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.

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 Plug and Play Robust Distributed Control with Ellipsoidal Parametric Uncertainty System

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Hong Wang-jian ◽  
Wang Yan-xiang
Keyword(s):  
Linear System ◽  
Distributed Control ◽  
Control Strategy ◽  
State Feedback ◽  
Parametric Uncertainty ◽  
State Feedback Control ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Plug And Play ◽  
Necessary And Sufficient

We consider a continuous linear time invariant system with ellipsoidal parametric uncertainty structured into subsystems. Since the design of a local controller uses only information on a subsystem and its neighbours, we combine the plug and play idea and robust distributed control to propose one distributed control strategy for linear system with ellipsoidal parametric uncertainty. Firstly for linear system with ellipsoidal parametric uncertainty, a necessary and sufficient condition for robust state feedback control is proposed by means of linear matrix inequality. If this necessary and sufficient condition is satisfied, this robust state feedback gain matrix can be easily derived to guarantee robust stability and prescribed closed loop performance. Secondly the plug and play idea is introduced in the design process. Finally by one example of aircraft flutter model parameter identification, the efficiency of the proposed control strategy can be easily realized.

STABILIZING HIGHER PERIODIC ORBITS

1994 ◽  
Vol 04 (02) ◽  
pp. 457-460 ◽  
Author(s):  
M. PASKOTA ◽  
A.I. MEES ◽  
K.L. TEO
Keyword(s):  
Dynamical Systems ◽  
Periodic Orbits ◽  
State Feedback ◽  
State Feedback Control ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Chaotic Dynamical Systems ◽  
Linear State ◽  
Necessary And Sufficient ◽  
Bounded Perturbations

In this paper, we consider stabilization of chaotic dynamical systems onto higher periodic orbits. We give a necessary and sufficient condition for using local linear state feedback control for this purpose. The control is achieved using small, bounded perturbations, and the method proposed is shown to be effective even in the presence of relatively small random dynamical noise.

scholarly journals Losslessness of Nonlinear Stochastic Discrete-Time Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Xikui Liu ◽  
Yan Li ◽  
Ning Gao
Keyword(s):  
Discrete Time ◽  
State Feedback ◽  
Zero Dynamics ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Discrete Time System ◽  
Time System ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems

This paper will study stochastic losslessness theory for nonlinear stochastic discrete-time systems, which are expressed by the Itô-type difference equations. A necessary and sufficient condition is developed for a nonlinear stochastic discrete-time system to be lossless. By the stochastic lossless theory, we show that a nonlinear stochastic discrete-time system can be lossless via state feedback if and only if it has relative degree0,…,0and lossless zero dynamics. The effectiveness of the proposed results is illustrated by a numerical example.

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 Convergence Theorems for Operators Sequences on Functionals of Discrete-Time Normal Martingales

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Jinshu Chen
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Discrete Time ◽  
Existence And Uniqueness ◽  
Continuous Dependence ◽  
Functional Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
Convergence Of Operators

We aim to investigate the convergence of operators sequences acting on functionals of discrete-time normal martingales M. We first apply the 2D-Fock transform for operators from the testing functional space S(M) to the generalized functional space S⁎(M) and obtain a necessary and sufficient condition for such operators sequences to be strongly convergent. We then discuss the integration of these operator-valued functions. Finally, we apply the results obtained here and establish the existence and uniqueness of solution to quantum stochastic differential equations in terms of operators acting on functionals of discrete-time normal martingales M. And also we prove the continuity and continuous dependence on initial values of the solution.

scholarly journals Positive Stabilization of Linear Differential Algebraic Equation System

2016 ◽  
Vol 2016 ◽  
pp. 1-3 ◽  
Author(s):  
Muhafzan
Keyword(s):  
Algebraic Equation ◽  
State Feedback ◽  
Closed Loop ◽  
Equation System ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Closed Loop System ◽  
Differential Algebraic Equation ◽  
Linear Differential ◽  
Necessary And Sufficient

We study in this paper the existence of a feedback for linear differential algebraic equation system such that the closed-loop system is positive and stable. A necessary and sufficient condition for such existence has been established. This result can be used to detect the existence of a state feedback law that makes the linear differential algebraic equation system in closed loop positive and stable.

scholarly journals Controllability of Linear Discrete-Time Systems with Both Delayed States and Delayed Inputs

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Hong Shi ◽  
Guangming Xie ◽  
Wenguang Luo
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Control Delay ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
And Control ◽  
Time Systems ◽  
Time Linear

The controllability issues for discrete-time linear systems with delay in state and control are addressed. By introducing a new concept, the controllability realization index (CRI), the characteristic of controllability is revealed. An easily testable necessary and sufficient condition for the controllability of discrete-time linear systems with state and control delay is established.

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