Necessary conditions for impulsive nonlinear optimal control problems without a priori normality assumptions
The authors develop a substantially new approach for an abstract minimization problem with equality constraints, inequality constraints, and constraints given by an inclusion in a convex cone. An extremal principle based on the conception of local maximum principle, notion of a critical cone of variations, and defined quadratic forms is proved. First-order and second-order necessary conditions of optimality for an impulsive control problem relayed on the extremal principle are derived. No a priori normality assumptions are required. These condition, remain informative for abnormal control processes. The results obtained also differ substantially from these conditions that follow from the maximum principle when the optimal trajectory is absolutely continuous, i.e. with no impulses. Two illustrating examples are given to show the power of the results.
scientific article; zbMATH DE number 2162399