Five-valued Boolean functions play an important role in the design of symmetric cryptography.While the design and properties of single-output almost optimal five-valued spectra Boolean functions have been extensively ...Five-valued Boolean functions play an important role in the design of symmetric cryptography.While the design and properties of single-output almost optimal five-valued spectra Boolean functions have been extensively studied over the past few decades,there has been limited research on the construction of almost optimal five-valued spectra vectorial Boolean functions.In this paper,we present a construction method for even-variable 2-output almost optimal five-valued spectra balanced Boolean functions,whose Walsh spectra values belong to the set{0,±2^(n/2),±2^(n/2+1)},at the same time,we discuss the existence of sufficient conditions in the construction.Additionally,this paper presents a novel construction method for balanced single-output Boolean functions with even variables featuring a special five-valued spectral structure,whose Walsh spectra values are constrained to the set{0,±2^(n/2),±3·2^(n/2)}.These functions provide new canonical examples for the study of Boolean function spectral theory.展开更多
Set stabilization is one of the essential problems in engineering systems, and self-triggered control(STC) can save the storage space for interactive information, and can be successfully applied in networked control s...Set stabilization is one of the essential problems in engineering systems, and self-triggered control(STC) can save the storage space for interactive information, and can be successfully applied in networked control systems with limited communication resources. In this study, the set stabilization problem and STC design of Boolean control networks are investigated via the semi-tensor product technique. On the one hand, the largest control invariant subset is calculated in terms of the strongly connected components of the state transition graph, by which a graph-theoretical condition for set stabilization is derived. On the other hand, a characteristic function is exploited to determine the triggering mechanism and feasible controls. Based on this, the minimum-time and minimum-triggering open-loop, state-feedback and output-feedback STCs for set stabilization are designed,respectively. As classic applications of self-triggered set stabilization, self-triggered synchronization, self-triggered output tracking and self-triggered output regulation are discussed as well. Additionally, several practical examples are given to illustrate the effectiveness of theoretical results.展开更多
Discrete event system(DES)models promote system engineering,including system design,verification,and assessment.The advancement in manufacturing technology has endowed us to fabricate complex industrial systems.Conseq...Discrete event system(DES)models promote system engineering,including system design,verification,and assessment.The advancement in manufacturing technology has endowed us to fabricate complex industrial systems.Consequently,the adoption of advanced modeling methodologies adept at handling complexity and scalability is imperative.Moreover,industrial systems are no longer quiescent,thus the intelligent operations of the systems should be dynamically specified in the model.In this paper,the composition of the subsystem behaviors is studied to generate the complexity and scalability of the global system model,and a Boolean semantic specifying algorithm is proposed for generating dynamic intelligent operations in the model.In traditional modeling approaches,the change or addition of specifications always necessitates the complete resubmission of the system model,a resource-consuming and error-prone process.Compared with traditional approaches,our approach has three remarkable advantages:(i)an established Boolean semantic can be fitful for all kinds of systems;(ii)there is no need to resubmit the system model whenever there is a change or addition of the operations;(iii)multiple specifying tasks can be easily achieved by continuously adding a new semantic.Thus,this general modeling approach has wide potential for future complex and intelligent industrial systems.展开更多
Dear Editor,This letter deals with the set stabilization of stochastic Boolean control networks(SBCNs)by the pinning control strategy,which is to realize the full control for systems by imposing control inputs on a fr...Dear Editor,This letter deals with the set stabilization of stochastic Boolean control networks(SBCNs)by the pinning control strategy,which is to realize the full control for systems by imposing control inputs on a fraction of agents.展开更多
基金National Natural Science Foundation of China(62272360)。
文摘Five-valued Boolean functions play an important role in the design of symmetric cryptography.While the design and properties of single-output almost optimal five-valued spectra Boolean functions have been extensively studied over the past few decades,there has been limited research on the construction of almost optimal five-valued spectra vectorial Boolean functions.In this paper,we present a construction method for even-variable 2-output almost optimal five-valued spectra balanced Boolean functions,whose Walsh spectra values belong to the set{0,±2^(n/2),±2^(n/2+1)},at the same time,we discuss the existence of sufficient conditions in the construction.Additionally,this paper presents a novel construction method for balanced single-output Boolean functions with even variables featuring a special five-valued spectral structure,whose Walsh spectra values are constrained to the set{0,±2^(n/2),±3·2^(n/2)}.These functions provide new canonical examples for the study of Boolean function spectral theory.
基金supported by the National Natural Science Foundation of China (62273201,62173209,72134004,62303170)the Research Fund for the Taishan Scholar Project of Shandong Province of China (TSTP20221103)。
文摘Set stabilization is one of the essential problems in engineering systems, and self-triggered control(STC) can save the storage space for interactive information, and can be successfully applied in networked control systems with limited communication resources. In this study, the set stabilization problem and STC design of Boolean control networks are investigated via the semi-tensor product technique. On the one hand, the largest control invariant subset is calculated in terms of the strongly connected components of the state transition graph, by which a graph-theoretical condition for set stabilization is derived. On the other hand, a characteristic function is exploited to determine the triggering mechanism and feasible controls. Based on this, the minimum-time and minimum-triggering open-loop, state-feedback and output-feedback STCs for set stabilization are designed,respectively. As classic applications of self-triggered set stabilization, self-triggered synchronization, self-triggered output tracking and self-triggered output regulation are discussed as well. Additionally, several practical examples are given to illustrate the effectiveness of theoretical results.
基金supported by the National Natural Science Foundation of China(U21B2074,52105070).
文摘Discrete event system(DES)models promote system engineering,including system design,verification,and assessment.The advancement in manufacturing technology has endowed us to fabricate complex industrial systems.Consequently,the adoption of advanced modeling methodologies adept at handling complexity and scalability is imperative.Moreover,industrial systems are no longer quiescent,thus the intelligent operations of the systems should be dynamically specified in the model.In this paper,the composition of the subsystem behaviors is studied to generate the complexity and scalability of the global system model,and a Boolean semantic specifying algorithm is proposed for generating dynamic intelligent operations in the model.In traditional modeling approaches,the change or addition of specifications always necessitates the complete resubmission of the system model,a resource-consuming and error-prone process.Compared with traditional approaches,our approach has three remarkable advantages:(i)an established Boolean semantic can be fitful for all kinds of systems;(ii)there is no need to resubmit the system model whenever there is a change or addition of the operations;(iii)multiple specifying tasks can be easily achieved by continuously adding a new semantic.Thus,this general modeling approach has wide potential for future complex and intelligent industrial systems.
基金supported by the National Key Research and Development Project of China(2020YFA0714301)the National Natural Science Foundation of China(61833005)。
文摘Dear Editor,This letter deals with the set stabilization of stochastic Boolean control networks(SBCNs)by the pinning control strategy,which is to realize the full control for systems by imposing control inputs on a fraction of agents.
