On Singular Arcs and Surfaces in a Class of Quadratic Minimization Problems

摘要

A class of quadratic minimization problems is studied whose optimal control functions are partially singular. An explicit expression is obtained for the (n - 1) dimensional singular surface and it is shown that the optimal value function is twice continuously differentiable across this surface; this allows the piecing together of known sufficiency conditions for totally singular and totally bang-bang arcs to obtain sufficient conditions for optimality for this class of partially singular problems. A neighboring optimal feedback control law is suggested by these results. The closing sections of the paper are concerned with sufficient conditions for nonexistence of optimal singular controls in quadratic minimization problems. (Author)