6 research outputs found
Pinning Controllability of Boolean Networks: Application to Large-Scale Genetic Networks
This paper focuses on making up for the drawback of recent results about
pinning controllability of Boolean control networks (BCNs). First of all, a
sufficient criterion is derived for the controllability of BCNs. Based on this
criterion, to make an arbitrary BCN be controllable, an efficient method is
developed to design the feasible pinning strategy which involves identifying
pinning nodes and determining control form. Comparing with the traditional
pinning approach of which time complexity is , the time complexity
of this pinning method is reduced to with the number
of state variables , that of input variables and the largest in-degree
among all nodes . Since a practical genetic network is always sparsely
connected, is far less than despite its size being large-scale.
Finally, a T-cell receptor kinetics model with state nodes and input
nodes is considered to demonstrate the application of obtained theoretical
results
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.) SVs rather
than the traditionary algebraic state space representation w.r.t. states.
The application of NS information dramatically reduces the time complexity from
to , where and 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
On quotients of Boolean control networks
In this paper, we focus on the study of quotients of Boolean control networks
(BCNs) with the motivation that they might serve as smaller models that still
carry enough information about the original network. Given a BCN and an
equivalence relation on the state set, we consider a labeled transition system
that is generated by the BCN. The resulting quotient transition system then
naturally captures the quotient dynamics of the BCN concerned. We therefore
develop a method for constructing a Boolean system that behaves equivalently to
the resulting quotient transition system. The use of the obtained quotient
system for control design is discussed and we show that for BCNs, controller
synthesis can be done by first designing a controller for a quotient and
subsequently lifting it to the original model. We finally demonstrate the
applicability of the proposed techniques on a biological example
A New Approach to Pinning Control of Boolean Networks
Boolean networks (BNs) are discrete-time systems where nodes are
inter-connected (here we call such connection rule among nodes as network
structure), and the dynamics of each gene node is determined by logical
functions. In this paper, we propose a new approach on pinning control design
for global stabilization of BNs based on BNs' network structure, named as
network-structure-based distributed pinning control. By deleting the minimum
number of edges, the network structure becomes acyclic. Then, an efficient
distributed pinning control is designed to achieve global stabilization.
Compared with existing literature, the design of pinning control is not based
on the state transition matrix of BNs. Hence, the computational complexity in
this paper is reduced from to , where is
the number of nodes and is the largest number of in-neighbors of
nodes. In addition, without using state transition matrix, global state
information is no longer needed, the design of pinning control is just based on
neighbors' local information, which is easier to be implemented. The proposed
method is well demonstrated by several biological networks with different
sizes. The results are shown to be simple and concise, while the traditional
pinning control can not be applied for BNs with such a large dimension
Disturbance Decoupling and Instantaneous Fault Detection in Boolean Control Networks
The literature available on disturbance decoupling (DD) of Boolean control
network (BCN) is built on a restrictive notion of what constitutes as
disturbance decoupling. The results available on necessary and sufficient
conditions are of limited applicability because of their stringent
requirements. This work tries to expand the notion of DD in BCN to incorporate
a larger number of systems deemed unsuitable for DD. The methods available are
further restrictive in the sense that system is forced to follow trajectory
unaffected by the disturbances rather than decoupling disturbances while the
system follows its natural course. Some sufficient conditions are provided
under which the problem can be addressed. This work tries to establish the
notion of disturbance decoupling via feedback control,analogous to the
classical control theory. This approach though, is not limited to DD problems
and can be extended to the general control problems of BCNs. Determination of
observability, which is sufficient for the fault detection, is proven to be
NP-hard for Boolean Control Network. Algorithms based on reconstructability, a
necessary condition, of BCN turn out to be of exponential complexity in
general.In such cases it makes sense to search for the availability of some
special structure in BCN that could be utilized for fault detection with
minimal computational efforts. An attempt is made to address this problem by
introducing instantaneous fault detection (IFD) and providing necessary and
sufficient conditions for the same. Later necessary and sufficient conditions
are proposed for solving the problem of instantaneous fault detection along
with disturbance decoupling using a single controller