Observability Of Boolean Control Networks Research Articles

Observability of Boolean control networks with stochastic disturbances

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.

Structural Observability of Boolean Control Networks via Topology-Based Approach

This brief aims to investigate the structural observability of Boolean control networks, followed by the recent research stream, with available topology structure but unknown node dynamics. To begin with, two kinds of structural observability are defined along with two systems. Then, by adopting the dependency graphs, several necessary and sufficient conditions for structurally arbitrary-input and single-input observability are derived, respectively. Instead of employing the algebraic state space representation framework, this graphic-theoretical approach takes full advantage of node-to-node interaction, thus decreasing the time complexity to a great extent.

Observability Criteria for Boolean Networks

This article investigates observability of Boolean control networks (BCNs) and probabilistic Boolean networks (PBNs). First, weak observability of BCNs is discussed via the nonaugmented approach. The obtained result is then applied to determine (asymptotic) observability of PBNs. Finally, complexity of algorithms based on new criteria is analyzed. Compared with existing ones, time and space complexity do not get worse, even are improved under some mild conditions.

Minimal observability of Boolean control networks

In this paper, the minimum observability of Boolean control networks (BCNs) is investigated. An augmented system is proposed to analyze the dynamical trajectories of state pairs, followed by an effective criterion for observability of BCNs utilizing graphic tools. A minimal observability problem is formulated based on the fact that observability of the underlying network is facilitated by injecting new measurements. By introducing an indicator matrix, the solution of added measurements in vector form can be converted into dealing with the equations, by which, all the feasible measurements can be derived. Furthermore, the solution of the least added measurements can be solved by a minimum set covering problem. Meanwhile, two examples are given to illustrate the theoretical results.

Controllability and Observability of Boolean Control Networks via Sampled-Data Control

In this paper, the controllability and observability of sampled-data Boolean control networks (SDBCNs) are investigated. New phenomena are observed in the study of the controllability and observability of SDBCNs. We routinely convert SDBCNs into linear discrete-time systems by the semitensor product of matrices. Necessary and sufficient conditions are derived for the controllability of SDBCNs. After that, we combine two SDBCNs with the same transition matrix into a new SDBCN to study the observability. Using an iterative algorithm, a stable row vector ${\mathcal {U}}^*$ , called the observability row vector, in finite iterations, is obtained. It is proved that an SDBCN is observable, if and only if $\Vert {\mathcal {U}}^*\Vert _1=N^2-N$ with $N:=2^n$ , where $n$ is the number of state-variables of BNs. Moreover, based on graph theory, a more effective algorithm is given to determine the observability of SDBCNs. Its complexity is not related to the length of the sampling period. In addition, some equivalent necessary and sufficient conditions are put forward for the observability of SDBCNs. Numerical examples are given to demonstrate the effectiveness of the obtained results.

Robust Controllability and Observability of Boolean Control Networks under Different Disturbances

This paper investigates robust controllability and observability of Boolean control networks under disturbances. Firstly, under unobservable disturbances, some sufficient conditions are obtained for robust controllability of BCNs. Then an algorithm is proposed to construct the least control sequences which drive the trajectory from a state to a given reachable state. If the disturbances are observable, by defining the order-preserving system, an efficient sufficient condition is obtained for robust controllability of BCNs. Finally, the robust observability problem is converted into an equivalent robust controllability via set controllability and is solved by using the results obtained for set controllability. Some numerical examples are presented to illustrate the obtained results.

Input observability of Boolean control networks

This paper devotes to the input observability, which also is called the nonsingularity or left invertibility, of general Boolean control networks. First, using graphic approach converts the global nonsingularity into pointwise finite-step nonsingularity. Subsequently, a series of matrix-form criterions are given to identify the nonsingularity, under which suitable inverse Boolean control networks can be designed. Finally, one application and one numerical example are used to illustrate the feasibility and validity of the obtained results.

Observability of Boolean Control Networks Using Parallel Extension and Set Reachability.

This brief reviews various definitions of observability for Boolean control networks (BCNs) and proposes a new one: output-feedback observability. This new definition applies to all BCNs whose initial states can be identified from the history of output measurements. A technique called parallel extension is then proposed to facilitate observability analysis. Furthermore, a technique called state transition graph reconstruction is proposed for analyzing the set reachability of BCNs, based on which new criteria for observability, single-input sequence observability, and arbitrary-input observability, are obtained. Using the proposed techniques, this brief proves that the problem of output-feedback observability can be recast as that of stabilizing a logic dynamical system with output feedback. Then, a necessary and sufficient condition for static output feedback observability is proposed. The relationships between the different definitions of observability are discussed, and the main results are illustrated with examples.

Observability of Boolean networks via set controllability approach

Controllability and observability of Boolean control networks (BCNs) are two fundamental properties. But verification of the latter is much harder than the former. This paper considers the observability of BCNs via controllability. First, set controllability is proposed, and a necessary and sufficient condition is obtained. Then a technique is developed to convert observability into an equivalent set controllability problem. Using the result for set controllability, a necessary and sufficient condition is also obtained for the observability of BCNs.

Observability of Boolean Control Networks with Time-Variant Delays in States

This paper gives an equivalent condition for the observability of Boolean control networks (BCNs) with time-variant delays in states under a mild assumption by using the graph-theoretic method under the framework of the semi-tensor product of matrices. First, the BCN under consideration is split into a finite number of subsystems with no time delays. Second, the observability of the BCN is verified by testing the observability of the so-called observability constructed path (a special subsystem without time delays) based on graph theory. These results extend the recent related results on the observability of BCNs. Examples are shown to illustrate the effectiveness of the results.

Observability of Boolean control networks

We show some new results on the observability of Boolean control networks (BCNs). First, to study the observability, we combine two BCNs with the same transition matrix into a new BCN. Then, we propose the concept of a reachable set that results in a given set of initial states, and we derive four additional necessary and sufficient conditions for the observability of BCNs. In addition, we present an algoriTheoRemark and construct an observability graph to determine the observability of BCNs. Finally, we illustrate the obtained results using three numerical examples.

Observability of Boolean Control Networks: A Unified Approach Based on Finite Automata

The problem on how to determine the observability of Boolean control networks (BCNs) has been open for five years already. In this paper, we propose a unified approach to determine all the four types of observability of BCNs in the literature. We define the concept of weighted pair graphs for BCNs. In the sense of each observability, we use the so-called weighted pair graph to transform a BCN to a finite automaton, and then we use the automaton to determine observability. In particular, the two types of observability that rely on initial states and inputs in the literature are determined. Finally, we show that no pairs of the four types of observability are equivalent, which reveals the essence of nonlinearity of BCNs.

A note on observability of Boolean control networks

The observability of Boolean control networks is investigated. The pairs of states are classified into three classes: (i) diagonal, (ii) h-distinguishable, and (iii) h-indistinguishable. For h-indistinguishable pairs, we construct a matrix W called the transferable matrix, which indicates the control-transferability among h-indistinguishable pairs. Modifying W yields a Boolean matrix U0, which is used as the initial matrix for an iterative algorithm. After finite iterations a stable U∗ is reached, which is called the observability matrix. It is proved that a Boolean control network is observable, if and only if, the last column of U∗, Colr+1(U∗)=1r. Some numerical examples are presented.

Controllability and observability of Boolean control networks with time-variant delays in states.

This brief investigates the controllability and observability of Boolean control networks with (not necessarily bounded) time-variant delays in states. After a brief introduction to converting a Boolean control network to an equivalent discrete-time bilinear dynamical system via the semi-tensor product of matrices, the system is split into a finite number of subsystems (constructed forest) with no time delays by using the idea of splitting time that is proposed in this brief. Then, the controllability and observability of the system are investigated by verifying any so-called controllability constructed path and any so-called observability constructed paths in the above forest, respectively, which generalize some recent relevant results. Matrix test criteria for the controllability and observability are given. The corresponding control design algorithms based on the controllability theorems are given. We also show that the computing complexity of our algorithm is much less than that of the existing algorithms.

Observability, Reconstructibility and State Observers of Boolean Control Networks

The aim of this paper is to introduce and characterize observability and reconstructibility properties for Boolean networks and Boolean control networks, described according to the algebraic approach proposed by D. Cheng and co-authors in the series of papers [3], [6], [7] and in the recent monography . A complete characterization of these properties, based both on the Boolean matrices involved in the network description and on the corresponding digraphs, is provided. Finally, the problem of state observer design for reconstructible BNs and BCNs is addressed, and two different solutions are proposed.

Observability of Boolean Control Networks With State Time Delays

This brief deals with the problem of the observability for the Boolean control networks with time delays in states. First, using semi-tensor product of matrices and the matrix expression of logic, the Boolean control networks with state delays can be converted into discrete time delay dynamics. Then, the observability of the Boolean control networks via two kinds of inputs is investigated by giving necessary and sufficient conditions. Finally, examples are given to illustrate the efficiency of the obtained results.

Controllability and observability of Boolean control networks

The controllability and observability of Boolean control networks are investigated. After a brief review on converting a logic dynamics to a discrete-time linear dynamics with a transition matrix, some formulas are obtained for retrieving network and its logical dynamic equations from this network transition matrix. Based on the discrete-time dynamics, the controllability via two kinds of inputs is revealed by providing the corresponding reachable sets precisely. Then the problem of observability is also solved by giving necessary and sufficient conditions.