Determining the Controllability Region for the Re-Entry of an Apollo-Type Spacecraft
In closed and open control loops, particularly in optimal control problems, the controllability region of the perturbations is a factor of importance. One looks for those controls which guarantee that the system stays within the controllability region: small perturbations must be compensated by suitable controlling in such a way that the controllability region is not left. In general, optimal control problems are characterized by a given quality functional, which has to be minimized, and by boundary conditions. Especially in closed optimal loops the terminal condition has to be fulfilled either exactly or within a prescribed neighborhood of the terminal point, when talking about real-time controlling. For the special problem of the atmospheric re-entry of an Apollo-type capsula the aim of this paper is to determine the controllability region and to characterize it by a manifold. This manifold will be constructed by methods of the stability theory, since the controllability region can be interpreted as a generalized epsilon-tube, where the nominal orbit that can be determined beforehand is flight-path stable. Some numerical results are presented.
KeywordsEquilibrium Point Controllability Region Optimal Control Problem LYAPUNOV Function Terminal Condition
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