基于微分对策的潜艇鱼雷攻击占位问题研究

Research of the Problem that how Submarine Occupy Torppedo Attack Position based on Differential Game Theories

针对潜艇鱼雷攻击占位问题,建立占位方案分析和优化的微分对策模型,采用影子目标法对问题进行简化。证明了在给定规避速度大小的条件下,潜艇最佳规避策略为直线运动。于是利用定性微分对策理论,给出潜艇可占领攻击阵位条件。以占位时间最短为优化目标,建立可占位情形下的占位方案优化模型,即可占位情形下的最短时间占位方案计算模型,给出最短时间占位方案解析计算公式。

The differential game models for submarine torpedo attack occupy position plan analysis and optimization have been provided, that using the shadow target to simply the problem description and the thoeroy derivation, the conclusion that the best strategy for submarine to escape with given velocity is linear motion. The conditions that submarine can occupy the attack position has been worked out using qualitative differential game theories and methods. The plan optimization model and the optimal plan calculate formula for the case that submarine can occupy attack position have been proposed by the aid of the optimal control theories and methods. The calculation results of the optimal occupy position plan have been verified by simulation.