2,214 research outputs found
Stability Analysis and Control of Several Classes of Logical Dynamic Systems and the Applications in Game Theory
With the rapid development of complex networks, logical dynamic systems have been
commonly used mathematical models for simulating Genetic Regulatory Networks (GRNs)
and Networked Evolutionary Games (NEGs), which have attracted considerable attention
from biology, economy and many other fields. By resorting to the Semi-Tensor Product
(STP) of matrices, logical dynamic systems can be equivalently converted into discrete time
linear systems with algebraic forms. Based on that, this thesis analyzes the stability and
studies the control design problems of several classes of logical dynamic systems. Moreover,
the obtained results are applied to investigate the control and optimization problems of
NEGs. The main results of this thesis are the following.
• The stability and event-triggered control for a class of k-Valued Logical Networks
(KVLNs) with time delays are studied. First, some necessary and sufficient con-
ditions are obtained to detect the stability of Delayed k-Valued Logical Networks
(DKVLNs). Second, the global stabilization problem under event-triggered control is
considered, and some necessary and sufficient conditions are presented for the sta-
bilization of Delayed k-Valued Logical Control Networks (DKVLCNs). Moreover, an
algorithm is proposed to construct all the event-triggered state feedback controllers
via antecedence solution technique.
• The robust control invariance and robust set stabilization problems for a class of Mix-
Valued Logical Control Networks (MVLCNs) with disturbances are studied. First, a
calculation method for the Largest Robust Control Invariant Set (LRCIS) contained
in a given set is introduced. Second, based on the Robust Control Invariant Subset
(RCIS) obtained, the robust set stabilization of MVLCNs is discussed, and some
new results are presented. Furthermore, the design algorithm of time-optimal state
feedback stabilizers via antecedence solution technique is derived.
• The robust set stability and robust set stabilization problems for a class of Probabilis-
tic Boolean Control Networks (PBCNs) with disturbances are studied. An algorithm
to determine the Largest Robust Invariant Set (LRIS) with probability 1 of a given
set for a Probabilistic Boolean Network (PBN) is proposed, and the necessary and
sufficient conditions to detect whether the PBN is globally finite-time stable to this
invariant set with probability 1 are established. Then, the PBNs with control inputs
are considered, and an algorithm for LRCIS with probability 1 is provided, based on
which, some necessary and sufficient conditions for finite-time robust set stabiliza-
tion with probability 1 of PBCNs are presented. Furthermore, the design scheme of
time-optimal state feedback stabilizers via antecedence solution technique is derived.
• The stabilization and set stabilization problems for a class of Switched Boolean Con-
trol Networks (SBCNs) with periodic switching signal are studied. First, algebraic
forms are constructed for SBCNs with periodic switching signal. Second, based on
the algebraic formulations, the stabilization and set stabilization of SBCNs with peri-
odic switching signal are discussed, and some new results are presented. Furthermore,
constructive procedure of open loop controllers is given, and the design algorithms of
switching-signal-dependent state feedback controllers via antecedence solution tech-
nique are derived.
• The dynamics and control problems for a class of NEGs with time-invariant delay in
strategies are studied. First, algebraic forms are constructed for Delayed Networked
Evolutionary Games (DNEGs). Second, based on the algebraic formulations, some
necessary and sufficient conditions for the global convergence of desired strategy pro-
file under a state feedback event-triggered controller are presented. Furthermore, the
constructive procedure and the number of all valid event-triggered state feedback
controllers are derived, which can make the game converge globally.
• The evolutionary dynamics and optimization problems of the networked evolutionary
boxed pig games with the mechanism of passive reward and punishment are studied.
First, an algorithm is provided to construct the algebraic formulation for the dynamics
of this kind of games. Then, the impact of reward and punishment parameters on the
final cooperation level of the whole network is discussed
Robust set stabilization of Boolean control networks with impulsive effects
This paper addresses the robust set stabilization problem of Boolean control networks (BCNs) with impulsive effects via the semi-tensor product method. Firstly, the closed-loop system consisting of a BCN with impulsive effects and a given state feedback control is converted into an algebraic form. Secondly, based on the algebraic form, some necessary and sufficient conditions are presented for the robust set stabilization of BCNs with impulsive effects under a given state feedback control and a free-form control sequence, respectively. Thirdly, as applications, some necessary and sufficient conditions are presented for robust partial stabilization and robust output tracking of BCNs with impulsive effects, respectively. The study of two illustrative examples shows that the obtained new results are effective
On delayed genetic regulatory networks with polytopic uncertainties: Robust stability analysis
Copyright [2008] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, we investigate the robust asymptotic stability problem of genetic regulatory networks with time-varying delays and polytopic parameter uncertainties. Both cases of differentiable and nondifferentiable time-delays are considered, and the convex polytopic description is utilized to characterize the genetic network model uncertainties. By using a Lyapunov functional approach and linear matrix inequality (LMI) techniques, the stability criteria for the uncertain delayed genetic networks are established in the form of LMIs, which can be readily verified by using standard numerical software. An important feature of the results reported here is that all the stability conditions are dependent on the upper and lower bounds of the delays, which is made possible by using up-to-date techniques for achieving delay dependence. Another feature of the results lies in that a novel Lyapunov functional dependent on the uncertain parameters is utilized, which renders the results to be potentially less conservative than those obtained via a fixed Lyapunov functional for the entire uncertainty domain. A genetic network example is employed to illustrate the applicability and usefulness of the developed theoretical results
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Filtering for nonlinear genetic regulatory networks with stochastic disturbances
In this paper, the filtering problem is investigated for nonlinear genetic regulatory networks with stochastic disturbances and time delays, where the nonlinear function describing the feedback regulation is assumed to satisfy the sector condition, the stochastic perturbation is in the form of a scalar Brownian motion, and the time delays exist in both the translation process and the feedback regulation process. The purpose of the addressed filtering problem is to estimate the true concentrations of the mRNA and protein. Specifically, we are interested in designing a linear filter such that, in the presence of time delays, stochastic disturbances as well as sector nonlinearities, the filtering dynamics of state estimation for the stochastic genetic regulatory network is exponentially mean square stable with a prescribed decay rate lower bound beta. By using the linear matrix inequality (LMI) technique, sufficient conditions are first derived for ensuring the desired filtering performance for the gene regulatory model, and the filter gain is then characterized in terms of the solution to an LMI, which can be easily solved by using standard software packages. A simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures
Amplitude chimeras and chimera death in dynamical networks
We find chimera states with respect to amplitude dynamics in a network of
Stuart-Landau oscillators. These partially coherent and partially incoherent
spatio-temporal patterns appear due to the interplay of nonlocal network
topology and symmetry-breaking coupling. As the coupling range is increased,
the oscillations are quenched, amplitude chimeras disappear and the network
enters a symmetry-breaking stationary state. This particular regime is a novel
pattern which we call chimera death. It is characterized by the coexistence of
spatially coherent and incoherent inhomogeneous steady states and therefore
combines the features of chimera state and oscillation death. Additionally, we
show two different transition scenarios from amplitude chimera to chimera
death. Moreover, for amplitude chimeras we uncover the mechanism of transition
towards in-phase synchronized regime and discuss the role of initial
conditions
Chimera states in complex networks: interplay of fractal topology and delay
Chimera states are an example of intriguing partial synchronization patterns
emerging in networks of identical oscillators. They consist of spatially
coexisting domains of coherent (synchronized) and incoherent (desynchronized)
dynamics. We analyze chimera states in networks of Van der Pol oscillators with
hierarchical connectivities, and elaborate the role of time delay introduced in
the coupling term. In the parameter plane of coupling strength and delay time
we find tongue-like regions of existence of chimera states alternating with
regions of existence of coherent travelling waves. We demonstrate that by
varying the time delay one can deliberately stabilize desired spatio-temporal
patterns in the system.Comment: arXiv admin note: text overlap with arXiv:1603.0017
On robust stability of stochastic genetic regulatory networks with time delays: A delay fractioning approach
Copyright [2009] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.Robust stability serves as an important regulation mechanism in system biology and synthetic biology. In this paper, the robust stability analysis problem is investigated for a class of nonlinear delayed genetic regulatory networks with parameter uncertainties and stochastic perturbations. The nonlinear function describing the feedback regulation satisfies the sector condition, the time delays exist in both translation and feedback regulation processes, and the state-dependent Brownian motions are introduced to reflect the inherent intrinsic and extrinsic noise perturbations. The purpose of the addressed stability analysis problem is to establish some easy-to-verify conditions under which the dynamics of the true concentrations of the messenger ribonucleic acid (mRNA) and protein is asymptotically stable irrespective of the norm-bounded modeling errors. By utilizing a new Lyapunov functional based on the idea of “delay fractioning”, we employ the linear matrix inequality (LMI) technique to derive delay-dependent sufficient conditions ensuring the robust stability of the gene regulatory networks. Note that the obtained results are formulated in terms of LMIs that can easily be solved using standard software packages. Simulation examples are exploited to illustrate the effectiveness of the proposed design procedures
Delayed Dynamical Systems: Networks, Chimeras and Reservoir Computing
We present a systematic approach to reveal the correspondence between time
delay dynamics and networks of coupled oscillators. After early demonstrations
of the usefulness of spatio-temporal representations of time-delay system
dynamics, extensive research on optoelectronic feedback loops has revealed
their immense potential for realizing complex system dynamics such as chimeras
in rings of coupled oscillators and applications to reservoir computing.
Delayed dynamical systems have been enriched in recent years through the
application of digital signal processing techniques. Very recently, we have
showed that one can significantly extend the capabilities and implement
networks with arbitrary topologies through the use of field programmable gate
arrays (FPGAs). This architecture allows the design of appropriate filters and
multiple time delays which greatly extend the possibilities for exploring
synchronization patterns in arbitrary topological networks. This has enabled us
to explore complex dynamics on networks with nodes that can be perfectly
identical, introduce parameter heterogeneities and multiple time delays, as
well as change network topologies to control the formation and evolution of
patterns of synchrony
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