The problem of controlling the -th derivative of an object state under a linear state constraint, where is an arbitrary natural number, is studied. According to the existing terminology in literature, this is a so-called state-constrained control problem of order (the term of depth is also used). This paper applies Pontryagins maximum principle to the problem under study and conducts a theoretical analysis of the resulting optimality conditions. Based on this analysis, a computational scheme for finding extremals is proposed.
A. A. Zhukova (Wed,) studied this question.