Necessary and Sufficient Conditions on Pinning Stabilization for Stochastic Boolean Networks

Finite-Time Stabilizers for Large-Scale Stochastic Boolean Networks

This article presents a distributed pinning control strategy aimed at achieving global stabilization of Markovian jump Boolean control networks. The strategy relies on network matrix information to choose controlled nodes and adopts the algebraic state space representation approach for designing pinning controllers. Initially, a sufficient criterion is established to verify the global stability of a given Markovian jump Boolean network (MJBN) with probability one at a specific state within finite time. To stabilize an unstable MJBN at a predetermined state, the selection of pinned nodes involves removing the minimal number of entries, ensuring that the network matrix transforms into a strictly lower (or upper) triangular form. For each pinned node, two types of state feedback controllers are developed: 1) mode-dependent and 2) mode-independent, with a focus on designing a minimally updating controller. The choice of controller type is determined by the feasibility condition of the mode-dependent pinning controller, which is articulated through the solvability of matrix equations. Finally, the theoretical results are illustrated by studying the T cell large granular lymphocyte survival signaling network consisting of 54 genes and 6 stimuli.

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.

Set stabilization of logical control networks: A minimum node control approach

In network systems, control using minimum nodes or pinning control can be effectively used for stabilization problems to cut down the cost of control. In this paper, we investigate the set stabilization problem of logical control networks. In particular, we study the set stabilization problem of probabilistic Boolean networks (PBNs) and probabilistic Boolean control networks (PBCNs) via controlling minimal nodes. Firstly, an algorithm is given to search for the minimum index set of pinning nodes. Then, based on the analysis of its high computational complexity, we present optimized algorithms with lower computational complexity to ascertain the network control using minimum node sets. Moreover, some sufficient and necessary conditions are proposed to ensure the feasibility and effectiveness of the proposed algorithms. Furthermore, a theorem is presented for PBCNs to devise all state-feedback controllers corresponding to the set of pinning nodes. Finally, two models of gene regulatory networks are considered to show the efficacy of obtained results.

Asynchronous Control of Stochastic Switched Boolean Control Networks With Piecewise-Homogeneous Dwell Time

In this article, the l₁ -induced performance of the stochastic switched Boolean control network (BCN) is investigated. The switched signal is considered to follow a time-varying probability distribution, the switching of which is considered to have a random dwell time. The asynchronous state feedback control (SFC) is studied to achieve the control objective. This kind of control can avoid the failure of the control due to the inconsistency between the system mode and the control mode, so the results obtained are more general. Using the semitensor product of matrices, the algebraic form of the considered BCN is represented. Under this framework, sufficient conditions are obtained to ensure that the closed-loop system is stochastic stabilized with a prescribed l₁ -induced performance level γ . Parameters can be solved by inequalities. In addition, when the dwell time converges to infinity, the probability distribution of the switched signal becomes fixed. Necessary and sufficient conditions are presented to ensure the stabilization of the closed system under asynchronous SFC as well as the design of the asynchronous SFC. Then, sufficient condition is obtained for the prescribed l₁ -induced performance level. Examples are presented to show the effectiveness of the obtained 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.

Resilient Asynchronous State Estimation for Markovian Jump Neural Networks Subject to Stochastic Nonlinearities and Sensor Saturations

This article studies the problem of dissipativity-based asynchronous state estimation for a class of discrete-time Markov jump neural networks subject to randomly occurring nonlinearities, sensor saturations, and stochastic parameter uncertainties. First, two stochastic nonlinearities occurring in the system are described by statistical means and obey two Bernoulli processes independently. Then, the hidden Markov model is used to characterize the real communication environment closely between the designed estimator and the system model due to the networked-induced phenomenons that also lead to randomly occurring parametric uncertainties of the estimator considered modeled by two Bernoulli processes. A new criterion is established to guarantee that the resulting error system is stochastically stable with predefined dissipativity performance. Finally, we provide a simulation example to validate the theoretical analysis.

Optimal Asynchronous Stabilization for Boolean Control Networks With Lebesgue Sampling

Using semitensor products (STPs) of matrices, sampled-data state-feedback control (SDSFC) with the Lebesgue sampling region S_τ is first considered to stabilize a Boolean control network (BCN) to a fixed point, under which a necessary and sufficient condition for stabilization is obtained when the considered BCN with the Lebesgue sampling region is converted to a switching system. Meanwhile, the corresponding asynchronous SDSFC gains are designed from a sequence of reachable sets. Then, an algorithm is shown to obtain the minimal number of controlling times and all states globally stabilize to the desired state with the fastest convergence rate under the minimal number of controlling times. Besides, the results have been extended to p Lebesgue sampling regions S_τi, i=1,2,…, p . And some results are presented for this situation, including the necessary and sufficient conditions stabilization under the p Lebesgue sampling regions, the asynchronous SDSFC gains, and the algorithm to obtain the optimal states sampling regions. Examples are listed to show the effectiveness of our results, and the biological example indicates that the SDSFC with Lebesgue sampling is also suitable for stochastic BCNs.

Sampled-Data Stabilization for Boolean Control Networks With Infinite Stochastic Sampling

Sampled-data state feedback control with stochastic sampling periods for Boolean control networks (BCNs) is investigated in this article. First, based on the algebraic form of BCNs, stochastic sampled-data state feedback control is applied to stabilize the considered system to a fixed point or a given set. Two kinds of distributions of stochastic sampling periods are considered. First, the distribution of sampling periods is assumed to be independent identically distributed (i.i.d.) in the range of any positive integers and the second distribution of sampling periods is assumed to follow an infinite Markov process. A BCN with infinite stochastic sampling periods proves to be equivalent to a finite stochastic switched system, based on which, necessary and sufficient conditions are given to guarantee the stabilization and set stabilization of the BCN with stochastic sampling periods. For the first one, two algorithms are given to guarantee the stabilization and set stabilization of the considered system. For the second one, necessary and sufficient conditions are all presented in the linear programming form. Examples are listed to show the effectiveness of our results.

HMM-Based Asynchronous H∞ Filtering for Fuzzy Singular Markovian Switching Systems With Retarded Time-Varying Delays

This article reports our study on asynchronous H_∞ filtering for fuzzy singular Markovian switching systems with retarded time-varying delays via the Takagi-Sugeno fuzzy control technique. The devised parallel distributed compensation fuzzy filter modes are described by a hidden Markovian model, which runs asynchronously with that of the original fuzzy singular Markovian switching delayed system. The fuzzy asynchronous filtering dealt with in this article contains synchronous and mode-independent filtering as special cases. Novel admissibility and filtering conditions are derived in terms of linear matrix inequalities so as to ensure the stochastic admissibility and the H_∞ performance level. Simulation examples including a single-link robot arm are employed to demonstrate the correctness and effectiveness of the proposed fuzzy asynchronous filtering technique.

Finite-Time L2-Gain Asynchronous Control for Continuous-Time Positive Hidden Markov Jump Systems via T-S Fuzzy Model Approach

This article investigates the finite-time asynchronous control problem for continuous-time positive hidden Markov jump systems (HMJSs) by using the Takagi-Sugeno fuzzy model method. Different from the existing methods, the Markov jump systems under consideration are considered with the hidden Markov model in the continuous-time case, that is, the Markov model consists of the hidden state and the observed state. We aim to derive a suitable controller that depends on the observation mode which makes the closed-loop fuzzy HMJSs be stochastically finite-time bounded and positive, and fulfill the given L₂ performance index. Applying the stochastic Lyapunov-Krasovskii functional (SLKF) methods, we establish sufficient conditions to obtain the finite-time state-feedback controller. Finally, a Lotka-Volterra population model is used to show the feasibility and validity of the main results.