Discrete maximum principle in systems with a delay in control

Abstract

In the paper, we consider a discrete optimal control problem with a delay in control. Taking into account the specificity of this problem, we offer a new research method. The essence of this method is that unlike previously known ones here we assume that the set of admissible speeds satisfies convexity type conditions at the moment t + h, but not at t, where h is time delay in the system. The discrete analog of Pontryagin’s maximum principle is obtained under weakened assumptions. An example showing the content-richness of the obtained result is given.