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Register a new userOnline Observability of Boolean Control Networks
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Added by
Guisen Wu
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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Observabililty is an important topic of Boolean control networks (BCNs). In this paper, we propose a new type of observability named online observability to present the sufficient and necessary condition of determining the initial states of BCNs, when their initial states cannot be reset. And we design an algorithm to decide whether a BCN has the online observability. Moreover, we prove that a BCN is identifiable iff it satisfies controllability and the online observability, which reveals the essence of identification problem of BCNs.
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It is known that determining the observability and reconstructibility of Boolean control networks (BCNs) are both NP-hard in the number of nodes of BCNs. In this paper, we use the aggregation method to overcome the challenging complexity problem in verifying the observability and reconstructibility of large-scale BCNs with special structures in some sense. First, we define a special class of aggregations that are compatible with observability and reconstructibility (i.e, observability and reconstructibility are meaningful for each part of the aggregation), and show that even for this special class of aggregations, the whole BCN being observable/reconstructible does not imply the resulting sub-BCNs being observable/reconstructible, and vice versa. Second, for acyclic aggregations in this special class, we prove that all resulting sub-BCNs being observable/reconstructible implies the whole BCN being observable/reconstructible. Third, we show that finding such acyclic special aggregations with sufficiently small parts can tremendously reduce computational complexity. Finally, we use the BCN T-cell receptor kinetics model to illustrate the efficiency of these results. In addition, the special aggregation method characterized in this paper can also be used to deal with the observability/reconstructibility of large-scale linear (special classes of nonlinear) control systems with special network structures.
A new analytical framework consisting of two phenomena: single sample and multiple samples, is proposed to deal with the identification problem of Boolean control networks (BCNs) systematically and comprehensively. Under this framework, the existing works on identification can be categorized as special cases of these two phenomena. Several effective criteria for determining the identifiability and the corresponding identification algorithms are proposed. Three important results are derived: (1) If a BN is observable, it is uniquely identifiable; (2) If a BCN is O1-observable, it is uniquely identifiable, where O1-observability is the most general form of the existing observability terms; (3) A BN or BCN may be identifiable, but not observable. In addition, remarks present some challenging future research and contain a preliminary attempt about how to identify unobservable systems.
In this paper, we study dynamical quantum networks which evolve according to Schrodinger equations but subject to sequential local or global quantum measurements. A network of qubits forms a composite quantum system whose state undergoes unitary evolution in between periodic measurements, leading to hybrid quantum dynamics with random jumps at discrete time instances along a continuous orbit. The measurements either act on the entire network of qubits, or only a subset of qubits. First of all, we reveal that this type of hybrid quantum dynamics induces probabilistic Boolean recursions representing the measurement outcomes. With global measurements, it is shown that such resulting Boolean recursions define Markov chains whose state-transitions are fully determined by the network Hamiltonian and the measurement observables. Particularly, we establish an explicit and algebraic representation of the underlying recursive random mapping driving such induced Markov chains. Next, with local measurements, the resulting probabilistic Boolean dynamics is shown to be no longer Markovian. The state transition probability at any given time becomes dependent on the entire history of the sample path, for which we establish a recursive way of computing such non-Markovian probability transitions. Finally, we adopt the classical bilinear control model for the continuous Schrodinger evolution, and show how the measurements affect the controllability of the quantum networks.
Much has been said about observability in system theory and control; however, it has been recently that observability in complex networks has seriously attracted the attention of researchers. This paper examines the state-of-the-art and discusses some issues raised due to complexity and stochasticity. These unresolved issues call for a new practical methodology. For stochastic systems, a degree of observability may be defined and the observability problem is not a binary (i.e., yes-no) question anymore. Here, we propose to employ a goal-seeking system to play a supervisory role in the network. Hence, improving the degree of observability would be a valid objective for the supervisory system. Towards this goal, the supervisor dynamically optimizes the observation process by reconfiguring the sensory parts in the network. A cognitive dynamic system is suggested as a proper choice for the supervisory system. In this framework, the network itself is viewed as the environment with which the cognitive dynamic system interacts. Computer experiments confirm the potential of the proposed approach for addressing some of the issues raised in networks due to complexity and stochasticity.
It has been shown that self-triggered control has the ability to reduce computational loads and deal with the cases with constrained resources by properly setting up the rules for updating the system control when necessary. In this paper, self-triggered stabilization of Boolean control networks (BCNs), including deterministic BCNs, probabilistic BCNs and Markovian switching BCNs, is first investigated via semi-tensor product of matrices and Lyapunov theory of Boolean networks. The self-triggered mechanism with the aim to determine when the controller should be updated is given based on the decrease of the corresponding Lyapunov functions between two successive sampling times. We show that the self-triggered controllers can be chosen as the conventional controllers without sampling, and also can be optimally constructed based on the triggering conditions.
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