  We present a novel class of minimax optimal control problems with positive
dynamics, linear objective function and homogeneous constraints. The proposed
problem class can be analyzed with dynamic programming and an explicit solution
to the Bellman equation can be obtained, revealing that the optimal control
policy (among all possible policies) is linear. This policy can in turn be
computed through standard value iterations. Moreover, the feedback matrix of
the optimal controller inherits the sparsity structure from the constraint
matrix of the problem statement. This permits structural controller constraints
in the problem design and simplifies the application to large-scale systems. We
use a simple example of voltage control in an electric network to illustrate
the problem setup.
