An attainable sets approach to optimal control of functional differential equations with function space terminal conditions

Control of Functional Differential Equations With Function Space Boundary Conditions

“…They show that for B = bGR (r -l) and n < 3, rank P = rank Q, and the conditions are necessary and sufficient. They offer a number of additional results: (see [7] The authors also sharpen the results mentioned above from [25].…”

“…One difference between the form of Theorem k.1 derived in [ 7] that given above is that in [7] the multiplier \i is only L^, not necessarily of bounded variation, so that for the neutral systems (l. …”

“…' " "Banks and Jacobs [7] use a geometric approach to the problem stated above. Using a class of unconstrained controls ^ = Lp([ t-., t..],R ) they eniploy attainable sets arguments (see [27]) in Wp ' ([ t..-h,t_]),R ) to de--rive-essentially the conditions in Theorem ^.1-with -normality (and-hence sufficiency) assured.…”

“…Using a class of unconstrained controls ^ = Lp([ t-., t..],R ) they eniploy attainable sets arguments (see [27]) in Wp ' ([ t..-h,t_]),R ) to de--rive-essentially the conditions in Theorem ^.1-with -normality (and-hence sufficiency) assured. The assumptions under which normality is guaranteed (controllability type assumptions on the system and the relatively weak hypothesis on BI p(t) = rank B(t) is constant on [t, -h,t..]) are muchless restrictive than those in [22], As is pointed out in [7], these assumptions are weak enough to include the general n order scalar neutral equation with scalar control in the class of systems to which the results are applicable.…”

Theory of equations of neutral type

“…A large number of investigations, devoted to problems of optimal control for objects described by differential equations with deviating argument of neutral type, are devoted to a certain extent to the transfer of the maximum principle to this case [19,102], [231,232,243,278,280,288,297], etc. In a series of papers (see, for example, [232,243,279,280]) one investigates the controlled system (6) where A1, A 2, A 3, B are constant or variable matrices and h is a constant lag. The interval [t 0, T] of the variation of the time t is fixed.…”