A NUMERICAL METHOD FOR SOLVING THE MINIMIZATION PROBLEM OF RESOURCE CONSUMPTION FOR LINEAR SYSTEMS WITH CONSTANT DELAYS IN THE STATE AND CONTROL
We propose a numerical method for solving the minimization problem of resource consumption for linear systems with constant time delay in both the phase states and the control. This method is a generalization of the method for solving the problem with delay only in the phase state. Global convergence of the method to a $\varepsilon$ optimal solution is proven. By an $\varepsilon$-optimal solution we mean an feasible control $u(t)$, $t\in [0,T]$, transferring the system into the $\varepsilon$-neighborhood of the origin on which the functional of the problem diﬀers from the optimal value at most by $\varepsilon$.