Image encryption algorithm for synchronously updating Boolean networks based on matrix semi-tensor product theory

Consider a networked evolutionary game (NEG). According to its strategy updating rule, a fundamental evolutionary equation (FEE) for each node is proposed, which is based on local information. Using FEEs, the network strategy profile dynamics (SPD) is expressed as a $k$ -valued (deterministic or probabilistic) logical dynamic system. The SPD is then used to analyze the network dynamic behaviors, such as the fixed points, the cycles, and the basins of attractions, etc. Particularly, when the homogeneous networked games are considered, a necessary and sufficient condition is presented to verify when a stationary stable profile exists. Then the equivalence of two NEGs is investigated. Finally, after a rigorous definition of controlled NEGs, some control problems, including controllability, stabilization, and network consensus, are considered, and some verifiable conditions are presented. Examples with various games are presented to illustrate the theoretical results. The basic tool for this approach is the semi-tensor product (STP) of matrices, which is a generalization of the conventional matrix product.

/pdf/modeling-analysis-and-control-of-networked-evolutionary-lgjudi4qt8.pdf

Modeling, Analysis and Control of Networked Evolutionary Games

State feedback stabilization for Boolean control networks is investigated in this technical note. Based on the algebraic representation of logical dynamics in terms of the semi-tensor product of matrices, a necessary and sufficient condition is derived for the existence of a globally stabilizing state feedback controller, and a general control design approach is proposed when global stabilization is feasible via state feedback. Instead of designing the logical form of a stabilizing feedback law directly, we first construct its algebraic representation and then convert the algebraic representation back to the logical form. An example is worked out to illustrate the proposed design procedure.

State Feedback Stabilization for Boolean Control Networks

Set stability and set stabilization of Boolean control networks based on invariant subsets

This technical note presents analytical investigations of reachability and controllability of Boolean control networks (BCNs) with pinning controllers. Based on semi-tensor product (STP) of matrices, BCNs with pinning controllers are converted into a discrete-time algebraic system. A formula is derived to calculate the number of different control sequences steering BCNs between two states in a given step, and then several necessary and sufficient criteria are derived for reachability and controllability of BCNs with pinning controllers. Moreover, we make a comparison among three forms of BCNs, which have similar algebraic representations. Finally, we obtain some efficient conditions to judge the dynamic structure of BCNs.

On Pinning Controllability of Boolean Control Networks

Controller design for disturbance decoupling of Boolean control networks

State feedback stabilization for probabilistic Boolean networks

Synchronization of Boolean networks with time delays

Boolean networks are currently receiving considerable attention as a computational scheme for system level analysis and modeling of biological systems. Studying control-related problems in Boolean networks may reveal new insights into the intrinsic control in complex biological systems and enable us to develop strategies for manipulating biological systems using exogenous inputs. This paper considers controllability and observability of Boolean biological networks. We propose a new approach, which draws from the rich theory of symbolic computation, to solve the problems. Consequently, simple necessary and sufficient conditions for reachability, controllability, and observability are obtained, and algorithmic tests for controllability and observability which are based on the Grobner basis method are presented. As practical applications, we apply the proposed approach to several different biological systems, namely, the mammalian cell-cycle network, the T-cell activation network, the large granular lymphocyte survival signaling network, and the Drosophila segment polarity network, gaining novel insights into the control and/or monitoring of the specific biological systems.

Meng Yang

Papers

State Feedback Stabilization for Boolean Control Networks

Controller design for disturbance decoupling of Boolean control networks

State feedback stabilization for probabilistic Boolean networks

Synchronization of Boolean networks with time delays

Controllability and observability of Boolean networks arising from biology