Quasilinearization Solutions of Differential Games and Evaluation of Suboptimal Strategies,
Abstract
The first-order necessary conditions for an optimal solution are derived for a very general problem in differential games. The problem statement includes terminal constraints, control and state variable inequality constraints, multiple arc solutions, and state variable discontinuities at specified and free corners. The problems of determining optimal solutions when the strategy of the opponent is known and when the strategy of the opponent is unknown and perhaps optimal are both treated. The comparison of the performances associated with these two cases provides a measure of the efficacy of a selected, suboptimal strategy. The first-order necessary conditions constitute a multi-point boundary value problem. The quasilinearization technique is extended to handle this problem, including the effects of control and state variable inequality constraints, multiple arc solutions, and discontinuities in the state and adjoint variables. This extension of quailinearization technique requires the linearization of the equations of motion, the Euler-Lagrange equations, the inequality constraint relationships, and the discontinuity conditions. The kth and (k-1)st iterations are then shown to be related by a complicated linear operator involving the inequality and discontinuity relationships. The kth iteration is constructed from the solution of the homogeneous and nonhomogeneous forms of the linear equations. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1971
- Accession Number
- AD0729896
Entities
People
- A. R. Stubberud
- C. T. Leondes
- E. B. Stear
- Rollyn Gene Graham
Organizations
- University of California, Los Angeles