We study the leader-following consensus stability and stabilization of networked multi-teleoperator systems with interval time-varying communication delays. With the construction of a suitable Lyapunov–Krasovskii fun...We study the leader-following consensus stability and stabilization of networked multi-teleoperator systems with interval time-varying communication delays. With the construction of a suitable Lyapunov–Krasovskii functional and the utilization of the reciprocally convex approach, novel delay-dependent consensus stability and stabilization conditions for the systems are established in terms of linear matrix inequalities, which can easily be solved by various effective optimization algorithms. One illustrative example is given to illustrate the effectiveness of the proposed methods.展开更多
This paper investigates the problem of delay-dependent robust stability analysis for a class of neutral systems with interval time-varying delays and nonlinear perturbations. Such nonlinear perturbations are with time...This paper investigates the problem of delay-dependent robust stability analysis for a class of neutral systems with interval time-varying delays and nonlinear perturbations. Such nonlinear perturbations are with time-varying but norm-bounded characteristics. Based on a new Lyapunov-Krasovskii functional, together ,sith a free-weighting matrices technique, improved delay-dependent stability criteria are established. It is shown that less conservative results can be obtained in terms of linear matrix inequalities （LMIs）. Numerical examples are provided to demonstrate the effectiveness and less conservatism of the proposed approach.展开更多
Using the matrix measure and delay differential inequality, the sufficient conditions were obtained for exponential stability of interval dynamical system with multidelay. These conditions are an improvement and exten...Using the matrix measure and delay differential inequality, the sufficient conditions were obtained for exponential stability of interval dynamical system with multidelay. These conditions are an improvement and extension of the results achieved in earlier papers presented by LIAO, LIU, ZHANG, SUN, et al.展开更多
This paper proposes a new non-intrusive hybrid interval method using derivative information for the dynamic response analysis of nonlinear systems with uncertain-but- bounded parameters and/or initial conditions. This...This paper proposes a new non-intrusive hybrid interval method using derivative information for the dynamic response analysis of nonlinear systems with uncertain-but- bounded parameters and/or initial conditions. This method provides tighter solution ranges compared to the existing polynomial approximation interval methods. Interval arith- metic using the Chebyshev basis and interval arithmetic using the general form modified affine basis for polynomials are developed to obtain tighter bounds for interval computation. To further reduce the overestimation caused by the ＂wrap- ping effect＂ of interval arithmetic, the derivative information of dynamic responses is used to achieve exact solutions when the dynamic responses are monotonic with respect to all the uncertain variables. Finally, two typical numerical examples with nonlinearity are applied to demonstrate the effective- ness of the proposed hybrid interval method, in particular, its ability to effectively control the overestimation for specific timepoints.展开更多
In this paper, the robust H∞control problem for a class of stochastic systems with interval time-varying and distributed delays is discussed. The system under study involves parameter uncertainty, stochastic disturba...In this paper, the robust H∞control problem for a class of stochastic systems with interval time-varying and distributed delays is discussed. The system under study involves parameter uncertainty, stochastic disturbance, interval time-varying,and distributed delay. The aim is to design a delay-dependent robust H∞control which ensures the robust asymptotic stability of the given system and to express it in the form of linear matrix inequalities（LMIs）. Numerical examples are given to demonstrate the effectiveness of the proposed method. The results are also compared with the existing results to show its conservativeness.展开更多
Optimal control system of state space is a conservative system, whose approximate method should be symplectic conservation. Based on the precise integration method, an algorithm of symplectic conservative perturbation...Optimal control system of state space is a conservative system, whose approximate method should be symplectic conservation. Based on the precise integration method, an algorithm of symplectic conservative perturbation is presented. It gives a uniform way to solve the linear quadratic control （LQ control） problems for linear timevarying systems accurately and efficiently, whose key points are solutions of differential Riccati equation （DRE） with variable coefficients and the state feedback equation. The method is symplectic conservative and has a good numerical stability and high precision. Numerical examples demonstrate the effectiveness of the proposed method.展开更多
This paper proposes a new non-intrusive trigonometric polynomial approximation interval method for the dynamic response analysis of nonlinear systems with uncertain-but-bounded parameters and/or initial conditions.Thi...This paper proposes a new non-intrusive trigonometric polynomial approximation interval method for the dynamic response analysis of nonlinear systems with uncertain-but-bounded parameters and/or initial conditions.This method provides tighter solution ranges compared to the existing approximation interval methods.We consider trigonometric approximation polynomials of three types:both cosine and sine functions,the sine function,and the cosine function.Thus,special interval arithmetic for trigonometric function without overestimation can be used to obtain interval results.The interval method using trigonometric approximation polynomials with a cosine functional form exhibits better performance than the existing Taylor interval method and Chebyshev interval method.Finally,two typical numerical examples with nonlinearity are applied to demonstrate the effectiveness of the proposed method.展开更多
1 A kind of non-chaotic dynamical systems on the symbolic space Let A<sub>0</sub>=A<sub>1</sub>=A<sub>2</sub>=…={0,1},and X=multiply from i=0 to ∞ A<sub>i</sub>. For e...1 A kind of non-chaotic dynamical systems on the symbolic space Let A<sub>0</sub>=A<sub>1</sub>=A<sub>2</sub>=…={0,1},and X=multiply from i=0 to ∞ A<sub>i</sub>. For every integer k≥2, define metrics d<sub>k</sub>and d<sub>k</sub>’ on X by d<sub>k</sub>（a,b）=max{k<sup>-i</sup>·|a<sub>i</sub>-b<sub>i</sub>|: i=0, 1, 2,…}, d<sub>k</sub>’（a, b）=sum from i=0 to ∞ k<sup>-i</sup>·|a<sub>i</sub>-b<sub>i</sub>| forany a=（a<sub>0</sub>, a<sub>0</sub>, a<sub>2</sub>,…） and any b=（b<sub>0</sub>, b<sub>1</sub>, b<sub>2</sub>,…）∈X. It is easy to see that all d<sub>k</sub> andd<sub>k</sub>’ induce the same topological structure. Thus we now may only consider d≡d<sub>2</sub>. Thespace （X, d） is usually called a symbolic space. For simplicity, write X for （X, d）. It展开更多
In this paper, we first consider the adaptive leader-following consensus problem for a class of nonlinear parameterized mixedorder multi-agent systems with unknown control coefficients and time-varying disturbance par...In this paper, we first consider the adaptive leader-following consensus problem for a class of nonlinear parameterized mixedorder multi-agent systems with unknown control coefficients and time-varying disturbance parameters of the same period. Neural networks and Fourier series expansions are used to describe the unknown nonlinear periodic time-varying parameterized function.A distributed control protocol is designed based on adaptive control, matrix theory, and Nussbaum function. The robustness of the distributed control protocol is analyzed by combining the stability analysis theory of closed-loop systems. On this basis, this paper discusses the case of time-varying disturbance parameters with non-identical periods, expanding the application scope of this control protocol. Finally, the effectiveness of the algorithm is verified by a simulation example.展开更多
The research of the imprecision of a nonequilibrium thermodynamic system is justifiedby the structural and parametric uncertainties of such systems. The paper gives an interval-valuedformulation of the phenomenologica...The research of the imprecision of a nonequilibrium thermodynamic system is justifiedby the structural and parametric uncertainties of such systems. The paper gives an interval-valuedformulation of the phenomenological equations and shows a realistic approach for studying the entropyproduction in Physical systems, the time trajectories of chemical reactions, etc. Using algorithms derivedfor special reaction systems, bundles of time trajectories with prescribed boundary possibility measuresare calculated.展开更多
基金MEST&DGIST(12-IT-04,Development of the Medical&IT Convergence System)the Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education,Science and Technology(Grant Nos.2011-0009273 and 2012-0000479)
文摘We study the leader-following consensus stability and stabilization of networked multi-teleoperator systems with interval time-varying communication delays. With the construction of a suitable Lyapunov–Krasovskii functional and the utilization of the reciprocally convex approach, novel delay-dependent consensus stability and stabilization conditions for the systems are established in terms of linear matrix inequalities, which can easily be solved by various effective optimization algorithms. One illustrative example is given to illustrate the effectiveness of the proposed methods.
基金Sponsored by the National Natural Science Foundation of China(Grant No.61004038)
文摘This paper investigates the problem of delay-dependent robust stability analysis for a class of neutral systems with interval time-varying delays and nonlinear perturbations. Such nonlinear perturbations are with time-varying but norm-bounded characteristics. Based on a new Lyapunov-Krasovskii functional, together ,sith a free-weighting matrices technique, improved delay-dependent stability criteria are established. It is shown that less conservative results can be obtained in terms of linear matrix inequalities （LMIs）. Numerical examples are provided to demonstrate the effectiveness and less conservatism of the proposed approach.
文摘Using the matrix measure and delay differential inequality, the sufficient conditions were obtained for exponential stability of interval dynamical system with multidelay. These conditions are an improvement and extension of the results achieved in earlier papers presented by LIAO, LIU, ZHANG, SUN, et al.
文摘This paper proposes a new non-intrusive hybrid interval method using derivative information for the dynamic response analysis of nonlinear systems with uncertain-but- bounded parameters and/or initial conditions. This method provides tighter solution ranges compared to the existing polynomial approximation interval methods. Interval arith- metic using the Chebyshev basis and interval arithmetic using the general form modified affine basis for polynomials are developed to obtain tighter bounds for interval computation. To further reduce the overestimation caused by the ＂wrap- ping effect＂ of interval arithmetic, the derivative information of dynamic responses is used to achieve exact solutions when the dynamic responses are monotonic with respect to all the uncertain variables. Finally, two typical numerical examples with nonlinearity are applied to demonstrate the effective- ness of the proposed hybrid interval method, in particular, its ability to effectively control the overestimation for specific timepoints.
基金Project supported by the Fund from the Department of Science and Technology(DST)(Grant No.SR/FTP/MS-039/2011)
文摘In this paper, the robust H∞control problem for a class of stochastic systems with interval time-varying and distributed delays is discussed. The system under study involves parameter uncertainty, stochastic disturbance, interval time-varying,and distributed delay. The aim is to design a delay-dependent robust H∞control which ensures the robust asymptotic stability of the given system and to express it in the form of linear matrix inequalities（LMIs）. Numerical examples are given to demonstrate the effectiveness of the proposed method. The results are also compared with the existing results to show its conservativeness.
基金supported by National Natural Science Foundation of China(61074093,61473048,61233008)the Open Research Project from SKLMCCS(20150101)Youth Talent Support Plan of Changsha University of Science and Technology
基金Project supported by the National Natural Science Foundation of China (No.10202004)
文摘Optimal control system of state space is a conservative system, whose approximate method should be symplectic conservation. Based on the precise integration method, an algorithm of symplectic conservative perturbation is presented. It gives a uniform way to solve the linear quadratic control （LQ control） problems for linear timevarying systems accurately and efficiently, whose key points are solutions of differential Riccati equation （DRE） with variable coefficients and the state feedback equation. The method is symplectic conservative and has a good numerical stability and high precision. Numerical examples demonstrate the effectiveness of the proposed method.
文摘This paper proposes a new non-intrusive trigonometric polynomial approximation interval method for the dynamic response analysis of nonlinear systems with uncertain-but-bounded parameters and/or initial conditions.This method provides tighter solution ranges compared to the existing approximation interval methods.We consider trigonometric approximation polynomials of three types:both cosine and sine functions,the sine function,and the cosine function.Thus,special interval arithmetic for trigonometric function without overestimation can be used to obtain interval results.The interval method using trigonometric approximation polynomials with a cosine functional form exhibits better performance than the existing Taylor interval method and Chebyshev interval method.Finally,two typical numerical examples with nonlinearity are applied to demonstrate the effectiveness of the proposed method.
基金Project supported by the National Natural Science Foundation of China.
文摘1 A kind of non-chaotic dynamical systems on the symbolic space Let A<sub>0</sub>=A<sub>1</sub>=A<sub>2</sub>=…={0,1},and X=multiply from i=0 to ∞ A<sub>i</sub>. For every integer k≥2, define metrics d<sub>k</sub>and d<sub>k</sub>’ on X by d<sub>k</sub>（a,b）=max{k<sup>-i</sup>·|a<sub>i</sub>-b<sub>i</sub>|: i=0, 1, 2,…}, d<sub>k</sub>’（a, b）=sum from i=0 to ∞ k<sup>-i</sup>·|a<sub>i</sub>-b<sub>i</sub>| forany a=（a<sub>0</sub>, a<sub>0</sub>, a<sub>2</sub>,…） and any b=（b<sub>0</sub>, b<sub>1</sub>, b<sub>2</sub>,…）∈X. It is easy to see that all d<sub>k</sub> andd<sub>k</sub>’ induce the same topological structure. Thus we now may only consider d≡d<sub>2</sub>. Thespace （X, d） is usually called a symbolic space. For simplicity, write X for （X, d）. It
基金supported by the National Natural Science Foundation of China (Grant Nos. 62063031,62106186,62073254,62103136)the Fundamental Research Funds for the Central Universities (Grant Nos. XJS18012,QTZX22049,XJS220704,and 20101196862)the Young Talent Fund of University Association for Science and Technology in Shaanxi,China (Grant No. 20180502)。
文摘In this paper, we first consider the adaptive leader-following consensus problem for a class of nonlinear parameterized mixedorder multi-agent systems with unknown control coefficients and time-varying disturbance parameters of the same period. Neural networks and Fourier series expansions are used to describe the unknown nonlinear periodic time-varying parameterized function.A distributed control protocol is designed based on adaptive control, matrix theory, and Nussbaum function. The robustness of the distributed control protocol is analyzed by combining the stability analysis theory of closed-loop systems. On this basis, this paper discusses the case of time-varying disturbance parameters with non-identical periods, expanding the application scope of this control protocol. Finally, the effectiveness of the algorithm is verified by a simulation example.
文摘The research of the imprecision of a nonequilibrium thermodynamic system is justifiedby the structural and parametric uncertainties of such systems. The paper gives an interval-valuedformulation of the phenomenological equations and shows a realistic approach for studying the entropyproduction in Physical systems, the time trajectories of chemical reactions, etc. Using algorithms derivedfor special reaction systems, bundles of time trajectories with prescribed boundary possibility measuresare calculated.
