2022/10/04 by Hall, Jonas, Andersson, Sean B., Cassandras, Christos G.
#Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2210.01294
This work shows the existence of optimal control laws for persistent monitoring of mobile targets in a one-dimensional mission space and derives explicit solutions. The underlying performance metric consists of minimizing the total uncertainty accumulated over a finite mission time. We first demonstrate that the corresponding optimal control problem can be reduced to a finite-dimensional optimization problem, and then establish existence of an optimal solution. Motivated by this result, we construct a parametric reformulation for which an event based gradient descent method is utilized with the goal of deriving (locally optimal) solutions. We additionally provide a more practical parameterization that has attractive properties such as simplicity, flexibility, and robustness. Both parameterizations are validated through simulation.