Abstract:
The problem of controlling the $k$-th 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.
Key words:optimal control, maximum principle, phase constraints.
