Towards targeted exploration for non-stochastic disturbances
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.
- Identification and control: Joint input design and H∞subscript𝐻H_{\infty}italic_H start_POSTSUBSCRIPT ∞ end_POSTSUBSCRIPT state feedback with ellipsoidal parametric uncertainty via LMIs. Automatica, 44(2), 543–551.
- Combining prior knowledge and data for robust controller design. IEEE Transactions on Automatic Control, 68(8), 4618–4633.
- Trade-offs in learning controllers from noisy data. Systems & Control Letters, 154, 104985.
- Robust optimal identification experiment design for multisine excitation. Automatica, 125, 109431.
- Least costly identification experiment for control. Automatica, 42(10), 1651–1662.
- Learning robust LQ-controllers using application oriented exploration. IEEE Control Systems Letters, 4(1), 19–24.
- Fogel, E. (1979). System identification via membership set constraints with energy constrained noise. IEEE Transactions on Automatic Control, 24(5), 752–758.
- Optimal experiment designs with respect to the intended model application. Automatica, 22(5), 543–554.
- CVX: MATLAB software for disciplined convex programming, version 2.1.
- Input design via LMIs admitting frequency-wise model specifications in confidence regions. IEEE transactions on Automatic Control, 50(10), 1534–1549.
- An application-oriented approach to dual control with excitation for closed-loop identification. European Journal of Control, 29, 1–16.
- Pronzato, L. (2008). Optimal experimental design and some related control problems. Automatica, 44(2), 303–325.
- Accurate parameter estimation for safety-critical systems with unmodeled dynamics. Artificial Intelligence, 316, 103857.
- Robust exploration in linear quadratic reinforcement learning. In Advances in Neural Information Processing Systems, 15310–15320.
- From noisy data to feedback controllers: Nonconservative design via a matrix s-lemma. IEEE Transactions on Automatic Control, 67(1), 162–175.
- Sequential learning and control: Targeted exploration for robust performance. 10.48550/ARXIV.2301.07995.
- Robust dual control based on gain scheduling. In Proc. 59th IEEE Conference on Decision and Control (CDC), 2270–2277.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.