Control And Applications Of Boolean Networks Via Algebraic Method

This dissertation contains two main parts.Part 1 is the analysis and con-trol of large-scale Boolean networks.Part 2 is the input-output decoupling of Boolean control networks.In Chapter 1,the research background of Boolean networks,semi-tensor product,large-scale Boolean networks,de-coupling problems are introduced.Chapter 2 gives the definitions and properties of semi-tensor product,network aggregation,state space as well as the algebraic expressions of logical functions.Method to design large-scale Boolean networks based on prescribed attractors is presented in Chapter 3,such that the network contains desired attractors and does not contain undesired attractors,the size of the basin of the desired attractors is max-imized.Using network aggregation,the network is partitioned to several blocks.Based on that,a necessary and sufficient condition is proposed to ensure the network contains desired attractors and does not contain unde-sired attractors.An algorithm is given to construct the structure matrix of each subnetwork.In Chapter 4,we investigate the optimal one-bit per-turbation of large-scale Boolean networks,in other words,finding a one-bit perturbation,under that the difference between the size of the basin of the desired attractors and the size of the undesired attractors is maximized.The problem is analyzed based on network aggregation as well.The problem is solved in 5 steps,5 algorithms are presented in sequence.In Chapter 5,the steady-state distribution of large-scale probabilistic Boolean networks is studied.The problem is considered based on network aggregation too.Using semi-tensor product,each block has a unique probabilistic transition matrix.Based on which,two necessary and sufficient conditions of the existence of steady-state distributions for small-scale probabilistic Boolean networks is obtained.And an algorithm is derived to calculate the steady-state distri-butions of the whole network.In Chapter 6,the minimum-time control for constrained large-scale Boolean control networks is investigated.Under network aggregation,this problem is converted to finding the minimum time control for each subnetwork.Based on it,the method to find the minimum-time control for the whole networks is proposed.In Chapter 7,the input-output decoupling of Boolean control networks is discussed on the basis of its algebraic form and state space method.A necessary and sufficient con-dition of the existence of the comparable output friendly subspaces as well as the method to compute them are presented.Two kinds of controllers are design to solve the decoupling problem,including open-loop controller and state feedback controller.