The problem of controlling the kth derivative of an object state under a linear state constraint, where k 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 k (the term “of depth k ” is also used). This paper applies Pontryagin’s 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.
Zhukova et al. (Mon,) studied this question.