Sufficient conditions for relative minima of broken extremals in optimal control theory
In this paper the authors consider smoothly parametrized families of broken extremals related to optimal control problems. Roughly speaking, these are families of controlled trajectories parametrized by some parameter \(p\) with the controls being piecewise continuous and depending smoothly on \(p\), such that each trajectory satisfies necessary optimality conditions. For such families the authors derive sufficient conditions under which the values associated with these parameterized trajectories (given by the optimal control problem under consideration) solve the related Hamilton-Jacobi-Bellman equation. Based on this result, the authors conclude conditions under which the given family of trajectories is relatively optimal, i.e., optimal with respect to all other trajectories lying in some given set.
scientific article; zbMATH DE number 1764673
scientific article