Solution of an Optimal Sensing and Interception Problem Using Idempotent Methods

We consider a problem where one desires to intercept a vehicle before it reaches a specific (target) location. The vehicle travels on a road network. There are unattended ground sensors (UGSs) on the road network. The data obtained by a UGS is uploaded to an unmanned aerial vehicle (UAV) when the UAV overflies the UGS. There is an interceptor vehicle which may travel the road network. The interceptor uses intruder state estimates based on the data uploaded from the UGSs to the UAV. There is a negative payoff if the intruder is intercepted prior to reaching the target location, and a positive payoff if the intruder reaches the target location without having been previously intercepted. The intruder position is modeled as a Markov chain. The observations are corrupted by random noise. A dynamic programming approach is taken where the value is propagated using a min-plus curseof- dimensionality-free algorithm. The double-description method for convex polytopes is used to reduce computational loads.