Optimal Graph Laplacian

This paper provides a construction method of the nearest graph Laplacian to a matrix identified from measurement data of graph Laplacian dynamics that include biochemical systems, synchronization systems, and multi-agent systems. We consider the case where the network structure, i.e., the connection relationship of edges of a given graph, is known. A problem of finding the nearest graph Laplacian is formulated as a convex optimization problem. Thus, our problem can be solved using interior point methods. However, the complexity of each iteration by interior point methods is $O(n^6)$, where $n$ is the number of nodes of the network. That is, if $n$ is large, interior point methods cannot solve our problem within a practical time. To resolve this issue, we propose a simple and efficient algorithm with the calculation complexity $O(n^2)$. Simulation experiments demonstrate that our method is useful to perform data-driven modeling of graph Laplacian dynamics

A novel pinning observability strategy for large-scale Boolean networks and its applications

Observability is of biological and engineering significance for the study of large-scale Boolean networks (BNs), while sensors are commonly impossible or high-cost to be inflicted on all SVs. Taking an unobservable large-scale BNs into account, it is crucial to design an operably effective control strategy under which the controlled system achieves observability. In this paper, a novel pinning control strategy is developed for an unobservable BN. It takes advantage of the network structure (NS) with respect to (w.r.t.) $n$ SVs rather than the traditionary algebraic state space representation w.r.t. $2^n$ states. The application of NS information dramatically reduces the time complexity from $O(2^{2n})$ to $O(n2^{3\omega}+n^3)$, where $\omega$ and $p$ are respectively the largest out-degree of vertices and the number of senors. Moreover, the new approach is of benefit to identify the pinning nodes and concisely compute the corresponding feedback form for every pinning nodes. With regard to simulation, the T-LGL survival network with 18 SVs and T-cell receptor kinetics with 37 SVs and 3 input variables are investigated to demonstrate the availability of our theoretical results

Distributed Pinning Control Design for Probabilistic Boolean Networks

This paper investigates the stabilization of probabilistic Boolean networks (PBNs) via a novel pinning control strategy based on network structure. In a PBN, each node needs to choose a Boolean function from candidate Boolean function set at each time instance with certain probability. Owing to the stochasticity, the uniform state feedback controllers, which is independent of switching signal, might be out of work. Thereby, a criterion is derived to determine that under what condition uniform controllers can be applied, otherwise non-uniform controllers need to be utilized. Accordingly, an algorithm is designed to find a series of state feedback pinning controllers, under which such a PBN is stabilized to a prespecified steady state. It is worth pointing out that the pinning control used in this paper only requires local in-neighbors' information, rather than global information. Hence, it is also termed as distributed pinning control and reduces the computational complexity to a large extent. Profiting from this, it provides a potential to deal with some large-scale networks. Finally, the mammalian cell-cycle encountering a mutated phenotype is described as a PBN, and presented to demonstrate the obtained results