Model Predictive Control of Spreading Processes via Sparse Resource Allocation

In this paper, we propose a model predictive control (MPC) method for real-time intervention of spreading processes, such as epidemics and wildfire, over large-scale networks. The goal is to allocate budgeted resources each time step to minimize the risk of an undetected outbreak, i.e. the product of the probability of an outbreak and the impact of that outbreak. By using dynamic programming relaxation, the MPC controller is reformulated as a convex optimization problem, in particular an exponential cone programming. We also provide sufficient conditions for the closed-loop risks to asymptotically decrease and a method to estimate the upper bound of when the risk will monotonically decrease. Numerical results are provided for a wildfire example.