Second Variation Conditions for Problems with Parameterized Control
Abstract
The second variation sufficient conditions for minima for optimal parameterized control problems are developed. These conditions are derived directly from the second variation by introducing a new variable mu whose differential equation has the same form as the differential equation for lambda. The neighboring extremal trajectories are derived using the sweep method resulting in a set of Riccati equations. In addition, the neighboring extremal parameterized control law is derived. This is also done for the case when there are both parameterized and nonparameterized controls. A perfect differential is added to the second variation which reduces to a form involving the neighboring extremal parameterized control law. The second variation can thereby be reduced to a perfect square involving the neighboring extremal parameters. The second variation sufficient conditions are formulated using these results. Second variation conditions are developed for the class of problems in which there are both parameterized and nonparameterized controls. This development closely follows the case of strictly parameterized control. The second variation conditions are used to solve a missile intercept problem with a parameterized control. The model used is an EMRAAT (Enhanced Medium Range Air-to-Air Technology) class of missile with a single thrust phase. The control, which is the coefficient of lift, is parameterized and the control nodes are the parameters which maximize the terminal velocity. Optimal trajectories for several realistic scenarios are obtained using a shooting method. The sufficient conditions are applied to these optimal trajectories and are shown to be minimal.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1991
- Accession Number
- ADA357017
Entities
People
- Christopher N. D'souza
Organizations
- University of Texas at Austin