Switched Boolean Control Networks Research Articles

Robust controllability and stabilization of switched Boolean control networks subject to multi-bit function perturbations

This paper develops a new multi-bit perturbed controllability matrix method for solving the robust controllability and stabilization of switched Boolean control networks (SBCNs) with multi-bit function perturbations. By constructing both perturbed position index matrix and multi-bit perturbed controllability matrix for SBCNs, the space of state pairs is divided into two disjointed parts, which determine whether or not the paths between two arbitrary states are affected by function perturbations. Then, a sequence of perturbed reachable sets is constructed, and several criteria are presented for the robust controllability of SBCNs under the multi-bit function perturbations. As a generalization, a perturbed position index matrix and a sequence of perturbed reachable sets are designed for the closed-loop system, based on which, a necessary and sufficient condition is presented for the robust state-feedback stabilization of SBCNs under arbitrary switching signal. Numerical examples demonstrate that our new criteria work well for the multi-bit function perturbations and thus have more practical significance.

Set stabilizability of switched Boolean control networks via Ledley antecedence solution

This paper studies two kinds of set stabilizability issues of switched Boolean control networks (SBCNs) by Ledley antecedence solution, that is, pointwise set stabilizability and set stabilizability under arbitrary switching signals. Firstly, based on the state transition matrix of SBCNs, the mode-dependent truth matrix is defined. Secondly, using the mode-dependent truth matrix in every step, a switching signal and the corresponding Ledley antecedence solutions are determined. Furthermore, a state feedback switching signal and a state feedback control are obtained for the pointwise set stabilizability. Thirdly, with the help of all mode-dependent truth matrices, the Ledley antecedence solutions are derived for a set of Boolean inclusions, which admits a state feedback control for the set stabilizability under arbitrary switching signals. Finally, an example is given to show the effectiveness of the proposed results.

Stabilisation and set stabilisation of periodic switched Boolean control networks

This paper investigates the stabilisation and set stabilisation problems for a class of switched Boolean control networks (SBCNs) with periodic switching signal via a semi-tensor product method. First, algebraic forms are constructed for SBCNs with periodic switching signal. Second, based on the algebraic formulations, the stabilisation and set stabilisation of SBCNs with periodic switching signal are discussed, and some new results are presented. Furthermore, constructive procedure of open loop controllers is given, and the design algorithms of switching signal-dependent state feedback controllers via antecedence solution technique are derived. The study of illustrative examples shows the good performance of the methods presented in this paper.

Finite automata approach to reconstructibility of switched Boolean control networks

This paper investigates the reconstructibility of switched Boolean control networks (SBCNs). Several new types of definition about reconstructibility are proposed where the existence and arbitrariness of the switching signal and the input sequence are inconsistent. A weighted pair graph describing all pairs of states which are indistinguished is defined. A deterministic finite automata method is applied into the reconstructibility analysis. Accordingly, several algorithms are designed to determine these types of reconstructibility. Moreover, for a given reconstructible SBCN, an algorithm for determining the current state is provided. Finally, an example is provided to demonstrate the effectiveness of the proposed algorithms and results.

Observability of switched Boolean control networks using algebraic forms

<p style='text-indent:20px;'>This paper addresses the observability of a switched Boolean control network (SBCN) using semi-tensor product (STP) of matrices. First, the observability of the SBCN is determined under desirable switching signals and arbitrary switching signals by encoding the switching signal as a boolean input. Then an algorithm is designed for determining the observability. Furthermore, feedback control laws are obtained to guarantee the observability of SBCNs. Examples and corresponding state trajectory graphs are given to illustrate the effectiveness of the given results.

Feedback stabilization control design for switched Boolean control networks

In this paper, the design of all possible switching signal-dependent state feedback and output feedback stabilizers for switched Boolean control networks (SBCNs) under arbitrary switching signal is investigated. By making use of the algebraic state-space approach to SBCNs, necessary and sufficient conditions for the stabilization at a given equilibrium point are presented. A new algorithm is proposed to determine all possible complete families of controllable sets for SBCNs, thereby all possible switching signal-dependent state feedback and output feedback controllers are obtained. Furthermore, we derive necessary and sufficient conditions for the solvability of the output regulation problem, and we show that, upon satisfying such conditions, also this problem can be solved by means of switching signal-dependent state feedback and output feedback controllers. At last, the proposed results are supported by examples.

Sampled-Data Set Stabilization of Switched Boolean Control Networks

In this paper, the set stabilization of switched Boolean control networks (SBCNs) under sampled-data feedback control is addressed. Here, the control input is switching signal-dependent, and SBCNs can switch only at the sampling instants. First, the sampled point control invariant subset (SPCIS) of SBCNs is defined, and an algorithm is provided to obtain the largest SPCIS under arbitrary switching signal. Based on the largest SPCIS, some necessary and sufficient conditions are presented for the set stabilization of SBCNs by switching signal-dependent sampled-data (SSDSD) state feedback control. Furthermore, a constructive procedure is given to design all possible SSDSD state feedback controllers. Finally, some examples are presented to illustrate the effectiveness of the obtained results.

Output Tracking Control Design of Switched Boolean Control Networks

In this letter, the output tracking control design of switched Boolean control networks (SBCNs) is investigated via state feedback and output feedback control. The algebraic state-space representation method which resorts to the semi-tensor product (STP) of matrices is utilized; necessary and sufficient conditions for the solvability of the output tracking control problem are presented. A constructive procedure is given to obtain all possible switching signal-dependent state feedback and output feedback controllers under arbitrary switching signals such that the output of SBCNs tracks a time-varying reference trajectory. Finally, a SBCN model of the lactose regulation in the Escherichia Coli bacteria is considered to illustrate the effectiveness of the proposed results.

Input–output decoupling control design for switched Boolean control networks

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.

Time-optimal state feedback stabilization of switched Boolean control networks

This paper investigates the time-optimal state-feedback stabilization of switched Boolean control networks (SBCNs). Based on the properties of the semi-tensor product (STP) of matrices, a technique is proposed to merge the switching signal and all inputs of subnetworks into a single input variable. This technique allows us to transfer a SBCN to an equivalent non-switching logical control network (LCN) and eases the analysis and design process significantly. So long as a state-feedback stabilizer is obtained for the resulting non-switching LCN, it can then be decomposed uniquely into the respective state feedbacks of the sub-networks and the state-dependent switching law. Based on this technique, the controllability and stabilisability of such SBCNs are solved and an algorithm for finding all time-optimal switching state feedbacks is proposed. An example is described to illustrate the main results and the design process proposed in this paper.

Finite automata approach to observability of switched Boolean control networks

In this paper, the observability of switched Boolean control networks (SBCNs) is determined. First, a new concept of weighted pair graphs for SBCNs is defined. Second, the weighted pair graph is used to transform an SBCN into a deterministic finite automaton (DFA). Lastly, the observability of the SBCN is determined by testing the completeness of the DFA. Based on these results, algorithms for determining the observability and the initial state are designed. The computational complexity of this algorithm is doubly exponential in the number of nodes of SBCNs. Furthermore, more effective sufficient or necessary conditions for the observability of SBCNs are obtained directly from weighted pair graphs. The computational complexity of these conditions is exponential in the number of nodes of SBCNs.

MIS approach analyzing the controllability of switched boolean networks with higher order

Controllability of higher order switched Boolean control networks (SBCNs) is investigated in this paper. Two algebraic forms of higher order SBCNs are derived. A necessary and sufficient condition of controllability for higher order SBCNs is obtained. An algorithm is derived to calculate the corresponding control and switching-law which drive a point to a given reachable point. Then we talk about the compatibility between our main results and other systems. Finally, two illustrative examples are given to show the validity of the main results.

Controllability and observability of switched Boolean control networks

The controllability and observability are investigated for a class of switched Boolean control networks (SBCNs). Using semi-tensor product of matrices, the dynamics of an SBCN can be transformed into an algebraic form. The model-input-state (MIS) matrix of an SBCN is introduced and studied for the first time. This matrix contains complete information of the MIS mapping. A necessary and sufficient condition for the controllability of SBCN is obtained. The corresponding control and switching law, which drive a point to a given reachable point are designed. A sufficient condition for the observability of an SBCN is given. Moreover, under the assumption of controllability, one necessary and sufficient condition is derived for the observability.