Optimistic vs Pessimistic Uncertainty Model Unfalsification
This paper builds on the results of my Master’s thesis and was presented at the 2025 IEEE Conference on Decision and Control (CDC) in Rio de Janeiro, Brazil.
In robust control, a controller is modified based on an uncertainty model to ensure stability and, optionally, constraint satisfaction despite worst-case disturbances. Data-driven approaches are commonly used to identify such an uncertainty model. However, since the true nature of uncertainties ultimately remains unknown, the notion of identifying an uncertainty model is misleading: no amount of data can fully reflect system uncertainty. Following philosopher Karl Popper’s notion of falsifiability, we therefore look for ways to unfalsify an uncertainty model instead, i. e. systematically challenging it with the available data to gain confidence in its validity.
The paper proposes two complementary formulations of this problem. The optimistic approach determines the smallest uncertainties that could explain the given data, while the pessimistic approach finds the largest possible uncertainties suggested by the data. The pessimistic problem is revealed to be a semi-infinite program, which we solve using the local reduction algorithm. We also show that the optimistic and pessimistic approaches are mathematical duals: the optimistic uncertainty model constitutes a strict lower bound, falsifying all less conservative models, while the pessimistic model can be taken as a loose upper bound.
Both approaches were tested using an uncertain linear model with data from a simulated nonlinear pendulum-on-a-cart system simulated, with the Julia package SimpleSim.jl. The experiments confirm the theory: the optimistic objective grows monotonically as more data is added, and the pessimistic solution upper-bounds the optimistic one.