On Delayed Action System Control Under Equality and Inequality Constraints

Abstract

A necessary condition is presented in the form of Pontryagin's maximum principle for the problem of optimally controlling a delayed action system ẋ(t)=f(x(t), x(t-h), u(t), u(t-h), t) subject to various functional equality and inequality constraints. It is further shown that the necessary condition becomes also a sufficient condition for normal linear systems under typical convexity assumptions. Then it is discussed that the results can be effectively utilized to solve classes of (i) function-target control problems, (ii) nonzero duration rendezvous problems and (iii) control problems subject to certain functional constraints.