LAUSR

During the past few decades, logical network (LN) systems, including Boolean network (BN) systems, have shown successful development and great potential applications due to the development of utility theory and effective tools. Logical network systems which admit logical evolution behavior, have been applied in various fields. The widely concerned fields include networked evolutionary game, gene regularity networks, social and economic networks, combustion engines, coding and decoding, and other research areas concerning about logical behaviors. Due to scale, complexity and dynamics, some complex networks are difficult to analyze the performance, while modeling by LNs makes it relatively simple to observe the logical evolution. Recently, an algebraic state space approach has been proposed to model and analyze the logical behaviors of logical control networks (LCNs). One of the main challenges in LN systems is that how to find or learn the best strategy of LCNs in a complex and uncertain environment. This special issue aims to collect the latest development, trends, and novel techniques of analysis, optimization and learning in LCN systems and their applications, and to encourage readers to participate in this promising and challenging research area. The papers included in the issue can be divided into four groups with a survey paper, in which Y. Wu, D. Cheng, B. Ghosh, and T. Shen are devoted to provide an overview of recent advances in optimal control, optimization, and game theory for networked systems. The first group of papers addresses topology structure, stability, controllability, observability analysis of LN systems. Specifically, the first paper of this group by D. Chen and Z. Liu investigates topologies on quotient space of matrices via semi-tensor product. The paper by Y. Guo, Y. Shen, and W. Gui studies the stability of state-triggered impulsive BNs based on a hybrid index model. The controllability and observability of state dependent switched BCNs with input constraints are investigated by Y. Li, J. Li, Z. Ma, J. Feng, H. Wang. A new concept called original disturbance decoupling is proposed and necessary and sufficient conditions for the original disturbance decoupling for BCNs are given by Y. Li, and J. Zhu. A necessary and sufficient condition of subspace controllability of BNs via subnetworks and free inputs is presented in the work of Z. Ji. The paper by Q. Zhang, J. Feng, B. Wang, M. Meng addresses the bisimulations of BCNs with impulsive effects. The problem of simplifying BNs using STP is considered in the work of Y. Yan, J. Yue, and Z. Chen. The second group of papers focuses on optimal control and learning for BCNs. The paper by J. pan, J. Feng, M. Meng, and J. Zhao investigates the minimum time control of large-scale BCNs with constraints by the Partitioning Technique. An optimal control approach to solve the set stabilization problem for deterministic BCNs is proposed by J. Gao, S. Lin, J. Fan, and Y. Hu. By introducing the concepts of inverse Boolean function and updatable set, a Bayesian learning approach to estimate selection probabilities of PBNs is developed in the paper by M. Toyoda. The third group of papers presents applications of LNs and BCNs to Game theory and finite automata, where the STP as an efficient approach. The first paper of this group by C. Li, F. He, and H. Yao studies the effect of different inner products, especially the standard inner product and the weighted inner product, on the orthogonal decomposition of finite games. The second paper by X. Gao, J. Wang, and D. Yang discusses the stability and stabilization of a class of evolutionary games with time delays via the STP method. The third paper by L. Deng, S. Fu, and P. Zhu investigates the state feedback control design problem to avoid players going bankrupt for a class of networked evolutionary games. The problems of reachability and controllability of probabilistic finite automata are investigated by Z. Zhang, Z. Chen, and Z. Liu under the framework of STP of matrices. Furthermore, Language acceptability of finite automata is considered by J. Yue, Y. Yan, and Z. Chen based on theory of STP of matrices. The last group of papers reports various novel controller and observer design for BCNs. The paper by H. Qi, and Y. Qiao studies dynamics and control of a class of singular Boolean networks, which consist of two parts: difference part and algebraic part. The paper by L. Sun, J. Lu, J. Lou, and L. Li designs a sampled-data state feedback controller for set stabilization of BCNs. L. Tong, J. Liang, and H. Chen designs an event-based state feedback controller for