The Maximum Principle for Relaxed Hereditary Differential Systems with Function Space end Condition

Abstract

This paper contains a proof of the global pointwise maximum principle for relaxed hereditary differential systems with general function space end condition. First a multiplier theorem establishes the existence of Lagrange multipliers (I0, I), where 10 R+ and is in the dual of the Sobolev space Wn'[-r, 0]. Then can be identified with an element of W"'[-r, 0] provided that the optimal trajectory satisfies a *

A Twofold Spline Approximation for Finite Horizon LQG Control of Hereditary Systems

“…It is well known that the solution of the linear quadratic regulation problem and of the optimal Gaussian filtering problem for linear delay systems is found in terms of infinite dimensional operators [7,8,9,10,11,12,13,17,23,31,36,37,39]. On the other hand, implementation of a control/filtering scheme in this case requires a finite dimensional approximation of such operators.…”

On the necessary conditions for optimal control of retarded systems

“…Here, we wish to make some specific remarks concerning the results which appear in the extant literature. In particular, we refer to the papers of Banks and Kent [51, Banks and Manitius [6], Kurcyusz [15], Colonius and Hinrichsen [101, and to the paper of Colonius [9]. A review of the different approaches and their corresponding range of applicability may be found in the survey of Manitius [16].…”

A penalty function proof of a Lagrange multiplier theorem with application to linear delay systems

“…Because of their infinite dimensional character, problems with function space end condition present great difficulties (see [4,5]). Concerning the important case of pointwise control restrictions, [9,10,14], and [15] contain maximum principles with nontriviality of the adjoint variable guaranteed. However, certain regularity conditions had to be assumed which imply for the considered Problem 2 that Rank Bo=n.…”