Necessary and sufficient vertex partition conditions for input–output decoupling of Boolean control networks

Automatica ◽  
2022 ◽  
Vol 137 ◽  
pp. 110097
Author(s):  
Yifeng Li ◽  
Jiandong Zhu
Keyword(s):  
Input Output ◽  
Control Networks ◽  
Vertex Partition ◽  
Necessary And Sufficient

Sampled-Data State Feedback Stabilization of Boolean Control Networks

2016 ◽  
Vol 28 (4) ◽  
pp. 778-799 ◽  
Author(s):  
Yang Liu ◽  
Jinde Cao ◽  
Liangjie Sun ◽  
Jianquan Lu
Keyword(s):  
State Feedback ◽  
Sufficient Conditions ◽  
Feedback Stabilization ◽  
Necessary And Sufficient Conditions ◽  
State Feedback Control ◽  
Global Stabilization ◽  
Sampled Data ◽  
Control Networks ◽  
Piecewise Constant Control ◽  
Necessary And Sufficient

In this letter, we investigate the sampled-data state feedback control (SDSFC) problem of Boolean control networks (BCNs). Some necessary and sufficient conditions are obtained for the global stabilization of BCNs by SDSFC. Different from conventional state feedback controls, new phenomena observed the study of SDSFC. Based on the controllability matrix, we derive some necessary and sufficient conditions under which the trajectories of BCNs can be stabilized to a fixed point by piecewise constant control (PCC). It is proved that the global stabilization of BCNs under SDSFC is equivalent to that by PCC. Moreover, algorithms are given to construct the sampled-data state feedback controllers. Numerical examples are given to illustrate the efficiency of the obtained results.

P-D Feedback for Decoupling and Pole Assignment of Singular Systems

1998 ◽  
Vol 120 (3) ◽  
pp. 378-388 ◽  
Author(s):  
F. N. Koumboulis ◽  
B. G. Mertzios
Keyword(s):  
Closed Loop ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Pole Assignment ◽  
Loop System ◽  
Necessary And Sufficient Conditions ◽  
Algebraic Equations ◽  
Input Output ◽  
Closed Loop System ◽  
Necessary And Sufficient

The problem of reducing a multi input-multi output system to many single input-single output systems, namely the problem of input-output decoupling, is studied for the case of singular systems i.e., for systems described by dynamic and algebraic equations. The problem of input-output decoupling with simultaneous arbitrary pole assignment, via proportional plus derivative (P-D) state feedback, is extensively solved. The general explicit expression of all P-D controllers solving the decoupling problem is determined. The general form of the diagonal elements of the decoupled closed-loop system is proven to be in a form having a fixed numerator polynomial and an arbitrary denominator polynomial. The necessary and sufficient conditions for the solvability of the problem of decoupling with simultaneous asymptotic stabilizability or arbitrary pole assignment are established. Furthermore, the necessary and sufficient conditions for decoupling with simultaneous impulse elimination, as well as the necessary and sufficient conditions for decoupling with arbitrary assignment of the finite and infinite poles of the closed-loop system, are established.

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 Robust set stabilization of Boolean control networks with impulsive effects

2018 ◽  
Vol 23 (4) ◽  
pp. 553-567 ◽  
Author(s):  
Xiaojing Xu ◽  
Yansheng Liu ◽  
Haitao Li ◽  
Fuad E. Alsaadi
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
State Feedback Control ◽  
Impulsive Effects ◽  
Algebraic Form ◽  
Control Networks ◽  
Set Stabilization ◽  
Necessary And Sufficient

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.

Input‐Output Decoupling of Boolean Control Networks

2018 ◽  
Vol 20 (6) ◽  
pp. 2185-2194 ◽  
Author(s):  
Jinfeng Pan ◽  
Jun‐E Feng ◽  
Juan Yao ◽  
Jianli Zhao
Keyword(s):  
Input Output ◽  
Control Networks
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