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1.
This paper investigates the observability of singular Boolean control networks (SBCNs) with state delays. First, via Cheng product, the considered system is converted into its algebraic form. Then, under the uniqueness of the solution, two methods are proposed to transform the system into a general Boolean control network (BCN). Therefore, the considered system’s observability is equivalent to the BCN’s observability. Subsequently, the restricted input-state incidence matrix is introduced and some necessary and sufficient conditions are presented for the observability of BCNs with state delays. Finally, two illustrative examples are presented to show that the main results obtained are effective in analyzing the observability of SBCNs with state delays.  相似文献   

2.
We investigate the input–output decoupling problem of switched Boolean control networks (SBCNs) in this paper. Based on the matrix expression of Boolean functions, the dynamics of SBCNs are converted into an algebraic form via semi-tensor product of matrices first. Then, using the redundant variable separation technique, we give the necessary and sufficient conditions for the existence of three kinds of controllers to detect whether an SBCN can be input–output decomposed or not, respectively, including the open-loop controllers, the state feedback controllers, and the output feedback controllers. Meanwhile, a constructive procedure is presented to construct the open-loop controllers, as well as the state feedback controllers and output feedback controllers. Finally, an illustrative example is given to show that the new results obtained are effective.  相似文献   

3.
Boolean control networks are a kind of discrete logical dynamical systems. They are recently attracting considerable interest as computational models for genetic and cellular networks. In this paper, we investigate the cascading state-space decomposition problem for Boolean control networks by nested method. Firstly, based on the semi-tensor product of matrices, we obtain some algebraic conditions for the cascading state-space decomposition. Secondly, the multi-layer nested block matrix is defined, and two necessary and sufficient conditions are put forward based on this kind of matrices. Besides, a method is given to design controllers. Finally, an example is given to display the effectiveness of the method provided in this paper.  相似文献   

4.
In this paper, the observability problem of Boolean control networks (BCNs) with stochastic disturbances is investigated via two kinds of control schemes: deterministic control and state feedback control. Firstly, based on the proposed indicator matrix, a simplified system of the original augmented Boolean system is constructed. Based on the analysis of the auxiliary system, observability of the original BCN is converted to determine whether an observable set can be reached from another unobservable set. After that, some necessary and sufficient conditions are obtained to judge the observability of BCNs. At the same time, two algorithms are proposed for designing these two types of control sequences. Finally, numerical simulations are also provided to demonstrate feasibility of the theoretical results.  相似文献   

5.
This paper investigates the time optimal control and optimal infinite-horizon control for a switched Boolean network. First, the switched Boolean network can be converted into a discrete switched system by using the semi-tensor product of matrices. Second, algorithms for time optimal control and optimal infinite-horizon control of the switched Boolean network are presented. Moreover, constrained optimal infinite-horizon control is studied. Finally, illustrative examples are given to show the efficiency of the obtained results.  相似文献   

6.
This paper presents solution of the optimal linear-quadratic controller problem for unobservable integral Volterra systems with continuous/discontinuous states under deterministic uncertainties, over continuous/discontinuous observations. Due to the separation principle for integral systems, the initial continuous problem is split into the optimal minmax filtering problem for integral Volterra systems with deterministic uncertainties over continuous/discontinuous observations and the optimal linear-quadratic control (regulator) problem for observable deterministic integral Volterra systems with continuous/discontinuous states. As a result, the system of the optimal controller equations are obtained, including the linear equation for the optimally controlled minmax estimate and two Riccati equations for its ellipsoid matrix (optimal gain matrix of the filter) and the optimal regulator gain matrix. Then, in the discontinuous problems, the equation for the optimal controller and the equations for the optimal filter and regulator gain matrices are obtained using the filtering procedure for deriving the filtering equations over discontinuous observations proceeding from the known filtering equations over continuous ones and the dual results in the optimal control problem for integral systems. The technical example illustrating application of the obtained results is finally given.  相似文献   

7.
In this paper, the finite horizon tracking control problem of probabilistic Boolean control networks (PBCNs) is studied. For a given reference output trajectory, two trackability definitions are introduced according to whether the tracking probability is 1. Under the framework of the semi-tensor product, some necessary and sufficient conditions are obtained to determine whether the reference output trajectory is trackable with probability (probability one) by a PBCN starting from a given initial state. Based on this, two algorithms are proposed to determine the maximum tracking probability and the corresponding optimal control policy sequence. By determining the tracking error of the reference output trajectory, two related optimal control problems are considered: one is to minimize the expected value of the total tracking error, and the other is to minimize the maximum tracking error. Inspired by dynamic programming, corresponding algorithms are given to solve these two problems. Finally, two examples are given to verify the validity and correctness of the results.  相似文献   

8.
Using the algebraic state space representation (ASSR) method, this paper investigates the set stability and synchronization of Boolean networks with probabilistic time delays (PTDs). Firstly, an equivalent stochastic system is established for the Boolean network with PTDs by using the ASSR method. Secondly, based on the probabilistic state transition matrix of equivalent stochastic system, a necessary and sufficient condition is proposed for the set stability of Boolean networks with PTDs. Thirdly, as an application of set stability, the synchronization of coupled Boolean networks with PTDs is studied, and a necessary and sufficient condition is presented. Finally, an illustrative example is given to demonstrate the effectiveness of the obtained new results.  相似文献   

9.
This paper investigates steady-state distributions of probabilistic Boolean networks via cascading aggregation. Under this approach, the problem is converted to computing least square solutions to several corresponding equations. Two necessary and sufficient conditions for the existence of the steady-state distributions for probabilistic Boolean networks are given firstly. Secondly, an algorithm for finding the steady-state distributions of probabilistic probabilistic Boolean networks is given. Finally, a numerical example is given to show the effectiveness of the proposed method.  相似文献   

10.
Derived from a simplified intelligent traffic control system, sampled-data controllability and stabilizability of Boolean control networks are considered. Compared with the existing case of uniform (periodic) sampling in Boolean control networks, the nonuniform one is more general. Using linear span with integral coefficients, the distribution of sampling points can be obtained. Then by constructing novel systems, some necessary and sufficient conditions are proposed to determine sampled-data controllability and stabilizability. Finally, two illustrative examples, which are on apoptosis networks and traffic control systems, respectively, are worked out to show the effectiveness of the obtained results.  相似文献   

11.
This paper studies the stabilization problem of Boolean control networks with stochastic impulses, where stochastic impulses model is described as a series of possible regulatory models with corresponding probabilities. The stochastic impulses model makes the research more realistic. The global stabilization problem is trying to drive all states to reach the predefined target with probability 1. A necessary and sufficient condition is presented to judge whether a given system is globally stabilizable. Meanwhile, an algorithm is proposed to stabilize the given system by designing a state feedback controller and different impulses strategies. As an extension, these results are applied to analyze the global stabilization to a fixed state of probability Boolean control networks with stochastic impulses. Finally, two examples are given to demonstrate the effectiveness of the obtained results.  相似文献   

12.
In this paper, we study the state feedback stabilization of dynamic-algebraic Boolean control networks (DABCNs). Using a novel normalization approach, we present necessary and sufficient conditions for the feedback stabilization of DABCNs, and a construction method for the corresponding feedback controllers is proposed. Reduced order feedback stabilization is also studied in this paper. Two examples are given to illustrate the obtained results.  相似文献   

13.
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14.
Set stabilization of probabilistic Boolean control networks (PBCNs) is investigated in this paper and some interesting results are derived. The main results consist of three parts. (1) A definition of set stabilizability with probability one by closed-loop control is proposed for PBCNs, which is not a natural extension from deterministic Boolean control networks to PBCNs due to the random feature of PBCNs. (2) A necessary and sufficient set stabilizability condition is provided for PBCNs. (3) An algorithm for designing a state feedback controller is developed. It is guaranteed that all designed controllers can stabilize a PBCN to a given subset with probability one. The design method is constructive, so it is convenient to use this method in practical application. The results derived above are fundamental and important, since based on them many problems about PBCNs can be solved, for example partial stabilization, synchronization, and so on. Finally, a practical example is employed to show the effectiveness of our results.  相似文献   

15.
In this paper, the optimal consensus control problem of nonlinear multi-agent systems(MASs) with completely unknown dynamics is considered. The problem is formulated in a differential graphical game approach which can be solved by Hamilton-Jacobi (HJ) equations. The main difficulty in solving the HJ equations lies in the nonlinear coupling between equations. Based on the Adaptive Dynamic Programming (ADP) technique, an VI-PI mixed HDP algorithm is proposed to solve the HJ equations distributedly. With the PI step, a suitable iterative initial value can be obtained according to the initial policies. Then, VI steps are run to get the optimal solution with exponential convergence rate. Neural networks (NNs) are applied to approximate the value functions, which makes the data-driven end-to-end learning possible. A numerical simulation is conducted to show the effectiveness of the proposed algorithm.  相似文献   

16.
Determining an input matrix, i.e., locating predefined number of nodes (named “key nodes”) connected to external control sources that provide control signals, so as to minimize the cost of controlling a preselected subset of nodes (named “target nodes”) in directed networks is an outstanding issue. This problem arises especially in large natural and technological networks. To address this issue, we focus on directed networks with linear dynamics and propose an iterative method, termed as “L0-norm constraint based projected gradient method” (LPGM) in which the input matrix B is involved as a matrix variable. By introducing a chain rule for matrix differentiation, the gradient of the cost function with respect to B can be derived. This allows us to search B by applying probabilistic projection operator between two spaces, i.e., a real valued matrix space RN?×?M and a L0 norm matrix space RL0N×M by restricting the L0 norm of B as a fixed value of M. Then, the nodes that correspond to the M nonzero elements of the obtained input matrix (denoted as BL0) are selected as M key nodes, and each external control source is connected to a single key node. Simulation examples in real-life networks are presented to verify the potential of the proposed method. An interesting phenomenon we uncovered is that generally the control cost of scale free (SF) networks is higher than Erdos-Renyi (ER) networks using the same number of external control sources to control the same size of target nodes of networks with the same network size and mean degree. This work will deepen the understanding of optimal target control problems and provide new insights to locate key nodes for achieving minimum-cost control of target nodes in directed networks.  相似文献   

17.
This paper introduces the Lebesgue sampling approach to the robust stabilization of Boolean control networks (BCNs) with external disturbances. Given a Lebesgue sampling region and a feedback control, a time aggregated system is obtained via the semi-tensor product method. Then, a new criterion is presented for the robust stabilization of time aggregated system. Furthermore, given a signal of Lebesgue sampling, a sequence of the Lebesgue type robust reachable sets is constructed. Based on these reachable sets, several algorithms are presented to design both Lebesgue sampling region and sampled-data state feedback control for the robust stabilization of BCNs.  相似文献   

18.
This paper investigates the fault detectability of Boolean control networks. To deal with different circumstances, passive fault detectability and four types of active fault detectability are proposed for the first time. For passive fault detectability, in line with observed input-output data, several discriminant conditions are put forward. For active fault detectability, by resorting to an auxiliary system, the essence of active fault detectabilty is revealed via reachability. Subsequently, corresponding to different types of active fault detectability, algebraic criteria that facilitate verification are provided. At the same time, the relationships of four types of active fault detectability are discussed as well. In addition, an approach for calculating fault detection time is given by combining passive fault detectability with active fault detectability. Finally, the effectiveness of the results obtained is elaborated by several examples.  相似文献   

19.
In this work, we consider an optimal control problem of a class of stochastic differential equations driven by additive noise with aftereffect appearing in control. We develop a semigroup theory of the driving deterministic neutral system and identify explicitly the adjoint operator of the corresponding infinitesimal generator. We formulate the time delay equation under consideration into an infinite dimensional stochastic control system without time lag by means of the adjoint theory established. Consequently, we can deal with the associated optimal control problem through the study of a Hamilton–Jacob–Bellman (HJB) equation. Last, we present an example whose optimal control can be explicitly determined to illustrate our theory.  相似文献   

20.
This paper investigates the event-triggered control design for state/output synchronization of switched k-valued logical control networks (SKVLCNs). Firstly, based on the algebraic form of SKVLCNs, some necessary and sufficient conditions are presented for the event-triggered state/output synchronization of SKVLCNs. Secondly, using the partitioning technique of matrix, a constructive procedure is proposed to design state feedback event-triggered controllers for the synchronization of SKVLCNs. Finally, an illustrative example is worked out to show the effectiveness of the obtained new results.  相似文献   

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