Trajectory Optimization in the Presence of Constraints
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH
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In many aerospace problems, it is necessary to determine vehicle trajectories that satisfy constraints. Typically two types of constraints are of interest. First, it may be desirable to satisfy a set of boundary conditions. Second, it may be necessary to limit the motion of the vehicle so that physical limits and hardware limits are not exceeded. In addition to these requirements, it may be necessary to optimize some measure of vehicle performance. In this thesis, the square root sweep method is used to solve a discrete-time linear quadratic optimal control problem. The optimal control problem arises from a Mayer form continuous-time nonlinear optimization problem. A method for solving the optimal control problem is derived. Called the square root sweep algorithm, the solution consists of a set of backward recursions for a set of square root parameters. The square root sweep algorithm is shown to be capable of treating Mayer form optimization problems. Heuristics for obtaining solutions are discussed. The square root sweep algorithm is used to solve several example optimization problems. Theses.