Local Synchronization of Interconnected Boolean Networks With Stochastic Disturbances

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.

Sequential Fusion Estimation for Multirate Complex Networks With Uniform Quantization: A Zonotopic Set-Membership Approach

In this article, the sequential fusion estimation problem is investigated for multirate complex networks (MRCNs) with uniformly quantized measurements. The process and measurement noises, which are unknown-yet-bounded (UYB), are restrained into a family of zonotopes, and the multiple sensors are allowed to have different sampling periods. To facilitate digital transmissions, the sensor measurements are uniformly quantized before being sent to the remote estimator. The purpose of this article is to design a sequential set-membership estimator such that, in the simultaneous presence of UYB noises, multirate samplings, and uniform quantization effects, the estimation error (after each measurement update) is confined to a zonotope with minimum F -radius at each time instant. By introducing certain virtual measurements, the MRCNs are first transformed into single-rate ones exhibiting a switching phenomenon. Then, by utilizing the properties of zonotopes, the desired zonotopes are derived, which contain the estimation error dynamics after each measurement update. Subsequently, the gain matrices of the sequential estimator are derived by minimizing the F -radii of these zonotopes, and the uniform boundedness is analyzed for the F -radius of the zonotope containing the estimation error after all measurement updates. Furthermore, sufficient conditions are derived to ensure the existence of the desired uniform upper/lower bounds. Finally, an illustrated example is proposed to show the effectiveness of the proposed sequential fusion estimation method.

Sampled-Data-Based Secure Synchronization Control for Chaotic Lur'e Systems Subject to Denial-of-Service Attacks

This article investigates the sampled-data-based secure synchronization control problem for chaotic Lur'e systems subject to power-constrained denial-of-service (DoS) attacks, which can block data packets' transmission in communication channels. To eliminate the adverse effects, a resilient sampled data control scheme consisting of a secure controller and communication protocol is designed by considering the attack signals and periodic sampling mechanism simultaneously. Then, a novel index, i.e., the maximum anti-attack ratio, is proposed to measure the secure level. On this basis, a multi-interval-dependent functional is established for the resulting closed-loop system model. The main feature of the developed functional lies in that it can fully use the information of resilient sampling intervals and DoS attacks. In combination with the convex combination method, discrete-time Lyapunov theory, and some inequality estimate techniques, two sufficient conditions are, respectively, derived to achieve sampled-data-based secure synchronization of drive-response systems against DoS attacks. Compared with the existing Lyapunov functionals, the advantages of the proposed multi-interval-dependent functional are analyzed in detail. Finally, a synchronization example and an application to secure communication are provided to display the effectiveness and validity of the obtained results.

Weak Stabilization of Boolean Networks Under State-Flipped Control

In this brief, stabilization of Boolean networks (BNs) by flipping a subset of nodes is considered, here we call such action state-flipped control. The state-flipped control implies that the logical variables of certain nodes are flipped from 1 to 0 or 0 to 1 as time flows. Under state-flipped control on certain nodes, a state-flipped-transition matrix is defined to describe the impact on the state transition space. Weak stabilization is first defined and then some criteria are presented to judge the same. An algorithm is proposed to find a stabilizing kernel such that BNs can achieve weak stabilization to the desired state with in-degree more than 0. By defining a reachable set, another approach is proposed to verify weak stabilization, and an algorithm is given to obtain a flip sequence steering an initial state to a given target state. Subsequently, the issue of finding flip sequences to steer BNs from weak stabilization to global stabilization is addressed. In addition, a model-free reinforcement algorithm, namely the Q -learning ( [Formula: see text]) algorithm, is developed to find flip sequences to achieve global stabilization. Finally, several numerical examples are given to illustrate the obtained theoretical results.

Stabilizing Large-Scale Probabilistic Boolean Networks by Pinning Control

This article aims to stabilize probabilistic Boolean networks (PBNs) via a novel pinning control strategy. In a PBN, the state evolution of each gene switches among a collection of candidate Boolean functions with preassigned probability distributions, which govern the activation frequency of each Boolean function. Due to the existence of stochasticity, the mode-independent pinning controller might be disabled. Thus, both mode-independent and mode-dependent pinning controller are required here. Moreover, a criterion is derived to determine whether mode-independent controllers are applicable while the pinned nodes are given. It is worth pointing out that this pinning control is based on the n×n network structure rather than 2ⁿ ×2ⁿ state transition matrix. Therefore, compared with the existing results, this pinning control strategy is more practicable and has the ability to handle large-scale networks, especially sparsely connected networks. To demonstrate the effectiveness of the designed control scheme, a PBN that describes the mammalian cell-cycle encountering a mutated phenotype is discussed as a simulation.

State Estimation for Probabilistic Boolean Networks via Outputs Observation

This article studies the state estimation for probabilistic Boolean networks via observing output sequences. Detectability describes the ability of an observer to uniquely estimate system states. By defining the probability of an observed output sequence, a new concept called detectability measure is proposed. The detectability measure is defined as the limit of the sum of probabilities of all detectable output sequences when the length of output sequences goes to infinity, and it can be regarded as a quantitative assessment of state estimation. A stochastic state estimator is designed by defining a corresponding nondeterministic stochastic finite automaton, which combines the information of state estimation and probability of output sequences. The proposed concept of detectability measure further performs the quantitative analysis on detectability. Furthermore, by defining a Markov chain, the calculation of detectability measure is converted to the calculation of the sum of probabilities of certain specific states in Markov chain. Finally, numerical examples are given to illustrate the obtained theoretical results.

Resolution of Fuzzy Relational Inequalities with Boolean Semi-Tensor Product Composition

Resolution of fuzzy relational inequalities (FRIs) plays a significant role in decision-making, image compression and fuzzy control. This paper studies the resolution of a kind of FRIs with Boolean semi-tensor product composition. First, by resorting to the column stacking technique, the equivalent form of FRIs with Boolean semi-tensor product composition is obtained, which is a system of FRIs (SFRIs) with max–min composition. Second, based on the semi-tensor product method, all the solutions to FRIs with Boolean semi-tensor product composition are obtained by finding all possible parameter set solutions. Finally, a general procedure is developed for the resolution of FRIs with Boolean semi-tensor product composition. Two illustrative examples are worked out to show the effectiveness of the obtained new results.

Asymptotical Feedback Set Stabilization of Probabilistic Boolean Control Networks

In this article, we investigate the asymptotical feedback set stabilization in distribution of probabilistic Boolean control networks (PBCNs). We prove that a PBCN is asymptotically feedback stabilizable to a given subset if and only if (iff) it constitutes asymptotically feedback stabilizable to the largest control-invariant subset (LCIS) contained in this subset. We proposed an algorithm to calculate the LCIS contained in any given subset with the necessary and sufficient condition for asymptotical set stabilizability in terms of obtaining the reachability matrix. In addition, we propose a method to design stabilizing feedback based on a state-space partition. Finally, the results were applied to solve asymptotical feedback output tracking and asymptotical feedback synchronization of PBCNs. Examples were detailed to demonstrate the feasibility of the proposed method and results.

On Optimal Time-Varying Feedback Controllability for Probabilistic Boolean Control Networks

This brief studies controllability for probabilistic Boolean control network (PBCN) with time-varying feedback control laws. The concept of feedback controllability with an arbitrary probability for PBCNs is formulated first, and a control problem to maximize the probability of time-varying feedback controllability is investigated afterward. By introducing semitensor product (STP) technique, an equivalent multistage decision problem is deduced, and then a novel optimization algorithm is proposed to obtain the maximum probability of controllability and the corresponding optimal feedback law simultaneously. The advantages of the time-varying optimal controller obtained by the proposed algorithm, compared to the time-invariant one, are illustrated by numerical simulations.