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.

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.

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.

scholarly journals Necessary and Sufficient Dissipativity-Based Conditions for Feedback Stabilization

2022 ◽  
Author(s):  
Diego Madeira
Keyword(s):  
Controller Design ◽  
Sufficient Conditions ◽  
Feedback Stabilization ◽  
Necessary And Sufficient Conditions ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Full State ◽  
Full State Feedback ◽  
Necessary And Sufficient ◽  
Static Output

Using the notion of exponential QSR-dissipativity, this work presents necessary and sufficient conditions for exponential stabilizability of nonlinear systems by linear static output feedback (SOF). It is shown that, under mild assumptions, the exponential stabilization of the closed-loop system around the origin is equivalent to the exponential QSR-dissipativity of the plant. Furthermore, whereas strict QSR-dissipativity is only sufficient for SOF asymptotic stabilization, it is proved to be necessary and sufficient for full state feedback control. New necessary and sufficient conditions for SOF stabilizability of linear systems are presented as well, along with a linear and noniterative semidefinite strategy for controller design. Necessary linear matrix inequality (LMI) conditions for stabilization are also introduced. Some examples illustrate the usefulness of the proposed approach.

scholarly journals Necessary and Sufficient Dissipativity-Based Conditions for Feedback Stabilization

2022 ◽  
Author(s):  
Diego Madeira
Keyword(s):  
Controller Design ◽  
Sufficient Conditions ◽  
Feedback Stabilization ◽  
Necessary And Sufficient Conditions ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Full State ◽  
Full State Feedback ◽  
Necessary And Sufficient ◽  
Static Output

Using the notion of exponential QSR-dissipativity, this work presents necessary and sufficient conditions for exponential stabilizability of nonlinear systems by linear static output feedback (SOF). It is shown that, under mild assumptions, the exponential stabilization of the closed-loop system around the origin is equivalent to the exponential QSR-dissipativity of the plant. Furthermore, whereas strict QSR-dissipativity is only sufficient for SOF asymptotic stabilization, it is proved to be necessary and sufficient for full state feedback control. New necessary and sufficient conditions for SOF stabilizability of linear systems are presented as well, along with a linear and noniterative semidefinite strategy for controller design. Necessary linear matrix inequality (LMI) conditions for stabilization are also introduced. Some examples illustrate the usefulness of the proposed approach.

scholarly journals Necessary and Sufficient Conditions for Circle Formations of Mobile Agents with Coupling Delay via Sampled-Data Control

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Jianwei Zhao ◽  
Hongxiang Hu ◽  
Chen Wang ◽  
Guangming Xie
Keyword(s):  
Mobile Agents ◽  
Dimensional Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Order System ◽  
Sampled Data ◽  
Coupling Delay ◽  
Data Control ◽  
Sampled Data Control ◽  
Necessary And Sufficient

A circle forming problem for a group of mobile agents governed by first-order system is investigated, where each agent can only sense the relative angular positions of its neighboring two agents with time delay and move on the one-dimensional space of a given circle. To solve this problem, a novel decentralized sampled-data control law is proposed. By combining algebraic graph theory with control theory, some necessary and sufficient conditions are established to guarantee that all the mobile agents form a pregiven circle formation asymptotically. Moreover, the ranges of the sampling period and the coupling delay are determined, respectively. Finally, the theoretical results are demonstrated by numerical simulations.

Sampled-Data State Feedback Control for the Set Stabilization of Boolean Control Networks

2020 ◽  
Vol 50 (4) ◽  
pp. 1580-1589 ◽  
Author(s):  
Shiyong Zhu ◽  
Yang Liu ◽  
Jungang Lou ◽  
Jianquan Lu ◽  
Fuad E. Alsaadi
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
State Feedback Control ◽  
Sampled Data ◽  
Control Networks ◽  
Set Stabilization
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