The paper offers a self-contained account of the theory of first and second order necessary conditions for optimal control problems (with state constraints) based on new principles coming from variational analysis. The key element of the theory is reduction of the problem to unconstrained minimization of a Bolza-type functional with necessarily non-differentiable integrand and off-integral term. This allows to substantially shorten and simplify the proofs and to get new results not detected earlier by traditional variational techniques. This includes a totally new and easily verifiable second order necessary condition for a strong minimum in the classical problem of calculus of variations. The condition is a consequence of a new and more general second order necessary condition for optimal control problems with state constraints. Simple examples show that the new conditions may work when all known necessary conditions fail.

本文提供了基于变分分析的新原理的最优控制问题（具有状态约束）的一阶和二阶必要条件理论的完整说明。该理论的关键要素是将问题简化为具有不可微积分和非积分项的Bolza型泛函的无约束最小化。这可以大大缩短和简化证明，并获得传统的变分技术无法较早发现的新结果。这包括一个全新的且易于验证的二阶必要条件，以求经典的微积分问题极小。该条件是具有状态约束的最优控制问题的新的和更通用的二阶必要条件的结果。