Multiple Constraints in Optimal Control Problems

The origin of multiple constraints on a control function in both lumped and distributed systems is investigated. Equivalence and comparability notions are discussed. It is pointed out that multiple constraints have a special significance in optimal control problems of infinite-dimensional systems. An opt.ima1 control problem wit.h more than one const.raint. on the cont.ro1 function is called a multipleconstraint, optimal control problem. This has received little attention in the past. One of t.he reasons, perhaps, is t.hat it adds [1)-[5] immense complexit,y to the optimal control problem solution m3t.h only one constraint. on the controlling function. Farious mult.iple constraints using geometrical and a.nalytical approaches have been discussed by Singh Q5J In t.his correspondence, physical motivations for multiple constraints occurring in both lumped and dist.ributed systems are presented. Let the t.mo normed constraints on the control function ~(t) be defined as