Haitao Li

On reachability and controllability of switched Boolean control networks

This paper investigates the reachability and controllability of switched Boolean control networks (BCNs) by using the semi-tensor product method. First, a kind of switching-input-state transfer graph is defined, based on which and the algebraic expression of switched BCNs we thus propose a new kind of switching-input-state incidence matrix that contains the complete information of the switching-input-state transfer graph. Second, by the switching-input-state incidence matrix, several necessary and sufficient conditions are obtained for the reachability and controllability of switched BCNs. Finally, an algorithm is established to find a switching sequence and a control scheme to realize the reachability of switched BCNs in the shortest time. The study of an illustrative example shows that the new results obtained in this paper are very effective in investigating the reachability and controllability of switched BCNs.

Brief paper: Boolean derivative calculation with application to fault detection of combinational circuits via the semi-tensor product method

Using the semi-tensor product method, this paper investigates the Boolean derivative calculation with application to fault detection of combinational circuits, and presents a number of new results. First, a new set of formulas is obtained to calculate the Boolean derivative by the semi-tensor product method. Then, the obtained new results are applied to detecting the multiple faults of combinational circuits, and a new detection method is proposed. Finally, two illustrative examples are studied by using the results obtained in this paper. The study of illustrative examples shows that the new detection method can be used for detection of more than two faults effectively.

Output tracking control of Boolean control networks via state feedback

This paper investigates the state feedback based output tracking control of Boolean control networks (BCNs) with a constant reference signal by using the semi-tensor product method. Based on the algebraic expression of BCNs and by constructing a series of reachable sets, a general procedure is proposed for the design of the state feedback laws for BCNs to track a constant reference signal. The study of an illustrative example shows that the obtained new results are effective in designing state feedback based output tracking controllers for BCNs to track a constant reference signal.

On robust control invariance of Boolean control networks

This paper investigates the robust control invariance of Boolean control networks (BCNs) via the semi-tensor product of matrices. Firstly, based on an algebraic state space representation of BCNs, two necessary and sufficient conditions are presented to check whether or not a given set is a robust control invariant set under a given state feedback controller. Secondly, by defining a series of suitable sets, all possible state feedback gain matrices under which a given set is a robust control invariant set are characterized. An illustrative example is presented to demonstrate the obtained new results.

Output feedback stabilization control design for Boolean control networks

This paper investigates the output feedback stabilization of Boolean control networks (BCNs) by using the semi-tensor product method and presents a number of new results. First, based on the algebraic expression of BCNs, a necessary and sufficient condition is presented for the existence of output feedback stabilizers. Second, a constructive procedure is proposed to design output feedback stabilization controllers for BCNs. The study of an illustrative example shows that the new results obtained in this paper are very effective in designing output feedback stabilizers for BCNs.

Output Regulation of Boolean Control Networks

This note investigates the output regulation of Boolean control networks (BCNs) by using the semi-tensor product of matrices, and presents a number of new results. Firstly, based on an algebraic state-space representation of BCNs, a necessary and sufficient condition is presented for the solvability of the output regulation problem. Secondly, an effective method is proposed for the control design of the output regulation problem by using an augmented system approach. The study of an illustrative example shows that the obtained new results are effective in dealing with the output regulation of BCNs.

Disturbance decoupling control design for switched Boolean control networks

Abstract This paper investigates a kind of disturbance decoupling problems (DDPs) for switched Boolean control networks (BCNs), that is, the disturbance-independent output decoupling problem, via the semi-tensor product of matrices. By converting the dynamics of switched BCNs into an algebraic form and using the redundant variable separation technique, all possible state feedback controllers are designed for the disturbance-independent output decoupling problem. Then, based on the obtained state feedback disturbance decoupling controllers and the system’s output equation, a constructive procedure is proposed to design all possible output feedback disturbance decoupling controllers. The study of two illustrative examples shows that the new results obtained in this paper are effective in designing disturbance decoupling controllers for switched BCNs.

Stable degree analysis for strategy profiles of evolutionary networked games

In this paper, we investigate the stable degree of strategy profile for evolutionary networked games by using the semi-tensor product method, and present a number of new results. First, we propose the concept of k-degree stability for strategy profiles based on a normal evolutionary networked game model. Second, using the semi-tensor product of matrices, we convert the game dynamics with “best imitate” strategy updating rule into an algebraic form. Third, based on the algebraic form of the game, we analyzed the stable degree of strategy profile, and proposed two necessary and sufficient conditions for the k-degree stability of strategy profile. Furthermore, we discuss the computation problem of the transient time within which a disturbed strategy profile can be restored, and also establish an algorithm for the verification of the stable degree of strategy profile. The study of an illustrative example shows that the new results obtained in this paper are very effective.摘要创新点基于矩阵半张量积这一新工具,本文研究了有限网络演化博弈中策略组合的稳定度分析问题。 主要创新在于: (1) 提出了玩家策略组合的 k 度稳定性的概念, (2) 针对最优模仿策略调整规则, 为博弈的演化过程建立一个严格的动力学方程, 并将其转化为代数形式, (3) 得到了策略组合 k 度稳定的两个充分必要条件, 在 MATLAB 的帮助下这些条件都是很容易验证的, 并且给出一个计算策略组合稳定度的算法。