  This paper considers the optimal design of input signals for the purpose of
discriminating among a finite number of affine models with uncontrolled inputs
and noise. Each affine model represents a different system operating mode,
corresponding to unobserved intents of other drivers or robots, or to fault
types or attack strategies, etc. The input design problem aims to find optimal
separating/discriminating (controlled) inputs such that the output trajectories
of all the affine models are guaranteed to be distinguishable from each other,
despite uncertainty in the initial condition and uncontrolled inputs as well as
the presence of process and measurement noise. We propose a novel formulation
to solve this problem, with an emphasis on guarantees for model discrimination
and optimality, in contrast to a previously proposed conservative formulation
using robust optimization. This new formulation can be recast as a bilevel
optimization problem and further reformulated as a mixed-integer linear program
(MILP). Moreover, our fairly general problem setting allows the incorporation
of objectives and/or responsibilities among rational agents. For instance, each
driver has to obey traffic rules, while simultaneously optimizing for safety,
comfort and energy efficiency. Finally, we demonstrate the effectiveness of our
approach for identifying the intention of other vehicles in several driving
scenarios.
