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Security‐level strategies for non‐linear stochastic pursuit‐evasion differential games
Author(s) -
Chompaisal A.,
Leondes C. T.
Publication year - 1981
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.4660020202
Subject(s) - pursuit evasion , hessian matrix , initialization , mathematical optimization , differential dynamic programming , optimal control , maximization , mathematics , saddle point , computer science , differential game , geometry , programming language
A first‐order algorithm is developed to solve for the security‐level strategies of differential games without an assumption that a saddle point exists. The inner optimization uses differential dynamic programming together with a convergence control method. The outer optimization uses a gradient method. The application of the algorithm is demonstrated by solving for numerical strategies for a realistic missile‐antimissile pursuit‐evasion problem. Two major advantages for this algorithm are that the initialization requires only a rough estimate of the nominal control and that the Hessian matrix of the Hamiltonian with respect to the control vector is positive (negative) definite for the minimization (maximization) problem only on the optimal path.