Second Variation Conditions for Optimal Control Problems with Parameters

The second variation sufficient conditions for minima for optimal control problems with parameterised control are devoloped. The neighboring extremal trajectories are derived using the sweep method resulting in a set of Riccati equations. After a perfect differential is added to the second variation, it is reduced to a perfect square involving the neighboring extremal parameters. The second variation conditions are formulated using these results. These conditions are applied to an optimal missile intercept problem using parameterised control.