LetΩ be a bounded symmetric domain in Cn. The purpose of this article is to define and characterize the general function space F（p, q, s） on Ω. Characterizing functions in the F（p, q, s） space is a work of consi...LetΩ be a bounded symmetric domain in Cn. The purpose of this article is to define and characterize the general function space F（p, q, s） on Ω. Characterizing functions in the F（p, q, s） space is a work of considerable interest nowadays. In this article, the authors give several equivalent descriptions of the functions in the F（p, q, s） space on Ω in terms of fractional differential operators. At the same time, the authors give the relationship between F（p, q, s） space and Bloch type space on Ω too.展开更多
Rotating Space Slender Flexible Structures(RSSFS)are extensively utilized in space operations because of their light weight,mobility,and low energy consumption.To realize the accurate space operation of the RSSFS,it i...Rotating Space Slender Flexible Structures(RSSFS)are extensively utilized in space operations because of their light weight,mobility,and low energy consumption.To realize the accurate space operation of the RSSFS,it is necessary to establish a precise mechanical model and develop a control algorithm with high precision.However,with the application of traditional control strategies,the RSSFS often suffers from the chattering phenomenon,which will aggravate structure vibration.In this paper,novel deformation description is put forward to balance modeling accuracy and computational efficiency of the RSSFS,which is better appropriate for real-time control.Besides,the Neural Network Sliding Mode Control(NNSMC)strategy modified by the hyperbolic tangent(tanh)function is put forward to compensate for modeling errors and reduce the chattering phenomenon,thereby improving the trajectory tracking accuracy of the RSSFS.Firstly,a mathematical model for the RSSFS is developed according to the novel deformation description and the vibration theory of flexible structure.Comparison of the deformation accuracy between different models proves that the novel modeling method proposed has high modeling accuracy.Next,the universal approximation property of the Radial Basis Function(RBF)neural network is put forward to determine and compensate for modeling errors,which consist of higher-order modes and the uncertainties of external disturbances.In addition,the tanh function is proposed as the reaching law in the conventional NNSMC strategy to suppress driving torque oscillation.The control law of modified NNSMC strategy and the adaptive law of weight coefficients are developed according to the Lyapunov theorem to guarantee the RSSFS stability.Finally,the simulation and physical experimental tests of the RSSFS with different control strategies are conducted.Experimental results show that the control law according to the novel deformation description and the modified NNSMC strategy can obtain accurate tracking of the rotation and reduce 展开更多
This note studies fully actuated linear systems in the frequency domain in terms of polynomial matrix description(PMD).For a controllable first-order linear state-space system model,by using the right coprime factoriz...This note studies fully actuated linear systems in the frequency domain in terms of polynomial matrix description(PMD).For a controllable first-order linear state-space system model,by using the right coprime factorization of its transfer function matrix,under the condition that the denominator matrix in the right coprime factorization is column reduced,it is equivalently transformed into a fully actuated PMD model,whose time-domain expression is just a high-order fully actuated(HOFA)system model.This method is a supplement to the previous one in the time-domain,and reveals a connection between the controllability of the first-order linear state-space system model and the fullactuation of its PMD model.Both continuous-time and discrete-time linear systems are considered.Some numerical examples are worked out to illustrate the effectiveness of the proposed approaches.展开更多
The paper deals with the performing of a critical analysis of the problems arising in matching the classical models of the statistical and phenomenological thermodynamics. The performed analysis shows that some concep...The paper deals with the performing of a critical analysis of the problems arising in matching the classical models of the statistical and phenomenological thermodynamics. The performed analysis shows that some concepts of the statistical and phenomenological methods of describing the classical systems do not quite correlate with each other. Particularly, in these methods various caloric ideal gas equations of state are employed, while the possibility existing in the thermodynamic cyclic processes to obtain the same distributions both due to a change of the particle concentration and owing to a change of temperature is not allowed for in the statistical methods. The above-mentioned difference of the equations of state is cleared away when using in the statistical functions corresponding to the canonical Gibbs equations instead of the Planck’s constant a new scale factor that depends on the parameters of a system and coincides with the Planck’s constant in going of the system to the degenerate state. Under such an approach, the statistical entropy is transformed into one of the forms of heat capacity. In its turn, the agreement of the methods under consideration in the question as to the dependence of the molecular distributions on the concentration of particles, apparently, will call for further refinement of the physical model of ideal gas and the techniques for its statistical description.展开更多
基金supported by the National Natural Science Foundation of China(11571104)the Hunan Provincial Innovation Foundation for Postgraduate(CX2017B220)Supported by the Construct Program of the Key Discipline in Hunan Province
文摘LetΩ be a bounded symmetric domain in Cn. The purpose of this article is to define and characterize the general function space F（p, q, s） on Ω. Characterizing functions in the F（p, q, s） space is a work of considerable interest nowadays. In this article, the authors give several equivalent descriptions of the functions in the F（p, q, s） space on Ω in terms of fractional differential operators. At the same time, the authors give the relationship between F（p, q, s） space and Bloch type space on Ω too.
基金Supported by the Applied Basic Research Program of Liaoning Province,China(No.2023JH2/101300159)the National Natural Science Foundation of China(No.52275090).
文摘Rotating Space Slender Flexible Structures(RSSFS)are extensively utilized in space operations because of their light weight,mobility,and low energy consumption.To realize the accurate space operation of the RSSFS,it is necessary to establish a precise mechanical model and develop a control algorithm with high precision.However,with the application of traditional control strategies,the RSSFS often suffers from the chattering phenomenon,which will aggravate structure vibration.In this paper,novel deformation description is put forward to balance modeling accuracy and computational efficiency of the RSSFS,which is better appropriate for real-time control.Besides,the Neural Network Sliding Mode Control(NNSMC)strategy modified by the hyperbolic tangent(tanh)function is put forward to compensate for modeling errors and reduce the chattering phenomenon,thereby improving the trajectory tracking accuracy of the RSSFS.Firstly,a mathematical model for the RSSFS is developed according to the novel deformation description and the vibration theory of flexible structure.Comparison of the deformation accuracy between different models proves that the novel modeling method proposed has high modeling accuracy.Next,the universal approximation property of the Radial Basis Function(RBF)neural network is put forward to determine and compensate for modeling errors,which consist of higher-order modes and the uncertainties of external disturbances.In addition,the tanh function is proposed as the reaching law in the conventional NNSMC strategy to suppress driving torque oscillation.The control law of modified NNSMC strategy and the adaptive law of weight coefficients are developed according to the Lyapunov theorem to guarantee the RSSFS stability.Finally,the simulation and physical experimental tests of the RSSFS with different control strategies are conducted.Experimental results show that the control law according to the novel deformation description and the modified NNSMC strategy can obtain accurate tracking of the rotation and reduce
基金the Science Center Program of the National Natural Science Foundation of China under Grant No.62188101the Major Program of National Natural Science Foundation of China under Grant Nos.61690210 and 61690212+1 种基金the National Natural Science Foundation of China under Grant No.61333003the Self-Planned Task of State Key Laboratory of Robotics and System(HIT)under Grant No.SKLRS201716A。
文摘This note studies fully actuated linear systems in the frequency domain in terms of polynomial matrix description(PMD).For a controllable first-order linear state-space system model,by using the right coprime factorization of its transfer function matrix,under the condition that the denominator matrix in the right coprime factorization is column reduced,it is equivalently transformed into a fully actuated PMD model,whose time-domain expression is just a high-order fully actuated(HOFA)system model.This method is a supplement to the previous one in the time-domain,and reveals a connection between the controllability of the first-order linear state-space system model and the fullactuation of its PMD model.Both continuous-time and discrete-time linear systems are considered.Some numerical examples are worked out to illustrate the effectiveness of the proposed approaches.
文摘The paper deals with the performing of a critical analysis of the problems arising in matching the classical models of the statistical and phenomenological thermodynamics. The performed analysis shows that some concepts of the statistical and phenomenological methods of describing the classical systems do not quite correlate with each other. Particularly, in these methods various caloric ideal gas equations of state are employed, while the possibility existing in the thermodynamic cyclic processes to obtain the same distributions both due to a change of the particle concentration and owing to a change of temperature is not allowed for in the statistical methods. The above-mentioned difference of the equations of state is cleared away when using in the statistical functions corresponding to the canonical Gibbs equations instead of the Planck’s constant a new scale factor that depends on the parameters of a system and coincides with the Planck’s constant in going of the system to the degenerate state. Under such an approach, the statistical entropy is transformed into one of the forms of heat capacity. In its turn, the agreement of the methods under consideration in the question as to the dependence of the molecular distributions on the concentration of particles, apparently, will call for further refinement of the physical model of ideal gas and the techniques for its statistical description.
