Maximum principle in linear problems with mixed convex restrictions (Q1066075)

Linear control problems with mixed convex restrictions which are discontinuous with respect to the time variable are considered. For a given functional J only the existence of the finite value inf J is assumed on the trajectories which are allowed by the restrictions. The formulation of the problem and the restrictions, critical and stationary values of J and solutions of the Euler equation for critical values of J are discussed in chapter 1. A maximum principle for the critical value \(J_ 0\) of the functional J is considered in chapter 2. It is proved that the maximum principle is equivalent to the extremality of \(J_ 0\). Connections with the classical Pontrjagin maximum principle are discussed.