Set Stability and Set Stabilization of Boolean Control Networks Avoiding Undesirable Set

The traditional set stability of Boolean networks (BNs) refers to whether all the states can converge to a given state subset. Different from the existing results, the set stability investigated in this paper is whether all states in a given initial set can converge to a given destination set. This paper studies the set stability and set stabilization avoiding undesirable sets of BNs and Boolean control networks (BCNs), respectively. First, by virtue of the semi-tensor product (STP) of matrices, the dynamics of BNs avoiding a given undesirable set are established. Then, the set reachability and set stability of BNs from the initial set to destination set avoiding an undesirable set are investigated, respectively. Furthermore, the set stabilization of BCNs from the initial set to destination set avoiding a given undesirable set are investigated. Finally, a design method for finding the time optimal set stabilizer is proposed, and an example is provided to illustrate the effectiveness of the results.

RESOURCE-ORIENTED PARALLEL PLANNING

This paper presents a new paradigm for constructing a partially ordered plan network, referred to as "resource-oriented parallel planning (RP2)". In resource-oriented parallel planning, goal states are grouped into a collection of goal state subsets, each of which consists of those goal states associated with a particular resource. A subplan is generated for each goal state subset by planning the flow of the corresponding resource, and thus satisfying the constraints specified by each of the goal state subsets. A complete plan is then constructed by synthesizing individual subplans based on the synchronization among subplans. A distinctive feature of RP2 is that each subplanner generates a conflict-free subplan by controlling the flow of a particular resource while synthesizing a complete plan in cooperation with other subplanners. This can be compared with the conventional state-oriented parallel planning, where each subplanner generates a subplan achieving a goal state while resolving conflicts among subplans in cooperation with other subplanners. RP2 makes use of resource reasoning in distinguishing important and unimportant resources associated with a goal. This allows each subplanner to hierarchically construct a resource-flow plan and to dynamically coordinate among subplanners in achieving a goal associated with more than one resource. The proposed scheme not only makes it possible to generate an optimal plan in terms of the maximum parallelism or the minimum depth of a plan network, but also makes it easier to implement the concurrent generation of parallel plans in a parallel and distributed processing environment.