scholarly journals Robust Invariant Set Analysis of Boolean Networks

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Bowen Li ◽  
Jungang Lou ◽  
Yang Liu ◽  
Zhen Wang
Keyword(s):  
Fixed Point ◽  
Output Feedback ◽  
Invariant Set ◽  
Boolean Networks ◽  
Sufficient Condition ◽  
Lac Operon ◽  
Feedback Controllers ◽  
Control Networks ◽  
E Coli ◽  
Necessary And Sufficient

In this paper, the robust invariant set (RIS) of Boolean (control) networks with disturbances is investigated. First, for a given fixed point, consider a special set called immediate neighborhoods of the fixed point; then a discrete derivative of Boolean functions at the fixed point is used to analyze the robust invariance, based on which a sufficient condition is obtained. Second, for more general sets, the robust output control invariant set (ROCIS) of Boolean control networks (BCNs) is investigated by semitensor product (STP) of matrices. Then, under a given output feedback controller, we obtain a necessary and sufficient condition to check whether a given set is robust control invariant set (RCIS). Furthermore, output feedback controllers are designed to make a set to be a RCIS. Finally, the proposed methods are illustrated by a reduced model of the lac operon in E. coli.

scholarly journals Event-Triggered Control for the Stabilization of Probabilistic Boolean Control Networks

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Shiyong Zhu ◽  
Jungang Lou ◽  
Yang Liu ◽  
Yuanyuan Li ◽  
Zhen Wang
Keyword(s):  
Discrete Time ◽  
State Feedback ◽  
State Feedback Control ◽  
Sufficient Condition ◽  
Global Stabilization ◽  
Necessary And Sufficient Condition ◽  
Feedback Controllers ◽  
Control Networks ◽  
Necessary And Sufficient ◽  
Event Triggered

This paper realizes global stabilization for probabilistic Boolean control networks (PBCNs) with event-triggered state feedback control (ETSFC). Via the semitensor product (STP) of matrices, PBCNs with ETSFC are converted into discrete-time algebraic systems, based on which a necessary and sufficient condition is derived for global stabilization of PBCNs. Furthermore, an algorithm is presented to design a class of feasible event-triggered state feedback controllers for global stabilization. Finally, an illustrative example shows the effectiveness of the obtained result.

Stabilization via output feedback for a type of uncertain time-varying port-controlled Hamiltonian system based on linear matrix inequality approach

2019 ◽  
Vol 41 (15) ◽  
pp. 4387-4397 ◽  
Author(s):  
Tianyi Zhao ◽  
Guangren Duan
Keyword(s):  
Output Feedback ◽  
Control Method ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Time Varying ◽  
Quadratic Stability ◽  
Pch System ◽  
Uncertain Time ◽  
Necessary And Sufficient ◽  
Output Equation

In this paper, the control of a type of uncertain time-varying port-controlled Hamiltonian (PCH) systems is investigated. As a matter of fact, the control method proposed in this paper is not based on passivity of PCH systems, but a general output equation is introduced inspired by the measured “information” in the systems in traditional control system theory and the problem of output feedback is considered. In this paper, a conception of p-quadratic stability of the type of PCH system is introduced, and the relationship between p-quadratic stability and Lyapunov stability is pointed out. Then, the problem for p-quadratic stabilization of the proposed system via static output feedback is solved in the following two cases, respectively. For the case of unperturbed output equation, a necessary and sufficient condition for the problem is derived in terms of two groups of linear matrix inequalities (LMIs); for the general case that the output equation also has time-varying perturbations, a sufficient condition for p-quadratic stable of closed-loop system is also given in terms of LMIs. It is also shown that conservatism can be greatly reduced when the perturbation variables in the uncertain PCH systems are restricted to vary within certain intervals. Finally, a numerical example is proposed in the end followed by a simulation to verify the effectiveness of the method proposed in this paper.

scholarly journals Controllability of Nonlinear Fractional Dynamical Systems with a Mittag–Leffler Kernel

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2139
Author(s):  
Jiale Sheng ◽  
Wei Jiang ◽  
Denghao Pang ◽  
Sen Wang
Keyword(s):  
Fixed Point ◽  
Dynamical Systems ◽  
Fixed Point Theorem ◽  
Laplace Transform ◽  
Point Theorem ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

This paper is concerned with controllability of nonlinear fractional dynamical systems with a Mittag–Leffler kernel. First, the solution of fractional dynamical systems with a Mittag–Leffler kernel is given by Laplace transform. In addition, one necessary and sufficient condition for controllability of linear fractional dynamical systems with Mittag–Leffler kernel is established. On this basis, we obtain one sufficient condition to guarantee controllability of nonlinear fractional dynamical systems with a Mittag–Leffler kernel by fixed point theorem. Finally, an example is given to illustrate the applicability of our results.

scholarly journals Necessary and sufficient conditions for common fixed point theorems in fuzzy metric space

2009 ◽  
Vol 42 (4) ◽  
Author(s):  
D. O’Regan ◽  
M. Abbas
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Sufficient Conditions ◽  
Fuzzy Metric Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
Common Fixed Point Theorems

AbstractThe aim of this paper is to provide a necessary and sufficient condition for the existence of a common fixed point of three maps

scholarly journals The fixed point set of a holomorphic isometry, the intersection of two real forms in a Hermitian symmetric space of compact type and symmetric triads

2015 ◽  
Vol 26 (06) ◽  
pp. 1541005 ◽  
Author(s):  
Osamu Ikawa ◽  
Makiko Sumi Tanaka ◽  
Hiroyuki Tasaki
Keyword(s):  
Fixed Point ◽  
Symmetric Space ◽  
Hermitian Symmetric Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Compact Type ◽  
Fixed Point Set ◽  
Point Set ◽  
Necessary And Sufficient ◽  
Real Forms

We show a necessary and sufficient condition that the fixed point set of a holomorphic isometry and the intersection of two real forms of a Hermitian symmetric space of compact type are discrete and prove that they are antipodal sets in the cases. We also consider some relations between the intersection of two real forms and the fixed point set of a certain holomorphic isometry.

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