Optimal synthesis and stabilization of time-delay dynamical systems

Abstract

A new approach to the solution of the classical optimal synthesis problem for linear time delay dynamical systems is under consideration. Positional solutions of optimal control problems are constructed by solving special algebraic equations over the optimal Lagrange vector and switching points of the optimal open-loop control at each current moment of a control process. A stabilization problem for two types of dynamical systems with delay (delay in feedback loop, delays in control) is investigated. Algorithms of constructing bounded stabilizing feedbacks based on positional solutions of special auxiliary optimal control problems are justified. Two schemes of realization of stabilizing feedbacks are proposed.