scholarly journals Robust Output Controllability Analysis and Control Design for Incomplete Boolean Networks with Disturbance Inputs

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Lei Deng ◽  
Shihua Fu ◽  
Ying Li ◽  
Peiyong Zhu
Keyword(s):  
Sufficient Conditions ◽  
Boolean Networks ◽  
Algebraic Form ◽  
Output Control ◽  
Optimal Output ◽  
Product Technique ◽  
Output Controllability ◽  
The Cost ◽  
Necessary And Sufficient ◽  
And Control

This paper addresses the problems of robust-output-controllability and robust optimal output control for incomplete Boolean control networks with disturbance inputs. First, by resorting to the semi-tensor product technique, the system is expressed as an algebraic form, based on which several necessary and sufficient conditions for the robust output controllability are presented. Second, the Mayer-type robust optimal output control issue is studied and an algorithm is established to find a control scheme which can minimize the cost functional regardless of the effect of disturbance inputs. Finally, a numerical example is given to demonstrate the effectiveness of the obtained new results.

Synchronization of switched Boolean networks with impulsive effects

2018 ◽  
Vol 11 (06) ◽  
pp. 1850080 ◽  
Author(s):  
Xiaojing Xu ◽  
Yansheng Liu ◽  
Haitao Li ◽  
Fuad E. Alsaadi
Keyword(s):  
Sufficient Conditions ◽  
Boolean Networks ◽  
The State ◽  
Impulsive Effects ◽  
Space Representation ◽  
Algebraic Form ◽  
State Space Representation ◽  
Switching Signal ◽  
Output Synchronization ◽  
Necessary And Sufficient

This paper studies the state/output synchronization of switched Boolean networks (SBNs) with impulsive effects via the algebraic state space representation (ASSR) approach. First, an algebraic form is established for SBNs with impulsive effects via ASSR. Second, based on the algebraic form, some necessary and sufficient conditions are presented for the state/output synchronization of SBNs with impulsive effects under arbitrary switching signals. Third, two special kinds of switching signals, that is, free switching signal and feedback switching signal, are considered for the state synchronization of SBNs with impulsive effects. Finally, two illustrative examples are worked out to show the effectiveness of the obtained results.

Synchronization in mutual-coupled temporal Boolean networks

2017 ◽  
Vol 40 (7) ◽  
pp. 2211-2216 ◽  
Author(s):  
Qiang Wei ◽  
Cheng-jun Xie
Keyword(s):  
Theoretical Analysis ◽  
Tensor Product ◽  
Sufficient Conditions ◽  
Boolean Networks ◽  
Necessary And Sufficient Conditions ◽  
Complete Synchronization ◽  
Logical Relationship ◽  
Algebraic Form ◽  
Algebraic Forms ◽  
Necessary And Sufficient

In this paper, we first propose a mutual-coupled temporal Boolean networks model and then investigate complete synchronization in mutual-coupled temporal Boolean networks. The mutual-coupled temporal Boolean networks model with logical relationship is converted into an algebraic form based on a semi-tensor product. Necessary and sufficient conditions are derived to realize synchronization based on the algebraic forms. An example illustrates the effectiveness of the theoretical analysis.

Inventory optimization considering the vehicle capacity and specifics of cash flows at rental storage sites

2020 ◽  
pp. 77-90
Author(s):  
V.D. Gerami ◽  
I.G. Shidlovskii
Keyword(s):  
Supply Chain ◽  
Inventory Management ◽  
Sufficient Conditions ◽  
Cash Flows ◽  
Management Systems ◽  
Cargo Capacity ◽  
Special Modification ◽  
The Cost ◽  
Necessary And Sufficient ◽  
Vehicle Capacity

The article presents a special modification of the EOQ formula and its application to the accounting of the cargo capacity factor for the relevant procedures for optimizing deliveries when renting storage facilities. The specified development will allow managers to take into account the following process specifics in the format of a simulated supply chain when managing inventory. First of all, it will allow considering the most important factor of cargo capacity when optimizing stocks. Moreover, this formula will make it possible to find the optimal strategy for the supply of goods if, also, it is necessary to take into account the combined effect of several factors necessary for practice, which will undoubtedly affect decision-making procedures. Here we are talking about the need for additional consideration of the following essential attributes of the simulated cash flow of the supply chain: 1) time value of money; 2) deferral of payment of the cost of the order; 3) pre-agreed allowable delays in the receipt of revenue from goods sold. Developed analysis and optimization procedures have been implemented to models of this type that are interesting and important for a business. This — inventory management systems, the format of which is related to the special concept of efficient supply. We are talking about models where the presence of the specified delays for the outgoing cash flows allows you to pay for the order and the corresponding costs of the supply chain from the corresponding revenue on the re-order interval. Accordingly, the necessary and sufficient conditions are established based on which managers will be able to identify models of the specified type. The purpose of the article is to draw the attention of managers to real opportunities to improve the efficiency of inventory management systems by taking into account these factors for a simulated supply chain.

scholarly journals First and second order optimality conditions for the control of Fokker-Planck equations

2021 ◽  
Vol 27 ◽  
pp. 15
Author(s):  
M. Soledad Aronna ◽  
Fredi Tröltzsch
Keyword(s):  
Control Variable ◽  
Sufficient Conditions ◽  
Planck Equation ◽  
Second Order ◽  
Optimal Controls ◽  
Main Emphasis ◽  
The Cost ◽  
Necessary And Sufficient ◽  
Fokker Planck Equations ◽  
Fokker Planck

In this article we study an optimal control problem subject to the Fokker-Planck equation ∂tρ − ν∆ρ − div(ρB[u]) = 0 The control variable u is time-dependent and possibly multidimensional, and the function B depends on the space variable and the control. The cost functional is of tracking type and includes a quadratic regularization term on the control. For this problem, we prove existence of optimal controls and first order necessary conditions. Main emphasis is placed on second order necessary and sufficient conditions.

Generalized WG inverse

2020 ◽  
pp. 2150072
Author(s):  
Sanzhang Xu ◽  
Hongxing Wang ◽  
Jianlong Chen ◽  
Xiaofeng Chen ◽  
Tiwei Zhao
Keyword(s):  
Generalized Inverse ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Algebraic Form ◽  
Necessary And Sufficient

In this paper, we introduce a generalized inverse of a matrix, namely, the generalized WG inverse, which a generalization of the WG inverse. Several necessary and sufficient conditions such that a matrix to be generalized WG invertible are obtained. Moreover, the formulae of generalized WG inverse of a matrix are given. Finally, we give a algebraic form of the generalized WG inverse.

scholarly journals Controllability, Reachability, and Stabilizability of Finite Automata: A Controllability Matrix Method

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Yalu Li ◽  
Wenhui Dou ◽  
Haitao Li ◽  
Xin Liu
Keyword(s):  
Matrix Method ◽  
Finite Automata ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Algebraic Form ◽  
Controllability Matrix ◽  
Necessary And Sufficient ◽  
Semitensor Product Of Matrices ◽  
Product Of Matrices ◽  
Inputs And Outputs

This paper investigates the controllability, reachability, and stabilizability of finite automata by using the semitensor product of matrices. Firstly, by expressing the states, inputs, and outputs as vector forms, an algebraic form is obtained for finite automata. Secondly, based on the algebraic form, a controllability matrix is constructed for finite automata. Thirdly, some necessary and sufficient conditions are presented for the controllability, reachability, and stabilizability of finite automata by using the controllability matrix. Finally, an illustrative example is given to support the obtained new results.

AN OPTIMIZATION APPROACH TO THE DESIGN OF CONSTRAINED REGULATORS FOR UNCERTAIN DISCRETE-TIME SYSTEMS

2006 ◽  
Vol 15 (03) ◽  
pp. 373-387
Author(s):  
M. VASSILAKI ◽  
G. BITSORIS
Keyword(s):  
Discrete Time ◽  
Sufficient Conditions ◽  
Optimization Approach ◽  
Control Constraints ◽  
Existence Of A Solution ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
And Control ◽  
Time Systems ◽  
State And Control Constraints

In this paper the regulation problem of linear discrete-time systems with uncertain parameters under state and control constraints is studied. In the first part of the paper, two theorems concerning necessary and sufficient conditions for the existence of a solution to this problem are presented. Due to the constructive form of the proof of these theorems, these results can be used to the development of techniques for the derivation of a control law transferring to the origin any state belonging to a given set of initial states while respecting the state and control constraints.

ON FLOW BARRIERS AND SWITCHABILITY IN DISCONTINUOUS DYNAMICAL SYSTEMS

2011 ◽  
Vol 21 (01) ◽  
pp. 1-76 ◽  
Author(s):  
ALBERT C. J. LUO
Keyword(s):  
Dynamical Systems ◽  
Vector Fields ◽  
Sufficient Conditions ◽  
Friction Model ◽  
Necessary And Sufficient Conditions ◽  
Separation Boundary ◽  
Boundary Flow ◽  
Pass Through ◽  
Necessary And Sufficient ◽  
And Control

In this paper, the theory of flow barriers in discontinuous dynamical systems is systematically presented as a new theory for the first time, which helps one rethink the existing theories of stability and control in dynamical systems. The concept of flow barriers in discontinuous dynamical systems is introduced, and the passability of a flow to the separation boundary with flow barriers is presented. Because the flow barriers exist on the separation boundary, the switchability of a flow to such a separation boundary is changed accordingly. The coming and leaving flow barriers in passable flows are discussed first, and the necessary and sufficient conditions for a flow to pass through the boundary with flow barrier are developed. Flow barriers for sink and source flows are also discussed. Once the sink flow is formed, the boundary flow will exist. When the boundary flow disappears from the boundary, the boundary flow barrier on the boundary may exist, which is independent of vector fields in the corresponding domains. Thus, the necessary and sufficient conditions for formations and vanishing of the boundary flow are developed. A periodically forced friction model is presented as an example for a better understanding of flow barrier existence in physical problems. The flow barrier theory presented in this paper may provide a theoretic base to further develop control theory and stability.

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.

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