Stochastic guidance laws in satellite pursuit-evasion
Two player pursuit-evasion differential games have been defined and solved for many low-order deterministic versions of the problem. In these formulations of the game, both players are assumed to have knowledge of the state and the control capabilities of each. Solution requires that the optimal min-max controls be found in terms of the state, for a specific index of performance. This typically means that trajectories be determined in the state space, by retrograde integration of the dynamic equations. In a statistical version of the pursuit-evasion problem, the number of state variables is tripled, and new considerations arise. In addition to the state, P's estimate of the state, E's estimate of the state, and the associated covariances, the optimal controls are subject to several interpretations. Among the more difficult of these from the analyst's point of view is the elementary feinting strategy of E, which is nonoptimal for the deterministic game, but which is used when E's estimate of the state is better than P's, ``so as best to confound P's prediction''. The presence of noise in the driving equations and in the data makes the stochastic version difficult to define unequivocally, even for very low- order dynamic models. The analyses of specific problems of this type often do not include actual trajectories as determined by using the guidance algorithms in the equations of motion. More often, the problems are studied analytically to determine certain functions which are necessary or relevant to a solution. In the present study, a guidance algorithm is described and derived before being applied to a specific two spacecraft encounter. The following section describes the assumptions used, and dynamic and statistical equations are presented. This is followed by a section of numerical results presented graphically, for a specific set of independent parameters and input variables.
scientific article; zbMATH DE number 4049439