Set Stabilization of Probabilistic Boolean Control Networks: A Sampled-Data Control Approach

Attractor-Transition Control of Complex Biological Networks: A Constant Control Approach

This article presents attractor-transition control of complex biological networks represented by Boolean networks (BNs) wherein the BN is steered from a prescribed initial attractor toward a desired one. The proposed approach leverages the similarity between attractors and Boolean algebraic properties embedded in the underlying state transition equations. To enhance the clarity of expression regarding stabilization toward the desired attractor, a simple coordinate transformation is performed on the considered BN. Based on the characteristics of transformed state equations, self-stabilizing state variables requiring no control efforts are derived in the first. Next, by applying the feedback vertex set (FVS) control scheme, control inputs stabilizing the remaining state variables are determined. The proposed control scheme exhibits versatility by accommodating both fixed-point and cyclic attractors. We validate the effectiveness of the proposed strategy through extensive numerical experiments conducted on random BNs as well as complex biological systems. In adherence to the reproducible research initiative, detailed results of numerical experiments and all the implementation codes are provided on the authors' website: https://github.com/choonlog/AttractorTransition.

Stability Analysis of Sampled-Data Systems Based on Sawtooth-Characteristic-Based Hierarchical Integral Inequality

The aim of this article is to investigate the stability of sampled-data systems (SDSs) by introducing a sawtooth-characteristic-based hierarchical integral inequality (SCBHII) and to obtain the maximum allowable sampling period that maintains the stability of the system. First, by associating the sawtooth characteristics of the input delay in SDSs with free matrices, an SCBHII is proposed; its accuracy improves as the hierarchy increases. Subsequently, a high-order two-sided looped-functional, which considers both the sampling multi-integral states and the sawtooth pattern, is introduced to cater to the aforementioned inequality. In addition, the system variables are augmented by sawtooth pattern-related terms, which eliminates the need for additional secondary processing when determining the negative-definiteness of derivatives with high-order terms. By combining the high-order two-sided looped-functional with the proposed SCBHII, a stability criterion for SDSs with reduced conservatism is achieved, presented in the form of linear matrix inequalities. The proposed inequality technique and the stability criterion are shown to be effective and superior through three numerical examples and a real-world simplified power market model.

Necessary and Sufficient Conditions for Event-Triggered Set Stabilizability of Markovian Jump Logical Networks

This technical paper utilizes the Lyapunov theory to characterize the event-triggered set stabilizability of Markovian jump logical control networks (MJLCNs). Whereas the existing result for checking the set stabilizability of MJLCNs is only sufficient, this technical paper further establishes its necessary and sufficient condition. First, the Lyapunov function is established to describe the set stabilizability of MJLCNs necessarily and sufficiently by combining recurrent switching modes and desired state set. Then, the triggering condition and the input updating mechanism are designed regarding the value change of the Lyapunov function. Finally, the effectiveness of theoretical results is demonstrated by a biological example concerning the lac operon in Escherichia coli.

Event-Triggered Output-Feedback Control for Synchronization of Delayed Neural Networks

This article proposes a novel discrete event-triggered scheme (DETS) for the synchronization of delayed neural networks (NNs) using the dynamic output-feedback controller (DOFC). The proposed DETS uses both the current and past samples to determine the next trigger, unlike the traditional event-triggered scheme (ETS) that uses only the current sample. The proposed DETS is employed in a dual setup for two network channels to significantly reduce redundant data transmission. A DOFC is designed to achieve the synchronization of the NNs. Stability criteria of the synchronisation error system are derived based on the Lyapunov-Krasovskii functional method, and the co-design of the DOFC and DETS parameters are accomplished using the Cone-complementarity linearization (CCL) approach. The effectiveness and advantages of the proposed method are illustrated considering an example of the chaotic system.

Stabilization of Markovian Jump Boolean Control Networks via Sampled-Data Control

In this article, we study the finite-time stabilization and the asymptotic stabilization with probability one of Markovian jump Boolean control networks (MJBCNs) by sampled-data state feedback controls (SDSFCs). Based on the semi-tensor product (STP), we introduce an augmented variable multiplied by the vector form of the switching signal and the state of MJBCN. We find that under SDSFC, the sequence of the states of the augmented variable at sampling instants satisfies the Markov property. Based on the convergences of the switching signal and the augmented variable, we obtain the sufficient and necessary criteria for the finite-time stabilization and the asymptotic stabilization of MJBCNs by SDSFCs, respectively. Moreover, for the two kinds of stabilization, the feedback matrices of SDSFCs are constructed, respectively. Finally, the obtained results are applied to an apoptosis network and a model of the lactose operon in the Escherichia Coli.

Control Design With Optimization for Fuzzy Steering-by-Wire System Based on Nash Game Theory

In this article, we apply a high-order control to a dynamical system with uncertainty. There are two characteristics. First, the uncertain part, which is time-varying but bounded, is described in a fuzzy aspect. Specifically, the uncertainty lies within a fuzzy set and the bound is regarded as a fuzzy number. Second, the systems are uniformly bounded and uniformly ultimately bounded with a deterministic controller based on the Lyapunov theory. To obtain better system performance and lower control input, we apply the noncooperative game theory to optimize the parameters by establishing a Nash game. Then, the D-operation is proposed for the uncertainty related to fuzzy numbers. Finally, we perform the numerical simulations of the steering-by-wire system for verification.

Stability and Stabilization in Probability of Probabilistic Boolean Networks

This article studies the stability in probability of probabilistic Boolean networks and stabilization in the probability of probabilistic Boolean control networks. To simulate more realistic cellular systems, the probability of stability/stabilization is not required to be a strict one. In this situation, the target state is indefinite to have a probability of transferring to itself. Thus, it is a challenging extension of the traditional probability-one problem, in which the self-transfer probability of the target state must be one. Some necessary and sufficient conditions are proposed via the semitensor product of matrices. Illustrative examples are also given to show the effectiveness of the derived results.