between voltage and current for the Hewlett-Packard memristor. By replacing Chua's diode with the active flux-controlled TiO 2 memristor, a chaotic circuit is obtained. By means of the conventional dynamic analysis method, dynamic behaviors of the chaotic circuit are investigated. Software simulation and theoretical analysis all indicate that this active memristor-based chaotic circuit has more complex behaviors. Furthermore, the integrated circuit experiment on the digital signal processor chip of this circuit was also realized.","PeriodicalId":22127,"journal":{"name":"Systems Science & Control Engineering: An Open Access Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80011486","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-12-01DOI: 10.1080/21642583.2013.878886
M. Lefebvre, F. Zitouni
The problem of optimally controlling one-dimensional diffusion processes until they leave a given interval is considered. By linearizing the Riccati differential equation satisfied by the derivative of the value function in the so-called linear quadratic Gaussian homing problem, we are able to obtain an exact expression for the solution to the general problem. Particular problems are solved explicitly.
{"title":"Analytical solutions to LQG homing problems in one dimension","authors":"M. Lefebvre, F. Zitouni","doi":"10.1080/21642583.2013.878886","DOIUrl":"https://doi.org/10.1080/21642583.2013.878886","url":null,"abstract":"The problem of optimally controlling one-dimensional diffusion processes until they leave a given interval is considered. By linearizing the Riccati differential equation satisfied by the derivative of the value function in the so-called linear quadratic Gaussian homing problem, we are able to obtain an exact expression for the solution to the general problem. Particular problems are solved explicitly.","PeriodicalId":22127,"journal":{"name":"Systems Science & Control Engineering: An Open Access Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72787807","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-12-01DOI: 10.1080/21642583.2013.877859
Xin Wang, E. Yaz, James Long
A novel state-dependent control approach for continuous-time nonlinear systems with general performance criteria is presented in this paper. This controller is optimally robust for model uncertainties and resilient against control feedback gain perturbations in achieving general performance criteria to secure quadratic optimality with inherent asymptotic stability property together with quadratic dissipative type of disturbance reduction. For the system model, unstructured uncertainty description is assumed, which incorporates commonly used types of uncertainties, such as norm-bounded and positive real uncertainties as special cases. By solving a state-dependent linear matrix inequality at each time, sufficient condition for the control solution can be found which satisfies the general performance criteria. The results of this paper unify existing results on nonlinear quadratic regulator, H∞ and positive real control. The efficacy of the proposed technique is demonstrated by numerical simulations of the nonlinear control of the inverted pendulum on a cart system.
{"title":"Robust and resilient state-dependent control of continuous-time nonlinear systems with general performance criteria","authors":"Xin Wang, E. Yaz, James Long","doi":"10.1080/21642583.2013.877859","DOIUrl":"https://doi.org/10.1080/21642583.2013.877859","url":null,"abstract":"A novel state-dependent control approach for continuous-time nonlinear systems with general performance criteria is presented in this paper. This controller is optimally robust for model uncertainties and resilient against control feedback gain perturbations in achieving general performance criteria to secure quadratic optimality with inherent asymptotic stability property together with quadratic dissipative type of disturbance reduction. For the system model, unstructured uncertainty description is assumed, which incorporates commonly used types of uncertainties, such as norm-bounded and positive real uncertainties as special cases. By solving a state-dependent linear matrix inequality at each time, sufficient condition for the control solution can be found which satisfies the general performance criteria. The results of this paper unify existing results on nonlinear quadratic regulator, H∞ and positive real control. The efficacy of the proposed technique is demonstrated by numerical simulations of the nonlinear control of the inverted pendulum on a cart system.","PeriodicalId":22127,"journal":{"name":"Systems Science & Control Engineering: An Open Access Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81655598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-12-01DOI: 10.1080/21642583.2014.886310
H. Jia, Q. Tao, Z.Q. Chen
The paper first discusses the recently reported fractional-order Lorenz system, analyzes it by using the frequency-domain approximation method and the time-domain approximation method, and finds its chaotic dynamics when the order of the fractional-order system varies from 2.8 to 2.9 in steps of 0.1. Especially for the fractional-order Lorenz system of the order as low as 2.9, the results obtained by the frequency-domain method are consistent with those obtained by the time-domain method. Some Lyapunov exponent diagrams, bifurcation diagrams, and phase orbits diagrams have also been shown to verify the chaotic dynamics of the fractional-order Lorenz system. Then, an analog circuit for the fractional-order Lorenz system of the order as low as 2.9 is designed to confirm its chaotic dynamic, the results from circuit experiment show that it is chaotic.
{"title":"Analysis and circuit design of a fractional-order Lorenz system with different fractional orders","authors":"H. Jia, Q. Tao, Z.Q. Chen","doi":"10.1080/21642583.2014.886310","DOIUrl":"https://doi.org/10.1080/21642583.2014.886310","url":null,"abstract":"The paper first discusses the recently reported fractional-order Lorenz system, analyzes it by using the frequency-domain approximation method and the time-domain approximation method, and finds its chaotic dynamics when the order of the fractional-order system varies from 2.8 to 2.9 in steps of 0.1. Especially for the fractional-order Lorenz system of the order as low as 2.9, the results obtained by the frequency-domain method are consistent with those obtained by the time-domain method. Some Lyapunov exponent diagrams, bifurcation diagrams, and phase orbits diagrams have also been shown to verify the chaotic dynamics of the fractional-order Lorenz system. Then, an analog circuit for the fractional-order Lorenz system of the order as low as 2.9 is designed to confirm its chaotic dynamic, the results from circuit experiment show that it is chaotic.","PeriodicalId":22127,"journal":{"name":"Systems Science & Control Engineering: An Open Access Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73189300","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-12-01DOI: 10.1080/21642583.2013.860057
Jianbin He, Jianping Cai
The Chen hyperchaotic systems are synchronized via linear feedback control and the parameter is identified by using the adaptive control techniques even though the parameter is unknown. It is proved by the Lyapunov stability theory that the response system is able to track the driving system well and the parameter is estimated exactly. Based on the synchronization of Chen hyperchaotic systems, a scheme of secure communication using the parameter modulation method is presented and the transmitted plaintext message can be successfully recovered. Finally, white Gaussian noise in different kinds of signal-to-noise ratio is conducted to evaluate the performance of the proposed secure communication scheme. The return maps of the transmitted signals are provided to show the higher degree of security. Numerical simulation shows its feasibility.
{"title":"Parameter modulation for secure communication via the synchronization of Chen hyperchaotic systems","authors":"Jianbin He, Jianping Cai","doi":"10.1080/21642583.2013.860057","DOIUrl":"https://doi.org/10.1080/21642583.2013.860057","url":null,"abstract":"The Chen hyperchaotic systems are synchronized via linear feedback control and the parameter is identified by using the adaptive control techniques even though the parameter is unknown. It is proved by the Lyapunov stability theory that the response system is able to track the driving system well and the parameter is estimated exactly. Based on the synchronization of Chen hyperchaotic systems, a scheme of secure communication using the parameter modulation method is presented and the transmitted plaintext message can be successfully recovered. Finally, white Gaussian noise in different kinds of signal-to-noise ratio is conducted to evaluate the performance of the proposed secure communication scheme. The return maps of the transmitted signals are provided to show the higher degree of security. Numerical simulation shows its feasibility.","PeriodicalId":22127,"journal":{"name":"Systems Science & Control Engineering: An Open Access Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85531740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-12-01DOI: 10.1080/21642583.2014.891955
Ruoxun Zhang, Jingbo Gong
The means to design the observer for a class of fractional-order chaotic systems is investigated. A novel Lyapunov function is proposed and a robust adaptive observer is designed to synchronize a given fractional-order chaotic system. The constructed observer could guarantee the error of state converges to zero asymptotically. Simulation results demonstrate the effectiveness and robustness of the proposed scheme.
{"title":"Synchronization of the fractional-order chaotic system via adaptive observer","authors":"Ruoxun Zhang, Jingbo Gong","doi":"10.1080/21642583.2014.891955","DOIUrl":"https://doi.org/10.1080/21642583.2014.891955","url":null,"abstract":"The means to design the observer for a class of fractional-order chaotic systems is investigated. A novel Lyapunov function is proposed and a robust adaptive observer is designed to synchronize a given fractional-order chaotic system. The constructed observer could guarantee the error of state converges to zero asymptotically. Simulation results demonstrate the effectiveness and robustness of the proposed scheme.","PeriodicalId":22127,"journal":{"name":"Systems Science & Control Engineering: An Open Access Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86288090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-12-01DOI: 10.1080/21642583.2013.879268
Fengjuan Chen, Shujiao Jin, Liqun Zhou
This paper studies a class of Duffing oscillator with a forcing parameter ϵ. We obtain Hénon-like attractors, rank one attractors, and periodic sinks as ϵ changes. Hénon-like attractors and rank one attractors are chaotic in the sense of SRB measures, while periodic sinks represent stable dynamics with a basin of positive Lebesgue measure. As ϵ→0, three attractors construct a dynamical pattern repeating with certain period. Through numerical simulations, we observe three attractors perfectly as well as the dynamical pattern.
{"title":"A nonlinear oscillator with strange attractors featured Sinai-Ruelle-Bowen measure","authors":"Fengjuan Chen, Shujiao Jin, Liqun Zhou","doi":"10.1080/21642583.2013.879268","DOIUrl":"https://doi.org/10.1080/21642583.2013.879268","url":null,"abstract":"This paper studies a class of Duffing oscillator with a forcing parameter ϵ. We obtain Hénon-like attractors, rank one attractors, and periodic sinks as ϵ changes. Hénon-like attractors and rank one attractors are chaotic in the sense of SRB measures, while periodic sinks represent stable dynamics with a basin of positive Lebesgue measure. As ϵ→0, three attractors construct a dynamical pattern repeating with certain period. Through numerical simulations, we observe three attractors perfectly as well as the dynamical pattern.","PeriodicalId":22127,"journal":{"name":"Systems Science & Control Engineering: An Open Access Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76903038","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-12-01DOI: 10.1080/21642583.2013.877857
Zhiquan Qin, R. Wu, Yanfen Lu
In this paper, the stability of fractional-order systems with the Riemann–Liouville derivative is discussed. By applying the Mittag-Leffler function, generalized Gronwall inequality and comparison principle to fractional differential systems, some sufficient conditions ensuring stability and asymptotic stability are given.
{"title":"Stability analysis of fractional-order systems with the Riemann–Liouville derivative","authors":"Zhiquan Qin, R. Wu, Yanfen Lu","doi":"10.1080/21642583.2013.877857","DOIUrl":"https://doi.org/10.1080/21642583.2013.877857","url":null,"abstract":"In this paper, the stability of fractional-order systems with the Riemann–Liouville derivative is discussed. By applying the Mittag-Leffler function, generalized Gronwall inequality and comparison principle to fractional differential systems, some sufficient conditions ensuring stability and asymptotic stability are given.","PeriodicalId":22127,"journal":{"name":"Systems Science & Control Engineering: An Open Access Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91534440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-11-07DOI: 10.1080/21642583.2013.870054
Jun Shen, J. Lam
This paper is concerned with the decay rate constrained exponential stability analysis for continuous-time positive systems with both time-varying discrete and distributed delays. A necessary and sufficient condition is first given to ensure that a positive system with distributed delay is exponentially stable and satisfies a prescribed decay rate. Furthermore, by exploiting the monotonicity of the trajectory of a constant delay system and comparing the trajectory of the time-varying delay system with that of the constant delay system, the results are extended to positive systems with both bounded time-varying discrete delays and distributed delays.
{"title":"Decay rate constrained stability analysis for positive systems with discrete and distributed delays","authors":"Jun Shen, J. Lam","doi":"10.1080/21642583.2013.870054","DOIUrl":"https://doi.org/10.1080/21642583.2013.870054","url":null,"abstract":"This paper is concerned with the decay rate constrained exponential stability analysis for continuous-time positive systems with both time-varying discrete and distributed delays. A necessary and sufficient condition is first given to ensure that a positive system with distributed delay is exponentially stable and satisfies a prescribed decay rate. Furthermore, by exploiting the monotonicity of the trajectory of a constant delay system and comparing the trajectory of the time-varying delay system with that of the constant delay system, the results are extended to positive systems with both bounded time-varying discrete delays and distributed delays.","PeriodicalId":22127,"journal":{"name":"Systems Science & Control Engineering: An Open Access Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83133091","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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