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1.
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   

2.
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   

3.
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   

4.
In this paper, we study the generalized cluster synchronization problem for the Boolean control networks (BCNs) with delays in both the states and the inputs. First, by using the method of semi-tensor product of matrices, the original network is transformed into an equivalent extended system. Next, based on the updated iterative equation of the system, two types of generalized cluster synchronization are investigated: 1) generalized internal cluster synchronization within the BCN, and 2) generalized cluster synchronization between the BCN and the target reference network. Some necessary and sufficient conditions are proposed guaranteeing the realization of the generalized cluster synchronization. What is more, the gain matrices of the state-feedback controllers are explicitly designed. Numerical simulations are also given to illustrate effectiveness of the theoretical results obtained.  相似文献   

5.
The classical criteria for controllability and observability are given a tensorial formulation which is then extended into Boolean form directly related to a digraph interpretation of system structure. This is examined in detail with particular reference to group theoretic aspects, invariant properties under transformation, the term rank test and the existence of zero eigenvalues.Within this framework the structural design concepts of potential controllability and observability are presented in generalised terms.  相似文献   

6.
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   

7.
In this paper, the data-driven adaptive dynamic programming (ADP) algorithm is proposed to deal with the optimal tracking problem for the general discrete-time (DT) systems with delays for the first time. The model-free ADP algorithm is presented by using only the system’s input, output and the reference trajectory of the finite steps of historical data. First, the augmented state equation is constructed based on the time-delay system and the reference system. Second, a novel data-driven state equation is derived by virtue of the history data composed of input, output and reference trajectory, which is considered as a state estimator.Then, a novel data-driven Bellman equation for the linear quadratic tracking (LQT) problem with delays is deduced. Finally, the data-driven ADP algorithm is designed to solve the LQT problem with delays and does not require any system dynamics. The simulation result demonstrates the validity of the proposed data-driven ADP algorithm in this paper for the LQT problem with delays.  相似文献   

8.
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   

9.
In this paper, we investigate the consensus tracking problem of nonlinear MASs with nonuniform time-varying input delays and external disturbances. For each follower, the composited disturbance observer and the state observer are employed to estimate bounded composited disturbances and unmeasured states, and a distributed observer based on output-feedback is proposed to approximate the leader’s states approachably. Sequentially, the consensus tracking control is converted into a stability control problem for the nonlinear MASs with nonuniform time-varying input delays. Subsequently, a distributed controller based on the truncated prediction approach is presented, which only depends on the boundary value of time-varying input delays. The distributed controller can render each follower synchronically stable via the Lyapunov stability theory. Finally, a group of single-link manipulators is used as an example to verify the effectiveness of the theoretical results.  相似文献   

10.
This paper is concerned with the problem of robust synchronization of a class of complex dynamical networks with time-varying delays and reaction–diffusion terms. To reflect most of the dynamical behaviors of the system, the parameter uncertainties are considered. A sampled-data controller with m stochastically varying sampling periods whose occurrence probabilities are given constants is considered. The control objective is that the trajectories of the system by designing suitable control schemes track the trajectories of the system with sample-data control. It is shown that, through Lyapunov stability theory, the proposed sample-data controllers are successful in ensuring the achievement of robust synchronization of complex dynamical networks even in the case of uncertainity and Markovian jumping parameters. By utilizing the Lyapunov functional method, Jensen’s inequality, Wirtinger’s inequality and lower bounds theorem, we establish a sufficient criterion such that, for all admissible parameter uncertainties, the complex dynamical network is robustly synchronized. The derived criteria are expressed in terms of linear matrix inequalities that can be easily checked by using the standard numerical software. Illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed results.  相似文献   

11.
《Journal of The Franklin Institute》2023,360(14):10728-10744
This paper deals with state estimation for a class of Lipschitz nonlinear systems under a time-varying disconnected communication network. A distributed observer consists of some local observers that are connected to each other through a communication network. We consider a situation where a communication network does not remain connected all the time, and the network may be caused by intermittent communication link failure. Moreover, each local observer has access to a local measurement, which may be insufficient to ensure the system’s observability, but the collection of all measurements in the network ensures observability. In this condition, the purpose is to design a distributed observer where the estimated state vectors of all local observers converge to the state vector of the system asymptotically, while local observers exchange estimated state vectors through a communication network and use their local measurements. According to theoretical analysis, a nonlinear and a robust nonlinear distributed observer exist when in addition to the union of all communication topologies being strongly connected during a time interval, the component of each communication graph is also strongly connected during each subinterval. The existence conditions of the distributed observers are derived in terms of a set of linear matrix inequalities (LMIs). Finally, the effectiveness of the presented method is numerically verified using some simulation examples.  相似文献   

12.
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   

13.
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   

14.
This paper studies the robust stabilization problem of a class of uncertain Lipschitz nonlinear systems with infinite distributed input delays. A novel robust predictor feedback controller is developed and the controller gain can be obtained via solving a linear matrix inequality. It is shown that the proposed robust predictor feedback controller can globally exponentially stabilize the concerned uncertain nonlinear system with infinite distributed input delays. The key to the proposed approach is the development of several new quadratic Lyapunov functionals. The obtained results are extended to the case of systems with both multiple constant input delays and infinite distributed input delays. It is noted that the obtained results include some existing results on systems with constant input delays or bounded distributed input delays as special cases. Finally, two examples of Chua’s circuit and spacecraft rendezvous system are presented to illustrate the effectiveness of the proposed robust controllers.  相似文献   

15.
For a continuous-time linear system with constant reference input, the network-based proportional-integral (PI) control is developed to solve the output tracking control problem by taking time-varying sampling and network-induced delays into account. A traditional PI control system is introduced to obtain the equilibriums of state and control input. Using the equilibriums, a discrete-time PI tracking controller in a network environment is constructed. The resulting network-based PI control system is described by an augmented system with two input delays and the output tracking objective is transformed into ensuring asymptotic stability of the augmented system. A delay-dependent stability condition is established by a discontinuous augmented Lyapunov–Krasovskii functional approach. The PI controller design result of in-wheel motor as a case study is provided in terms of linear matrix inequalities. Matlab simulation and experimental results resorting to a test-bed for ZigBee-based control of in-wheel motor are given to validate the proposed method.  相似文献   

16.
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   

17.
This paper is concerned with the stabilization of linear systems with both pointwise and distributed input delays, which can be arbitrarily large yet exactly known. The state vector used in the well-known Artstein transformation is firstly linked with the future state of the system. Pseudo-predictor feedback (PPF) approaches are then established to design memory stabilizing controllers. Necessary and sufficient conditions guaranteeing the stability of the closed-loop system are established in terms of the stability of some integral delay systems. Furthermore, since the PPF still is infinite-dimensional state feedback law and may cause difficulties in their practical implementation, truncated pseudo-predictor feedback (TPPF) approaches are established to design finite dimensional (memoryless) controllers. It is shown that the pointwise and distributed input delays can be compensated properly by the TPPF as long as the open-loop system is polynomially unstable. Finally, two numerical examples, one of which is the spacecraft rendezvous control system, are carried out to support the obtained theoretical results.  相似文献   

18.
The issue of non-fragile controller’s designed with reachable set estimation and time-delay for multi-agent systems(MASs) is investigated in this paper. The information interaction among agents is governed by a set of switching sequence, which can be described by continue-time discrete state semi-Markov process. By tree-transformation, the MASs firstly converted into reduced-order system, and properly considered the instability of the parameters with the dynamic behavior of the controller, a non-fragile controller is designed to describe the system’s performance cope with the perturbation from the controller. The sufficient conditions are established in forms of a series of linear matrix inequalities which are based on Lyapunov-Krasovskii method, and the agent’s state of error systems is bounded by a finite closed set will be guaranteed. Finally, the availability of the derived theoretical results are verified by two numerical simulations.  相似文献   

19.
A method is presented for constructing a nonreduced observer for a finite dimensional linear system. The systems considered are nth order, time-invariant or time-varying forced linear systems which are assumed to be bounded and uniformly completely state reconstructible. The observer dynamics are derived from an optimal estimation formulation which is related to the concept of observability. The cost functional used in this formulation includes a parameter which determines the relative weighting of the system output and the estimate of the initial system state. The result is a practical method of estimating the state of a linear system from noiseless measurements of the input and output. The results are also of theoretical significance in that a direct connection between reconstructibility and the existence of observers is established.  相似文献   

20.
In this paper, the consensus tracking problem is studied for a group of nonlinear heterogeneous multiagent systems with asymmetric state constraints and input delays. Different from the existing works, both input delays and asymmetric state constraints are assumed to be nonuniform and time-varying. By introducing a nonlinear mapping to handle the problem caused by state constraints, not only the feasibility condition is removed, but also the restriction on the constraint boundary functions is relaxed. The time-varying input delays are compensated by developing an auxiliary system. Furthermore, by utilizing the dynamic surface control method, neural network technology and the designed finite-time observer, the distributed adaptive control scheme is developed, which can achieve the synchronization between the followers’ output and the leader without the violation of full-state constraints. Finally, a numerical simulation is provided to verify the effectiveness of the proposed control protocol.  相似文献   

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