In this paper, stability and stabilization of Boolean networks with stochastic delays are studied via semi-tensor product of matrices. The stochastic delays, randomly attaining finite values, are modeled by Markov chains. By utilizing an augmented method, the considered Boolean network is first converted into two coupled Markovian switching systems without delays. Then, some stochastic stability results are obtained based on stability results of positive systems. Subsequently, the stabilization of Boolean networks with stochastic delays is further investigated, and an equivalent condition for the existence of feedback controllers is provided in terms of a convex programming problem, which can be easily solved and also conveniently applied to design controller gains. Finally, numerical examples are given to illustrate feasibility of the obtained results.

Stability and Stabilization of Boolean Networks With Stochastic Delays

This paper investigates the global stabilization problem of k-valued logical control networks (KVLCNs) via event-triggered control (ETC), where the control inputs only work at several certain individual states. Compared with traditional state feedback control, the designed ETC approach not only shortens the transient period of logical networks but also decreases the number of controller executions. The content of this paper is divided into two parts. In the first part, a necessary and sufficient criterion is derived for the event-triggered stabilization of KVLCNs, and a construction procedure is developed to design all time-optimal event-triggered stabilizers. In the second part, the switching-cost-optimal event-triggered stabilizer is designed to minimize the number of controller executions. A labeled digraph is obtained based on the dynamic of the overall system. Utilizing this digraph, we formulate a universal and unified procedure called the minimal spanning in-tree algorithm to minimize the triggering event set. Furthermore, we illustrate the effectiveness of obtained results through several numerical examples.

Stabilization of logical control networks: an event-triggered control approach

This paper investigates the robust control invariance of probabilistic Boolean control networks via the technique of semi-tensor product. Some essential conditions are obtained to check whether the set is a robust event-triggered control invariant set (RETCIS) through the given event-triggeredcontroller (ETC). Moreover, an algorithm is designed for ETC to ensure that the given set is RETCIS. At last, a model of the apoptosis network shows the effectiveness of the main results.

Robust Control Invariance of Probabilistic Boolean Control Networks via Event-Triggered Control

This paper realizes global stabilization for probabilistic Boolean control networks (PBCNs) with event-triggered state feedback control (ETSFC). Via the semitensor product (STP) of matrices, PBCNs with ETSFC are converted into discrete-time algebraic systems, based on which a necessary and sufficient condition is derived for global stabilization of PBCNs. Furthermore, an algorithm is presented to design a class of feasible event-triggered state feedback controllers for global stabilization. Finally, an illustrative example shows the effectiveness of the obtained result.

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Event-Triggered Control for the Stabilization of Probabilistic Boolean Control Networks

This paper investigates the robust synchronization of drive-response Boolean control networks (BCNs) with disturbances via semi-tensor product of matrices. Firstly, the definition of robust synchronization is presented for the drive-response BCNs with disturbances. Then, based on the algebraic state space representation of drive-response BCNs, the robustly reachable states/sets are presented to investigate robust synchronization of disturbed BCNs. According to the set of robustly reachable states, some necessary and sufficient criteria are obtained for robust synchronization of drive-response BCNs with disturbances under a given state feedback controller. Finally, an illustrative example is presented to demonstrate the obtained theoretical results.

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On Robust Synchronization of Drive-Response Boolean Control Networks with Disturbances

Using the approach of semi-tensor product of matrices, this study studies a class of event-triggered control for finite evolutionary networked games, where the control only works at some certain individual states First, by identifying `control does not work' as a new specific control strategy, the controlled game dynamics is converted into an algebraic form Second, to make the game converge globally, two necessary and sufficient conditions for the existence of event-triggered control are obtained Meanwhile, a constructive procedure is proposed to design state feedback control strategy and an adjustment method is presented to minimise the control times Finally, the developed theory results are illustrated by a numerical method

https://ietresearch.onlinelibrary.wiley.com/doi/epdf/10.1049/iet-cta.2017.0014

Huaxiang Zhang

Papers

Semi-tensor product method to a class of event-triggered control for finite evolutionary networked games