Finite Set Control Transcription for Optimal Control Applications

摘要

An enhanced method in optimization rooted in direct collocation is formulated to treat the finite set optimal control problem. This is motivated by applications in which a hybrid dynamical system is subject to ordinary differential continuity constraints, but control variables are contained within finite spaces. Resulting solutions display control discontinuities as variables switch between one feasible value to another. Solutions derived are characterized as optimal switching schedules between feasible control values. The methodology allows control switches to be determined over a continuous spectrum, overcoming many of the limitations associated with discretized solutions. Implementation details are presented and several applications demonstrate the method's utility and capability. Simple applications highlight the effectiveness of the methodology, while complicated dynamic systems showcase its relevance. A key example considers the challenges associated with libration point formations. Extensions are proposed for broader classes of hybrid systems.