Optimal control of difference, differential, and differential-difference inclusions

On duality in problems of optimal control described by convex differential inclusions of Goursat–Darboux type

“…The latter means that if some pair of admissible solutions satisfies this relation, then each of them is a solution of the corresponding (direct and dual) problem. We remark that a significant part of the investigations of Ekeland and Temam [8] for simple variational problems is connected with such problems, and there are similar results for ordinary differential inclusions [9][10][11][12][13].…”

The optimality principle for discrete and first order partial differential inclusions

“…0022-247X/$ -see front matter  2004 Elsevier Inc. All rights reserved. doi:10.1016/j.jmaa.2004.11.047 diffusion process (see, for example, [7][8][9][10][11][12][13][14][15][16]) can be reduced to this formulation described by multivalued mappings with discrete and continuous time and with distributed parameters. In [1,15] necessary conditions for an extremum are obtained for some control problems with distributed parameters in abstract Hilbert spaces.…”

“…A great number of problems in economic dynamics, as well as classical problems on optimal control, differential games, and so on, can be reduced to such investigations [2][3][4][5][6][7][8][9][10][11][12].…”

Optimal Control of Non-stationary Differential Linear Repetitive Processes

“…This fact, known as hidden convexity, is an important property of continuous time control systems which follows, in general, from the Lyapunov theorem on the convexity of the range of an integral operator acting on vector measures. This result is often used, see, for example, [3,8], to prove the convexity of the reachability set for control systems which are linear in the state variables.…”

“…Also it is well known, see, for example, [8], that R(d N , 0) is a closed set. Hence, for the sequence {z It is known [6] that the fundamental matrix Φ(τ, t) satisfies Φ(τ, s)Φ(s, t) = Φ(τ, t), 0 ≤ τ < s < t ≤ t * , and the Cauchy response formula now yields…”