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

Optimal Input Design for Affine Model Discrimination with Applications in Intention-Aware Vehicles