Singular arcs are a common feature in optimal control problems when the standard necessary conditions fail to reveal a candidate control. In some cases, a singular arc can be proven to be nonoptimal and discarded. In other cases, the solution can be resolved through additional convexity conditions on the Hamiltonian. A less common, but nonetheless interesting, scenario occurs when the singular arc appears with infinite order. This situation becomes apparent when the problem definition lacks sufficient information to identify a unique solution. In this work, we consider conditions under which singular optimal control problems may exhibit indeterminate behavior due to insufficiency of the cost objective and boundary conditions. The resulting problem is shown to be singular, but in a degenerate sense wherein the necessary conditions yield no new information. A relaxation approach is developed to repose the problem with augmented covariance dynamics. The method permits finite-order arcs producing a well-posed problem. The approach has relevance to engineering systems, which are almost always subject to some level of uncertainty in initial states or parameters. Examples are provided based on classical problems in optimal control, as well as aerospace mission design.
Auxiliary Minimum Covariance Resolution of Infinite-Order Singular Arcs
Journal of Guidance, Control, and Dynamics ; 45 , 10 ; 1847-1861
01.10.2022
Aufsatz (Zeitschrift)
Elektronische Ressource
Englisch
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