Optimal guidance of a team of mobile actuators for controlling a 1D diffusion process with unknown initial conditions

This paper proposes an optimization framework for steering a team of mobile actuators to control a diffusion process with unknown initial conditions. The optimization problem seeks a guidance strategy that minimizes the quadratic cost of controlling the diffusion process subject to the worst possible initial condition and the quadratic cost of steering the mobile actuators. We turn the problem into an unconstrained optimization and use a gradient-descent method to solve it. The solution of the proposed problem is suboptimal for the same problem with a known initial condition-even for the worst-case initial condition. This suboptimality property suggests the guidance strategy can be implemented when the initial condition of the diffusion process is unknown. A numerical example compares solutions with known and unknown initial conditions.