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
Boolean networks(BNs)introduced by Kauffman in[1]are of great significance in the description of gene interactions/evolutions in genetic regulatory networks.The regulation of genes can be achieved by adding external i...Boolean networks(BNs)introduced by Kauffman in[1]are of great significance in the description of gene interactions/evolutions in genetic regulatory networks.The regulation of genes can be achieved by adding external inputs into BNs.Consequently,Boolean control networks(BCNs)were established in[2].展开更多
We investigate the solution and stability of continuous-time cross-dimensional linear systems(CCDLSs)with dimension bounded by V-addition and V-product.Using the integral iteration method,the solution to CCDLSs can be...We investigate the solution and stability of continuous-time cross-dimensional linear systems(CCDLSs)with dimension bounded by V-addition and V-product.Using the integral iteration method,the solution to CCDLSs can be obtained.Based on the new algebraic expression of the solution and the Jordan decomposition method of matrix,a necessary and sufficient condition is derived for judging whether a CCDLS is asymptotically stable with a given initial state.This condition demonstrates a method for finding the domain of attraction and its relationships.Then,all the initial states that can be stabilized are studied,and a method for designing the corresponding controller is proposed.Two examples are presented to illustrate the validity of the theoretical results.展开更多
In this study,the output tracking of delayed logical control networks(DLCNs)with state and control constraints is further investigated.Compared with other delays,state-dependent delay updates its value depending on th...In this study,the output tracking of delayed logical control networks(DLCNs)with state and control constraints is further investigated.Compared with other delays,state-dependent delay updates its value depending on the current state values and a pseudo-logical function.Multiple constraints mean that state values are constrained in a nonempty set and the design of the controller is conditioned.Using the semi-tensor product of matrices,dynamical equations of DLCNs are converted into an algebraic description,and an equivalent augmented system is constructed.Based on the augmented system,the output tracking problem is transformed into a set stabilization problem.A deformation of the state transition matrix is computed,and a necessary and sufficient condition is derived for the output tracking of a DLCN with multi-constraint.This condition is easily verified by mathematical software.In addition,the admissible state-feedback controller is designed to enable the outputs of the DLCN to track the reference signal.Finally,theoretical results are illustrated by an example.展开更多
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This work was supported by the National Natural Science Foundation of China(62273201)the Research Fund for the Taishan Scholar Project of Shandong Province of China(tstp20221103)the Natural Science Foundation of Shandong Province(ZR2022QE267).
文摘Boolean networks(BNs)introduced by Kauffman in[1]are of great significance in the description of gene interactions/evolutions in genetic regulatory networks.The regulation of genes can be achieved by adding external inputs into BNs.Consequently,Boolean control networks(BCNs)were established in[2].
基金Project supported by the National Natural Science Foundation of China(Nos.61773371 and 61877036)the Natural Science Fund of Shandong Province,China(No.ZR2019MF002)。
文摘We investigate the solution and stability of continuous-time cross-dimensional linear systems(CCDLSs)with dimension bounded by V-addition and V-product.Using the integral iteration method,the solution to CCDLSs can be obtained.Based on the new algebraic expression of the solution and the Jordan decomposition method of matrix,a necessary and sufficient condition is derived for judging whether a CCDLS is asymptotically stable with a given initial state.This condition demonstrates a method for finding the domain of attraction and its relationships.Then,all the initial states that can be stabilized are studied,and a method for designing the corresponding controller is proposed.Two examples are presented to illustrate the validity of the theoretical results.
基金Project supported by the National Natural Science Foundation of China(Nos.61773371 and 61877036)the Natural Science Foundation of Shandong Province,China(No.ZR2019MF002)。
文摘In this study,the output tracking of delayed logical control networks(DLCNs)with state and control constraints is further investigated.Compared with other delays,state-dependent delay updates its value depending on the current state values and a pseudo-logical function.Multiple constraints mean that state values are constrained in a nonempty set and the design of the controller is conditioned.Using the semi-tensor product of matrices,dynamical equations of DLCNs are converted into an algebraic description,and an equivalent augmented system is constructed.Based on the augmented system,the output tracking problem is transformed into a set stabilization problem.A deformation of the state transition matrix is computed,and a necessary and sufficient condition is derived for the output tracking of a DLCN with multi-constraint.This condition is easily verified by mathematical software.In addition,the admissible state-feedback controller is designed to enable the outputs of the DLCN to track the reference signal.Finally,theoretical results are illustrated by an example.
