Towards targeted exploration for non-stochastic disturbances
Janani Venkatasubramanian, Johannes Köhler, Mark Cannon, Frank Allgöwer
TL;DR
This work addresses targeted exploration for discrete-time LTI systems with energy-bounded (non-stochastic) disturbances, avoiding independence or zero-mean assumptions. It develops a data-dependent ellipsoidal uncertainty bound for the unknown parameters and designs a multisine exploration input by solving a semidefinite program that minimizes energy while guaranteeing a prescribed parameter accuracy. A convex relaxation and tractable approximations yield an SDP-based procedure to compute excitation frequencies and amplitudes, with iterative refinement to reduce conservatism. Numerical results illustrate that non-stochastic targeted exploration yields smaller parameter error than stochastic strategies in the presence of energy-bounded unmodeled nonlinearities, and that optimal energy distribution across frequencies differs between disturbance models. The approach provides a principled bridge between classical robust identification and optimal experiment design, with potential extensions to robust controller design.
Abstract
We present a novel targeted exploration strategy for linear time-invariant systems without stochastic assumptions on the noise, i.e., without requiring independence or zero mean, allowing for deterministic model misspecifications. This work utilizes classical data-dependent uncertainty bounds on the least-squares parameter estimates in the presence of energy-bounded noise. We provide a sufficient condition on the exploration data that ensures a desired error bound on the estimated parameter. Using common approximations, we derive a semidefinite program to compute the optimal sinusoidal input excitation. Finally, we highlight the differences and commonalities between the developed non-stochastic targeted exploration strategy and conventional exploration strategies based on classical identification bounds through a numerical example.