矩阵半张量积理论及其在若干控制问题中的应用

项目名称： 矩阵半张量积理论及其在若干控制问题中的应用

项目编号： No.61273013

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 自动化技术、计算机技术

项目作者： 程代展

作者单位： 中国科学院数学与系统科学研究院

项目金额： 62万元

中文摘要： 理论研究面向若干前沿控制问题从基础理论和数值算法两个方面发展矩阵半张量积. 研究重点为: (1)布尔微积分; (2)伪布尔函数的半张量积方法; (3)半张量积的算法研究. 目的是将半张量积发展为处理有限集上的动态系统的便捷工具(暂称有限数学). 控制应用包括: (1)概率布尔网络控制: 以基因调控网络为对象, 将确定型布尔网络控制理论推广到概率布尔网络; (2)逻辑 - 连续动态系统的控制问题: 以多导弹协同作战为对象, 建立有效的动态模型, 以性能函数(如能量)为指标, 设计有效的混合控制规则; (3)基于博弈论的最优控制: 以人机无穷时间动态博弈为对象, 以半张量积刻模型, 以策略图的重构方法寻优, 研究带有贴现因子的优化控制; (4)耦合模糊控制的半张量积方法: 发展基于半张量积的多模糊关系理论与方法,并将其应用于具有强耦合控制的多输入系统模糊控制设计.

中文关键词： 矩阵半张量积；逻辑系统；网络演化博弈；势博弈；控制

英文摘要： Facing some frontier control problems, the theoretical research aims at developing semi-tensor product (STP) from two aspects: fundamental theory and numerical computation. The main research topics consist of (1) Boolean calculus; (2) STP approach to pseudo-Boolean functions; (3) Algorithms for STP. The overall purpose is to develop the theory of STP into a convenient tool in dealing with dynamics over finite sets (called, tentatively, Finite Math.) The control applications include (1) Probabilistic Boolean network: Taking the gene regularity network as example, the control theory of Boolean networks will be extended to probabilistic Boolean networks. (2) Control of logic - continuous mixed dynamic systems: Using multi-missile cooperating control as an object, a proper dynamic model for such systems need to be built first. Under a suitable performance criteria (such as energy), efficient mixed control laws will be proposed. (3) Game theory based optimal control: Considering machine-human dynamic games, STP is used to model it. Optimize the payment with discount factor by reconstructing strategy graph. (4) STP approach to coupled fuzzy control: Develop theory and method for fuzzy relations, and apply it to design of coupled fuzzy controls of multi-input systems.

英文关键词： Semi-tensor product of matrices；logical system；networked evolutionary game；potential game；control