Input-to-state stable MPC for constrained discrete-time nonlinear systems with bounded additive uncertainties
Abstract
In this paper a robust model predictive control (MPC) for constrained discrete-time nonlinear system with additive uncertainties is presented. This controller uses a terminal cost, terminal constraint and nominal predictions. The terminal region and constraints on the states are computed to get robust feasibility of the closed loop system for a given bound on the admissible uncertainties. Furthermore, it is proved that the closed-loop system is input-to-state stable with relation to the uncertainties. Therefore, the closed-loop system evolves towards a compact set where it is ultimately bounded. In case of decaying uncertainties, the closed-loop system is asymptotically stable. The convergence of the closed loop system is guaranteed despite the suboptimality of the solution.
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In [30] and [31], ISS of MPC with terminal ingredients was analyzed using a feasible control sequence, but the derived cumulative error bound increases with increasing prediction horizon, resulting in an overconservative cumulative error bound.
“In [30] and [31], ISS of MPC with terminal ingredients was analyzed where a feasible control sequence, which guarantees that input and state constraints are not violated, was employed. However, the derived cumulative error bound increases with increasing the prediction horizon. It results in an overconservative cumulative error bound”
From Incremental Model Predictive Control Exploiting Time-Delay Estimation for a Robot Manipulator (2022) · cites this paper as [30]
The cumulative error bound in this article does not increase as N increases.
“Different from the cumulative error bound ( Ls ( L f N -1 -1 / L f -1 ) + Lt L f N -1 ) d (where L f , Ls , and Lt are Lipschitz constants and d is the upper bound of the disturbance) derived in [30] and [31], the cumulative error bound in this article N := ( K ( 1 + K 0 P )/ 1 - √ ρ) √ (λ max ( P )λ max ( Q )/λ min ( Q )) ¯ ∗”
From Incremental Model Predictive Control Exploiting Time-Delay Estimation for a Robot Manipulator (2022) · cites this paper as [30]
In contrast to ISS analyses in [30] and [31], feasible control sequences are not required in this article.
“In contrast to ISS analyses in [30] and [31], feasible control sequences are not required in this article.”
From Incremental Model Predictive Control Exploiting Time-Delay Estimation for a Robot Manipulator (2022) · cites this paper as [30]
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Rubagotti, M., Raimondo, D. M., Ferrara, A., & Magni, L. (2011) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2010.2074590 · Cited by 196 · see citing works
A Robust Predictive Control Approach for Underwater Robotic Vehicles
Heshmati-Alamdari, S., Karras, G. C., Marantos, P., & Kyriakopoulos, K. J. (2020) · IEEE Transactions on Control Systems Technology · doi:10.1109/tcst.2019.2939248 · Cited by 117 · see citing works
Incremental Model Predictive Control Exploiting Time-Delay Estimation for a Robot Manipulator
Wang, Y., Leibold, M., Lee, J., Ye, W., Xie, J., & Buss, M. (2022) · IEEE Transactions on Control Systems Technology · doi:10.1109/tcst.2022.3142629 · Cited by 52 · see citing works
Kohler, J., Soloperto, R., Muller, M. A., & Allgower, F. (2021) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2020.2982585 · Cited by 19 · see citing works
- Authors
- Marruedo, D. L., Alamo, T., & Camacho, E. F.
- Affiliations
- Universidad de Sevilla (ES)
- ORCID
- Camacho, E.F.
- Venue
- Proceedings of the 41st IEEE Conference on Decision and Control, 2002.
- Publisher
- IEEE
- Published
- 2004-01-23
- Volume
- 4
- Pages
- 4619-4624
- ISSN
- 0191-2216 (ISSN-L)
- OpenAlex
- W2115562234
- Cited by
- 340
- References
- 13
- Citations by year
- 2026: 4 · 2025: 14 · 2024: 22 · 2023: 14 · 2022: 17 · 2021: 13 · 2020: 20 · 2019: 24 · 2018: 17 · 2017: 20 · 2016: 13 · 2015: 15 · 2014: 23 · 2013: 18 · 2012: 18
- FWCI
- 18.01
- Type
- conference paper
- Language
- en
- Open access
- closed
- Locations
- IEEE Conference on Decision and Control (CDC) (publishedVersion)
- Topics
- Physical Sciences › Engineering › Control and Systems Engineering › Advanced Control Systems Optimization
- Physical Sciences › Engineering › Control and Systems Engineering › Stability and Control of Uncertain Systems
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Formal Methods in Verification
- Keywords
- robust model predictive control, input-to-state stability, discrete-time nonlinear systems, terminal cost, terminal constraints, terminal region, robust feasibility, ultimate boundedness, asymptotic stability, suboptimal control
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