Efficient Input-Constrained Impulsive Optimal Control of Linear Systems with Application to Spacecraft Relative Motion
This work addresses the specific problem of constrained impulsive control for spacecraft motion, representing an incremental improvement by extending existing methods to include magnitude constraints.
The authors tackled the problem of impulsive optimal control for linear time-varying systems with input magnitude constraints, and demonstrated their algorithm on spacecraft relative motion control in Low Earth Orbit, achieving efficient online maneuver planning.
This work presents a novel algorithm for impulsive optimal control of linear time-varying systems with the inclusion of input magnitude constraints. Impulsive optimal control problems, where the optimal input solution is a sum of delta functions, are typically formulated as an optimization over a normed function space subject to integral equality constraints and can be efficiently solved for linear time-varying systems in their dual formulation. In this dual setting, the problem takes the form of a semi-infinite program which is readily solvable in online scenarios for constructing maneuver plans. This work augments the approach with the inclusion of magnitude constraints on the input over time windows of interest, which is shown to preserve the impulsive nature of the optimal solution and enable efficient solution procedures via semi-infinite programming. The resulting algorithm is demonstrated on the highly relevant problem of relative motion control of spacecraft in Low Earth Orbit (LEO).