Optimal processes governed by integral equation equations with unilateral constraint

AbstractAn optimal process with unilateral constraint is considered using relaxed controls. Existence of optimal control is automatic. Further, problems with linear and certain quadratic cost functions with linear integral and state constraints are such that the controls are actually ordinary, i.e., bounded measurable functions. In addition, if the control set is a convex polyhedron, the optimal controls take their values in the vertices of the polyhedron. Control processes governed by integral equations have been considered by V. R. Vinokurov (SIAM 7 (1969), 324–355). However, there existence is not shown for the general problem and optimality conditions are not available for the problem when state constraints are present. Furthermore, the above work has some errors as pointed out by L. W. Neustadt and J. Warga (SIAM 8 (1970), 572). Finally, we point out that the basic idea in our approach here is the same as in a forthcoming, paper (J. Optim. Theory Appl., in press)