In this paper,the approximate synchronization of leader-follower multiagent systems(MASs) over finite fields is studied in regard to local and global synchronization.First,the approximately synchronous state set(ASSS)...In this paper,the approximate synchronization of leader-follower multiagent systems(MASs) over finite fields is studied in regard to local and global synchronization.First,the approximately synchronous state set(ASSS) is obtained.Second,combined with ASSS and transient periods,some criteria for the local and global approximate synchronization of systems are given.Moreover,the algorithms for calculating the maximum approximately synchronous basin(MASB) and the maximum control invariant set(MCIS) are presented.Third,the global approximate synchronization of the system is achieved by designing the state feedback control,and a design algorithm of the controller using the truth matrix method is proposed.Moreover,the results of approximate synchronization are degenerated to complete synchronization.Last,two examples are shown to demonstrate the results of this paper.展开更多
In this survey paper, the synchronization will be initially studied for infinite dimensional dynamical systems of partial differential equations instead of finite dimensional systems of ordinary differential equations...In this survey paper, the synchronization will be initially studied for infinite dimensional dynamical systems of partial differential equations instead of finite dimensional systems of ordinary differential equations,and will be connected with the control theory via boundary controls in a finite time interval. More precisely,various kinds of exact boundary synchronization and approximate boundary synchronization will be introduced and realized by means of fewer boundary controls for a coupled system of wave equations with Dirichlet boundary controls. Moreover, as necessary conditions for various kinds of approximate boundary synchronization, criteria of Kalman's type are obtained. Finally, some prospects will be given.展开更多
在模糊推理中,基于贴近度的方法(简称SAR)是一种运算简便、且计算结果符合实际的推理方法。该方法的两种最基本的形式是扩展形式和还原形式。然而这两种形式都距离规则结论B太远,而扩展形式中最小的结果与还原形式中最大的结果也都过于...在模糊推理中,基于贴近度的方法(简称SAR)是一种运算简便、且计算结果符合实际的推理方法。该方法的两种最基本的形式是扩展形式和还原形式。然而这两种形式都距离规则结论B太远,而扩展形式中最小的结果与还原形式中最大的结果也都过于绝对。在已有的SAR方法中,采用的都是某个特殊的贴近度公式。在文献[Y.F.Li,K.Y.Qin,X.X.He.Some new approaches to constructing similarity measures.Fuzzy Sets and Systems,2014,234:46-60]中,我们给出了统一的贴近度的计算公式,证明了已有了多数贴近度公式都可以由所给出的统一贴近度公式得到。文章基于前期关于贴近度的工作,将统一的贴近度公式应用到SAR方法中,将扩展形式中最小的结果与还原形式中最大的结果求算数平均得到SAR方法的一种新的计算形式,并证明利用这种形式计算出的模糊推理的结果满足三条重要的推理原则:假言推理、近似性与逼近性。展开更多
For accelerator single-freedom nonlinear components,a general mathematicalmodel with its solution algorithm is developed,based on which a simulation type expertsystem can be built on IBM PC,automatically yielding any ...For accelerator single-freedom nonlinear components,a general mathematicalmodel with its solution algorithm is developed,based on which a simulation type expertsystem can be built on IBM PC,automatically yielding any order approximate analyti-cal solutions.展开更多
The scientific article examines the physical and mechanical properties of raw cotton stored in buntings in cotton palaces. Because during the storage of raw cotton in bunts, some of its properties deteriorate, some im...The scientific article examines the physical and mechanical properties of raw cotton stored in buntings in cotton palaces. Because during the storage of raw cotton in bunts, some of its properties deteriorate, some improvements. Therefore, the mathematical modeling of storage conditions of raw cotton in bunts and the physical and mechanical conditions that occur in it is of great importance. In the developed mathematical model, the main factor influencing the physical and mechanical properties of raw cotton is the change in temperature. Due to the temperature, kinetic and biological processes accumulated in the raw cotton in Bunt, it can spread over a large surface, first in a small-local state, over time with a nonlinear law. As a result, small changes in temperature lead to a qualitative change in physical properties. In determining the law of temperature distribution in the raw cotton in Bunt, Laplace’s differential equation of heat transfer was used. The differential equation of heat transfer in Laplace’s law was replaced by a system of ordinary differential equations by approximation. Conditions are solved in MAPLE-17 program by numerical method. As a result, graphs of temperature changes over time in raw cotton were obtained. In addition, the table shows the changes in density, pressure and mass of cotton, the height of the bun. As the density of the cotton raw material increases from the top layer of the bunt to the bottom layer, an increase in the temperature in it has been observed. This leads to overheating of the bottom layer of cotton and is the main reason for the deterioration of the quality of raw materials.展开更多
An expert system by Arity Prolog is developed for accelerator single-freedomnonlinear components.It automatically yields any order approximate analytical solu-tions for various accelerator single-freedom nonlinear com...An expert system by Arity Prolog is developed for accelerator single-freedomnonlinear components.It automatically yields any order approximate analytical solu-tions for various accelerator single-freedom nonlinear components.As an example,theeighth order approximate analytical solution is derived by this expert system for a gen-eral accelerator single-freedom nonlinear component,showing that the design of the ex-pert system is successful.展开更多
Approximate calculation methods of prevention maintenance period under the random distribution are given,and three kinds of approximate calculation models of prevention maintenance period based on different security d...Approximate calculation methods of prevention maintenance period under the random distribution are given,and three kinds of approximate calculation models of prevention maintenance period based on different security demands are come up with according to maintenance problems of machinery systems in modern enterprise and starting with different demands of systems. And then,how to make certain the best maintenance period by using the approximate calculation methods is illustrated by an exam- ple.展开更多
In the paper we discuss some properties of the state operators of the optimal obstacle control problem for elliptic variational inequality.Existence,uniqueness and regularity of the optimal control,problem are establi...In the paper we discuss some properties of the state operators of the optimal obstacle control problem for elliptic variational inequality.Existence,uniqueness and regularity of the optimal control,problem are established.In addition,the approximation of the optimal obstacle problem is also studied.展开更多
In this paper, approximate controllability of fractional order retarded semilinear systems is studied when the nonlinear term satisfies the newly formulated bounded integral contractor-type conditions. We have shown t...In this paper, approximate controllability of fractional order retarded semilinear systems is studied when the nonlinear term satisfies the newly formulated bounded integral contractor-type conditions. We have shown the existence and uniqueness of the mild solution for the fractional order retarded semilinear systems using an iterative procedure approach. Finally, we obtain the approximate controllability results of the system under simple condition.展开更多
This paper deals with the approximate controllability of semilinear neutral functional differential systems with state-dependent delay. The fractional power theory and α-norm are used to discuss the problem so that t...This paper deals with the approximate controllability of semilinear neutral functional differential systems with state-dependent delay. The fractional power theory and α-norm are used to discuss the problem so that the obtained results can apply to the systems involving derivatives of spatial variables. By methods of functional analysis and semigroup theory, sufficient conditions of approximate controllability are formulated and proved. Finally, an example is provided to illustrate the applications of the obtained results.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.62373178,62273201,and 62103176the Research Fundfor the Taishan Scholar Project of Shandong Province of China under Grant Nos.tstp20221103 and tstp20221103。
文摘In this paper,the approximate synchronization of leader-follower multiagent systems(MASs) over finite fields is studied in regard to local and global synchronization.First,the approximately synchronous state set(ASSS) is obtained.Second,combined with ASSS and transient periods,some criteria for the local and global approximate synchronization of systems are given.Moreover,the algorithms for calculating the maximum approximately synchronous basin(MASB) and the maximum control invariant set(MCIS) are presented.Third,the global approximate synchronization of the system is achieved by designing the state feedback control,and a design algorithm of the controller using the truth matrix method is proposed.Moreover,the results of approximate synchronization are degenerated to complete synchronization.Last,two examples are shown to demonstrate the results of this paper.
基金supported by National Basic Research Program of China(Grant No.2013CB834100)National Natural Science Foundation of China(Grant No.111211101)
文摘In this survey paper, the synchronization will be initially studied for infinite dimensional dynamical systems of partial differential equations instead of finite dimensional systems of ordinary differential equations,and will be connected with the control theory via boundary controls in a finite time interval. More precisely,various kinds of exact boundary synchronization and approximate boundary synchronization will be introduced and realized by means of fewer boundary controls for a coupled system of wave equations with Dirichlet boundary controls. Moreover, as necessary conditions for various kinds of approximate boundary synchronization, criteria of Kalman's type are obtained. Finally, some prospects will be given.
文摘在模糊推理中,基于贴近度的方法(简称SAR)是一种运算简便、且计算结果符合实际的推理方法。该方法的两种最基本的形式是扩展形式和还原形式。然而这两种形式都距离规则结论B太远,而扩展形式中最小的结果与还原形式中最大的结果也都过于绝对。在已有的SAR方法中,采用的都是某个特殊的贴近度公式。在文献[Y.F.Li,K.Y.Qin,X.X.He.Some new approaches to constructing similarity measures.Fuzzy Sets and Systems,2014,234:46-60]中,我们给出了统一的贴近度的计算公式,证明了已有了多数贴近度公式都可以由所给出的统一贴近度公式得到。文章基于前期关于贴近度的工作,将统一的贴近度公式应用到SAR方法中,将扩展形式中最小的结果与还原形式中最大的结果求算数平均得到SAR方法的一种新的计算形式,并证明利用这种形式计算出的模糊推理的结果满足三条重要的推理原则:假言推理、近似性与逼近性。
文摘For accelerator single-freedom nonlinear components,a general mathematicalmodel with its solution algorithm is developed,based on which a simulation type expertsystem can be built on IBM PC,automatically yielding any order approximate analyti-cal solutions.
文摘The scientific article examines the physical and mechanical properties of raw cotton stored in buntings in cotton palaces. Because during the storage of raw cotton in bunts, some of its properties deteriorate, some improvements. Therefore, the mathematical modeling of storage conditions of raw cotton in bunts and the physical and mechanical conditions that occur in it is of great importance. In the developed mathematical model, the main factor influencing the physical and mechanical properties of raw cotton is the change in temperature. Due to the temperature, kinetic and biological processes accumulated in the raw cotton in Bunt, it can spread over a large surface, first in a small-local state, over time with a nonlinear law. As a result, small changes in temperature lead to a qualitative change in physical properties. In determining the law of temperature distribution in the raw cotton in Bunt, Laplace’s differential equation of heat transfer was used. The differential equation of heat transfer in Laplace’s law was replaced by a system of ordinary differential equations by approximation. Conditions are solved in MAPLE-17 program by numerical method. As a result, graphs of temperature changes over time in raw cotton were obtained. In addition, the table shows the changes in density, pressure and mass of cotton, the height of the bun. As the density of the cotton raw material increases from the top layer of the bunt to the bottom layer, an increase in the temperature in it has been observed. This leads to overheating of the bottom layer of cotton and is the main reason for the deterioration of the quality of raw materials.
文摘An expert system by Arity Prolog is developed for accelerator single-freedomnonlinear components.It automatically yields any order approximate analytical solu-tions for various accelerator single-freedom nonlinear components.As an example,theeighth order approximate analytical solution is derived by this expert system for a gen-eral accelerator single-freedom nonlinear component,showing that the design of the ex-pert system is successful.
文摘Approximate calculation methods of prevention maintenance period under the random distribution are given,and three kinds of approximate calculation models of prevention maintenance period based on different security demands are come up with according to maintenance problems of machinery systems in modern enterprise and starting with different demands of systems. And then,how to make certain the best maintenance period by using the approximate calculation methods is illustrated by an exam- ple.
基金the National Natural Science Foundation of China(No.10472061)the Ph.D.Programs Foundation of Ministry of Education of China(No.20060280015)
文摘In the paper we discuss some properties of the state operators of the optimal obstacle control problem for elliptic variational inequality.Existence,uniqueness and regularity of the optimal control,problem are established.In addition,the approximation of the optimal obstacle problem is also studied.
文摘In this paper, approximate controllability of fractional order retarded semilinear systems is studied when the nonlinear term satisfies the newly formulated bounded integral contractor-type conditions. We have shown the existence and uniqueness of the mild solution for the fractional order retarded semilinear systems using an iterative procedure approach. Finally, we obtain the approximate controllability results of the system under simple condition.
基金supported by the National Natural Science Foundation of China(Nos.11171110,11371087)the Science and Technology Commission of Shanghai Municipality(No.13dz2260400)the Shanghai Leading Academic Discipline Project(No.B407)
文摘This paper deals with the approximate controllability of semilinear neutral functional differential systems with state-dependent delay. The fractional power theory and α-norm are used to discuss the problem so that the obtained results can apply to the systems involving derivatives of spatial variables. By methods of functional analysis and semigroup theory, sufficient conditions of approximate controllability are formulated and proved. Finally, an example is provided to illustrate the applications of the obtained results.
