57 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
Minimum observability of probabilistic Boolean networks
This paper studies the minimum observability of probabilistic Boolean
networks (PBNs), the main objective of which is to add the fewest measurements
to make an unobservable PBN become observable. First of all, the algebraic form
of a PBN is established with the help of semi-tensor product (STP) of matrices.
By combining the algebraic forms of two identical PBNs into a parallel system,
a method to search the states that need to be H-distinguishable is proposed
based on the robust set reachability technique. Secondly, a necessary and
sufficient condition is given to find the minimum measurements such that a
given set can be H-distinguishable. Moreover, by comparing the numbers of
measurements for all the feasible H-distinguishable state sets, the least
measurements that make the system observable are gained. Finally, an example is
given to verify the validity of the obtained results
Recommended from our members
State Estimation for Stochastic Time-Varying Boolean Networks
National Key R&D Program of China (Grant Number: 2018YFB1003800); 10.13039/501100001809-National Natural Science Foundation of China (Grant Number: 61673110, 61873148 and 61933007); Shanghai Sailing Program (Grant Number: 19YF1402400); 10.13039/501100006249-Donghua University (Grant Number: 104-07-0053019); Alexander von Humboldt Foundation of Germany
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