追捕逃逸型微分对策问题的识别域判别

研究了仿射非线性控制系统下的单目标两人追捕逃逸型微分对策问题,解决了该类控制系统在不等式约束区域上系统识别域的判别问题,给出了判别识别域的充分必要条件.首先利用生存理论及非光滑分析工具得到了仿射非线性控制系统的识别域判别定理,从而把对该非线性控制系统识别域的判别问题转化为求解凸不等式组的相容性问题.基于凸可行问题的求解方法给出了此问题的投影算法,并给出算法相应的收敛性定理.最后得到了仿射非线性系统下的两人追捕逃逸型微分对策问题的选择定理.

Determining the Discriminating Domain of Pursuit-evasion Games

The pursuit-evasion games with two players and one target for an affine nonlinear control system were investigated.The problem of determining the discriminating domain in the region with inequality constraints for this class of control system was solved and a necessary and sufficient condition was given out.Based on viability theory and nonsmooth analysis method,a theorem of determining the discriminating domain for the nonlinear system was obtained,so that the problem can be transformed into the problem of determining the consistency of convex inequalities.Then a projection algorithm for solving the problem was provided based on the algorithm of convex feasible problem.The convergence theorem of the algorithm was received and finally the alternative theorem for pursuit evasion games with two players was achieved.