A Simple Robust MPC for Linear Systems with Parametric and Additive Uncertainty
Abstract
We propose a simple and computationally efficient approach for designing a robust Model Predictive Controller (MPC) for constrained uncertain linear systems. The uncertainty is modeled as an additive disturbance and an additive error on the system dynamics matrices. Set based bounds for each component of the model uncertainty are assumed to be known. We separate the constraint tightening strategy into two parts, depending on the length of the MPC horizon. For a horizon length of one, the robust MPC problem is solved exactly, whereas for other horizon lengths, the model uncertainty is over-approximated with a net-additive component. The resulting MPC controller guarantees robust satisfaction of state and input constraints in closed-loop with the uncertain system. With appropriately designed terminal components and an adaptive horizon strategy, we prove the controller's recursive feasibility and stability of the origin. With numerical simulations, we demonstrate that our proposed approach gains up to 15x online computation speedup over a tube MPC strategy, while stabilizing about 98% of the latter's region of attraction.
Additional Information
© 2021 AACC. We thank Sarah Dean for constrained LQR source codes. Sponsors: ONR-N00014-18-1-2833, NSF-1931853, Marie Skłodowska-Curie grant 846421, and Ford motor company.Attached Files
Submitted - 2103.12351.pdf
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Additional details
- Eprint ID
- 110578
- Resolver ID
- CaltechAUTHORS:20210826-172400161
- N00014-18-1-2833
- Office of Naval Research (ONR)
- CMMI-1931853
- NSF
- 846421
- Marie Curie Fellowship
- Ford Motor Company
- Created
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2021-08-26Created from EPrint's datestamp field
- Updated
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2021-08-26Created from EPrint's last_modified field