Analysis And Control Of Large-scale Logical Dynamical Systems

In the past few decades,logical dynamical systems(LDSs)have been applied to many research fields,such as gene regulation,swarm intelligence,information security and so on,which have become a research focus of interdisciplinary subjects.The network topology of social networks,biological populations and gene regulatory networks often consists of a great number of vertices and edges.With the increase of network scale,the computational complexity of existing results on LDSs increases exponentially,which makes them hardly be applied to large-scale LDSs.This thesis investigates the analysis and control of large-scale LDSs by using the network aggregation method.The main contents of this thesis are listed as follows:1.The reachability and optimal control of large-scale Boolean control networks(BCNs)are studied.The definition of matchable condition is proposed,which together with the reachability of subnetworks leads to a necessary and sufficient condition for the reachability of large-scale BCNs.In addition,it is revealed that the reachability analysis of large-scale BCNs is not affected by the choice of partition satisfying the corresponding assumptions.For large-scale BCNs with a certain network structure,it is proved that acyclic aggregation can reduce the number of times for matchability when verifying the matchable condition.By resorting to the results on reachability,an algorithm is established to obtain all optimal solutions to the Mayer-type optimal control problem of large-scale BCNs.2.The observability of large-scale muti-valued logical control networks(MVLCNs)subject to function perturbation is investigated.Firstly,the pairs of states in product space are classified into three disjoint sets.Based on the transition graph of undistinguishable pairs of states,a new graph-based criterion is presented for the observability of MVLCNs,which lays the foundation for the study of robust observability.Then,based on the graph-based condition and parameter set approach,a graph-based framework is established for the robust observability of MVLCNs under function perturbation.Finally,considering large-scale MVLCNs subject to function perturbation,a criterion is proposed for the robust observability by virtue of the results on robust observability and acyclic aggregation.3.The network aggregation method is introduced to the strategy consensus analysis and synthesis of large-scale networked evolutionary matrix games(NEMGs),which provides an effective way for studying large-scale NEMGs with general network structure.On one hand,large-scale NEMGs are partitioned into several small-scale control sub-games.Then,a criterion is derived to verify the strategy profile reachability of control sub-games,and the matchable condition between control sub-games is proposed.By resorting to these efforts,a feasible necessary and sufficient condition is proposed to verify the strategy consensus of large-scale NEMGs.On the other hand,based on the strategy consensus analysis of largescale NEMGs,a necessary and sufficient condition is obtained to design control strategies for the strategy consensus of large-scale control NEMGs,which paves ways for other challenging synthesis issues of large-scale NEMGs.4.The obtained results are applied to systems biology and social networks.The reachability of colitis-associated colon cancer network from the state(Proliferation being “ON”,Apoptosis being “OFF”)to the state(Proliferation being “OFF”,Apoptosis being “ON”)is studied,which supports the necessity of verifying matchable condition.The robustness of observability for the T-cell receptor network is investigated.The strategy consensus of the NEMG for international trade between countries is preliminarily studied,and the control strategy under which the NEMG reaches a strategy consensus at strategy “Cooperation” is designed.The novelties of this thesis are two-fold.On one hand,by resorting to network aggregation method,several open problems including the controllability of large-scale BCNs,the observability of large-scale MVLCNs subject to function perturbation,and the strategy consensus of large-scale NEMGs are preliminarily solved.On the other hand,the matchable condition is developed for the analysis and control of large-scale LDSs,which makes it possible to investigate the reachability and strategy consensus of large-scale networks by using the information of subnetworks.