Sufficient Condition for a Control to be a Strong Minimum

摘要

The control literature either presents sufficient conditions for global optimality (for example, the Hamilton-Jacobi-Bellman theorem) or, if concerned with local optimality, restricts attention to comparison controls which are local in the L, sense. In this paper use is made of an exact expression for the change in cost duo to a change in control — a natural extension of a result due to weierstrass — to obtain sufficient conditions for a control to be a strong minimum (in the sense that comparison controls are merely required to be close in the L, sense).