Algebraic Method To Control And Application Of Logic Networks

In Chapter1of this dissertation, Boolean network and semi-tensor product are introduced for preliminary. The controllability and observability are investigated for a class of switched Boolean control networks (SBCNs) in Chapter2. Using semi-tensor product of matrices, the dynamics of an SBC-N can be transformed into an algebraic form. The model-input-state matrix of an SBCN is introduced and studied for the first time. This matrix contain-s complete information of the model-input-state mapping. A necessary and sufficient condition for the controllability of SBCN is obtained. The corre-sponding 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 also given. Moreover, under the assumption of controllability, one neces-sary and sufficient condition is derived for the observability. Controllability of higher order SBCNs is investigated in this chapter. Two algebraic forms of higher order SBCNs are derived. A necessary and sufficient condition of controllability for higher order SBCNs is obtained. Finally, two illustrative examples are given to show the validity of the main results. In Chapter3, we investigate the disturbance decoupling problems (DDPs) of mix-valued logical control networks (MLCNs) via semi-tensor product method. By us-ing prime factor decomposition, a unique Y-friendly subspace of mix-valued logical networks (MLNs) is derived. A necessary and sufficient condition is obtained for the solvability of DDPs. An algorithm is proposed to find all disturbance decoupling controllers. This approach is more operational than the existing results in which the Y-friendly subspace is not unique. Finally an illustrative numerical example is given to show the effectiveness of the proposed method. In Chapter4, the formation control (FC) problem is investigated via mix-valued logic approach. First, a trajectory tracking algo-rithm of MLCN is proposed. A new formulation of FC problems is established and a feedback controller is designed to solve FC problems. The mathemati-cal description of partial-formation control (PFC) problems is then designed as a structure of logical networks. An interesting practical example of PFC is also presented and discussed in detail.