Target Monitoring for Space Applications Using Optimal Periodic Control Laws

In this paper, we investigate the problem of designing control inputs for a linear time invariant control system to maintain, on average, close proximity to the target over a sufficiently long time period. We call this problem a target monitoring problem and formulate it as an optimal control problem. To achieve the objective, the running cost is described by a bounded, monotonically increasing function in the distance between the system state and the target. We focus on the class of periodic control inputs, which include constant control inputs as special cases. Amongst others, we provide necessary and/or sufficient conditions for the optimal solution to be proper, i.e., non-constant. We also establish efficient algorithms for finding the optimal control policy, followed by numerical studies on single and multiple-agent systems.