中文摘要：

应用测度序列R-收敛的新概念来描述函数空间中总极值问题解的有限维逼近,并利用变差积分途径来寻找这样的解.针对有约束问题,运用罚变差积分算法把所给问题转化为无约束问题,且给出一个非凸状态约束最优控制问题的数值例子以说明该算法的有效性.

英文摘要：

New concept of convergence （ R-convergence） of a sequence of measures was applied to characterize global minimizers in functional space as a sequence of approximating solutions in finite-dimensional spaces. A deviation integral approach was used to find such solutions. For a constrained problem,a penalized deviation integral algorithm was proposed to convert it to unconstrained ones. A numerical example on optimal control problem with non convex state constrains was given to show that the algorithm is efficient.