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1.
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   

2.
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   

3.
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   

4.
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   

5.
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   

6.
Constraints are very common for practical control systems. For logical systems, the existing technique of pre-feedback is an effective way of treating state-dependent constraints in control when the state is measurable. However, it is inapplicable for the case when measurement information is not available. In this situation, in order for the control input to not violate the state-dependent constraint, the control at each step must be selected from the common admissible controls of all possible states. Motivated by this observation, in this study, we propose a novel technique, termed the subset transition method, for finite-time controllability and stabilization of probabilistic logical dynamic control system (PLDCS) with a state-dependent control constraint. The main idea of this method is to construct an unconstrained deterministic logical control system over the power set of the state space, called the subset transition system (SubSTS), characterizing the transitional dynamics between subsets under common admissible controls. We prove that a control sequence is admissible with respect to all states in an initial subset if and only if it does not steer the SubSTS from the initial subset to the empty set. Based on this, necessary and sufficient conditions for set controllability and set stabilizability are obtained. Examples are presented to demonstrate the application of the obtained results.  相似文献   

7.
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   

8.
《Journal of The Franklin Institute》2023,360(14):10457-10475
Fault-tolerant control is a fundamental branch in the modern control theory, and has wide applications such as aerospace, automotive technology and nuclear engineering. Particularly, the study of faulty Boolean control networks (BCNs) is meaningful to the disease treatment. This paper focuses on both stuck-at fault and bridging fault in BCNs, and investigates the identification and stabilization of BCNs subject to these two faults. The basic mathematical tool is semi-tensor product (STP) of matrices, which is used to determine the algebraic formulation of faulty BCNs. Through the construction of invariant sets corresponding to the faulty nodes, the relations between these two faults and state transition matrices are presented, which is helpful to identify the faulty nodes. In addition, the robust stabilization of BCNs subject to these two faults is discussed and several new criteria are derived. Finally, the obtained results are applied to analyze the stabilization of oxidative stress response pathways.  相似文献   

9.
This paper investigates the stability and stabilizability of complex-valued memristive neural networks (CVMNNs) with random time-varying delays via non-fragile sampled-data control. Taking the influence of gain fluctuations into account, a non-fragile sampled-data controller is designed for CVMNNs. Compared with the existing control schemes, the one here is more applicable and can effectively save the communication resources. The assumption on activation functions of CVMNNs is relaxed by only needing the complex-valued activation functions satisfying the Lipschitz condition. By constructing a suitable Lyapunov–Krasovskii functional (LKF), new stability and stabilizability criteria are derived for CVMNNs. Different from the existing results with the maximum absolute values of memristive connection weights, our ones are based on the average values of the maximum and minimum of the memristive connection weights. Finally, numerical simulations are given to validate the effectiveness of the theoretical results.  相似文献   

10.
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   

11.
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   

12.
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   

13.
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14.
This paper investigates fractional-order fuzzy quaternion-valued BAM neural networks (FOFQBAMNNs) without decomposition. By virtue of a novel contraction mapping, the existence and uniqueness of the equilibrium point is yielded. Furthermore, according to some basic knowledge on fractional calculus, inequality techniques of fuzzy logic and reduction to absurdity, some criteria are yielded to guarantee finite-time stabilization of FOFQBAMNNs via original quaternion-valued controllers, and the settling times of corresponding finite-time stabilization are derived. Finally, the feasibility of our obtained theoretical results is illustrated by some numerical simulations.  相似文献   

15.
This paper investigates the optimal control problem for a class of Boolean control networks, called singular Boolean control networks (SBCNs), which consist of two parts: difference equations and algebraic equations. By constructing the truth matrix of Ledley solution, necessary and sufficient conditions are provided for the solvability of SBNs (or SBCNs). Then an effective algorithm is presented to design an optimal control sequence by using the controllability matrix of normalized Boolean control networks.  相似文献   

16.
This paper investigates the maximal perturbation bound problem for robust stabilizability of the fractional-order system with two-norm bounded perturbations or infinity-norm bounded perturbations. Firstly, a necessary condition and several sufficient conditions for robust stabilization are derived. Secondly, linear matrix inequality approaches for computing the maximal robust stabilizability perturbation bound of such perturbed fractional-order system with a linear state feedback controller, simultaneously obtaining the corresponding linear state feedback stabilizing controller are presented. With the help of the linear matrix inequality solvers, we can easily obtain the maximal robust stabilizability perturbation bound and the corresponding linear state feedback stabilizing controller. Finally, simulation examples are given to demonstrate the effectiveness of the proposed approaches.  相似文献   

17.
In this paper, we develop a matrix-based methodology to investigate the problems of stability and stabilizability for a deterministic finite automaton (DFA) in the framework of the semi-tensor product (STP) of matrices. First, we discuss the equilibrium point stability (resp., set stability) of a DFA, i.e., verifying whether or not all state trajectories starting from a subset of states converge to a specified equilibrium point (resp., subset of states). The necessary and sufficient conditions for verifying both stabilities are given, respectively. Second, equilibrium point stabilizability (resp., set stabilizability) of a DFA is investigated as verifying the issue of whether or not a DFA can be globally or locally stabilized to a specified equilibrium point (resp., subset of states) by a permissible state-feedback controller. Based on the pre-reachability set and invariant-subset defined in this paper, the matrix-based criteria for verifying equilibrium point stabilizability and set stabilizability are derived, respectively. Furthermore, for each type of stabilizability, all permissible state-feedback controllers for the case of minimal length state trajectories, called optimal state-feedback controllers, are characterized by using the proposed polynomial algorithms. Finally, two examples are presented to illustrate the effectiveness of the theoretical results.  相似文献   

18.
In this paper, the finite-time stabilization problem for memristor-based inertial neural networks (MINNs) with discontinuous activations (DAs) and distributed delays is investigated. To deal with the discontinuous property of the MINNs, the nonsmooth analysis theory is invoked. Furthermore, to simplify the MINNs with second-order state derivative, an order-reduced method is adopted. Then the second-order MINNs is transformed into a simpler first-order differential system. Moreover, the verifiable algebraic criteria are derived for the finite-time stabilization of MINNs with DAs and distributed delays under the designed control approach. Finally, the effectiveness of the obtained results are illustrated via numerical simulations.  相似文献   

19.
The paper is concerned with the modeling and stabilization problem of networked control systems under simultaneous consideration of bounded packet dropouts and occasionally missing control inputs. In particular, the focus of the paper is to capture the case where the packet dropouts and control inputs missing are subject to multiple sampling periods, and not periodic as in existing results. By input-delay approach and then fully considering the probability distribution characteristic of packet dropouts in the modeling, the original linear system is firstly transformed to a switched stochastic time-delay system. Meanwhile, the probability distribution values of stochastic delay taking values in m(m ≥ 2) given intervals can be explicitly obtained, which is of vital importance to analyse the stabilization problem of considered system. Secondly, by means of the average dwell time technique, some sufficient conditions in terms of linear matrix inequalities for the existence of desired stabilizing controller are derived. Finally, an illustrative example is given to illustrate the effectiveness of the proposed stabilizing controller and some less conservative results are obtained.  相似文献   

20.
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