The DOI matches its Crossref record; 36 of the 36 references it cites were found in a registry or an index.
Optimization over state feedback policies for robust control with constraints
Abstract
This paper is concerned with the optimal control of linear discrete-time systems subject to unknown but bounded state disturbances and mixed polytopic constraints on the state and input. It is shown that the class of admissible affine state feedback control policies with knowledge of prior states is equivalent to the class of admissible feedback policies that are affine functions of the past disturbance sequence. This implies that a broad class of constrained finite horizon robust and optimal control problems, where the optimization is over affine state feedback policies, can be solved in a computationally efficient fashion using convex optimization methods. This equivalence result is used to design a robust receding horizon control (RHC) state feedback policy such that the closed-loop system is input-to-state stable (ISS) and the constraints are satisfied for all time and all allowable disturbance sequences. The cost to be minimized in the associated finite horizon optimal control problem is quadratic in the disturbance-free state and input sequences. The value of the receding horizon control law can be calculated at each sample instant using a single, tractable and convex quadratic program (QP) if the disturbance set is polytopic, or a tractable second-order cone program (SOCP) if the disturbance set is given by a 2-norm bound.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Boyd, S., & Vandenberghe, L. (2004) · doi:10.1017/cbo9780511804441 · Cited by 56,601
Horn, R. A., & Johnson, C. R. (1985) · Cited by 22,203
Constrained model predictive control: Stability and optimality
Mayne, D. Q., Rawlings, J. B., Rao, C. V., & Scokaert, P. O. M. (2000) · Automatica · doi:10.1016/s0005-1098(99)00214-9 · Cited by 8,736
Predictive Control With Constraints
Maciejowski, J. M. (2001) · Cambridge University Engineering Department Publications Database · Cited by 4,368
Self-citationLee, J. H., Kaisare, N. S., & García, C. E. (2007) · Springer eBooks · doi:10.1002/9781394333325.fmatter · Cited by 3,766
Predictive control with constraints
Camacho, E. F. (2003) · Automatica · doi:10.1016/s0005-1098(03)00056-6 · Cited by 3,530
The explicit linear quadratic regulator for constrained systems
Bemporad, A., Morari, M., Dua, V., & Pistikopoulos, E. N. (2002) · Automatica · doi:10.1016/s0005-1098(01)00174-1 · Cited by 3,260
Optimization—Theory and Applications
Cesari, L. (1983) · Springer eBooks · doi:10.1007/978-1-4613-8165-5 · Cited by 2,559
Robust constrained model predictive control using linear matrix inequalities
Kothare, M. V., Balakrishnan, V., & Morari, M. (1996) · Automatica · doi:10.1016/0005-1098(96)00063-5 · Cited by 2,516
Applications of second-order cone programming
Lobo, M. S., Vandenberghe, L., Boyd, S., & Lebret, H. (1998) · Linear Algebra and its Applications · doi:10.1016/s0024-3795(98)10032-0 · Cited by 2,401
Blanchini, F. (1999) · Automatica · doi:10.1016/s0005-1098(99)00113-2 · Cited by 2,390
Convex Analysis and Optimization
Bertsekas, D. P., Nedić, A., & Ozdaglar, A. (2003) · DSpace@MIT (Massachusetts Institute of Technology) · Cited by 2,148
Robust model predictive control of constrained linear systems with bounded disturbances
Mayne, D. Q., Seron, M. M., & Raković, S. V. (2005) · Automatica · doi:10.1016/j.automatica.2004.08.019 · Cited by 1,672
Input-to-state stability for discrete-time nonlinear systems
Jiang, Z.-P., & Wang, Y. (2001) · Automatica · doi:10.1016/s0005-1098(01)00028-0 · Cited by 1,424
Adjustable robust solutions of uncertain linear programs
Ben-Tal, A., Goryashko, A., Guslitzer, E., & Nemirovski, A. (2004) · Mathematical Programming · doi:10.1007/s10107-003-0454-y · Cited by 1,380
Linear controller design: limits of performance
Boyd, S., & Barratt, C. H. (1991) · Prentice-Hall, Inc eBooks · Cited by 1,196
Min-max feedback model predictive control for constrained linear systems
Scokaert, P. O. M., & Mayne, D. Q. (1998) · IEEE Transactions on Automatic Control · doi:10.1109/9.704989 · Cited by 929
Adjustable robust solutions of uncertain linear programs
Ben-TalA., GoryashkoA., GuslitzerE., et al. (2004) · Mathematical Programming · doi:10.5555/2990016.3114320 · Cited by 849
Invariant approximations of the minimal robust positively Invariant set
Rakovic, S. V., Kerrigan, E. C., Kouramas, K. I., & Mayne, D. Q. (2005) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2005.843854 · Cited by 837
Self-citationSystems with persistent disturbances: predictive control with restricted constraints
Chisci, L., Rossiter, J. A., & Zappa, G. (2001) · Automatica · doi:10.1016/s0005-1098(01)00051-6 · Cited by 676
Robust model predictive control using tubes
Langson, W., Chryssochoos, I., Raković, S. V., & Mayne, D. Q. (2004) · Automatica · doi:10.1016/j.automatica.2003.08.009 · Cited by 672
Min-max control of constrained uncertain discrete-time linear systems
Bemporad, A., Borrelli, F., & Morari, M. (2003) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2003.816984 · Cited by 518
On the minimax reachability of target sets and target tubes
Bertsekas, D. P., & Rhodes, I. B. (1971) · Automatica · doi:10.1016/0005-1098(71)90066-5 · Cited by 436
Constrained Optimal Control of Linear and Hybrid Systems
(2003) · Lecture Notes in Control and Information Sciences · doi:10.1007/3-540-36225-8 · Cited by 429
Marruedo, D. L., Alamo, T., & Camacho, E. F. (2004) · Proceedings of the 41st IEEE Conference on Decision and Control, 2002. · doi:10.1109/cdc.2002.1185106 · Cited by 340
Minimax approaches to robust model predictive control
Löfberg, J. (2003) · Cited by 301
Infinite time reachability of state-space regions by using feedback control
Bertsekas, D. (1972) · IEEE Transactions on Automatic Control · doi:10.1109/tac.1972.1100085 · Cited by 286
Kerrigan, E. C., & Maciejowski, J. M. (2004) · International Journal of Robust and Nonlinear Control · doi:10.1002/rnc.889 · Cited by 222
Self-citationControl of Constrained Dynamic Systems
Mayne, D. Q. (2001) · European Journal of Control · doi:10.3166/ejc.7.87-99 · Cited by 214
(1990) · Birkhäuser Boston eBooks · doi:10.1007/978-1-4757-2108-9 · Cited by 182
Reducing conservativeness in predictive control of constrained systems with disturbances
Bemporad, A. (2002) · IEEE Conference on Decision and Control (CDC) · doi:10.1109/cdc.1998.758479 · Cited by 142
Robust Dynamic Programming for Min–Max Model Predictive Control of Constrained Uncertain Systems
Diehl, M., & Björnberg, J. E. (2004) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2004.838489 · Cited by 116
UNCERTAINTY- IMMUNIZED SOLUTIONS IN LINEAR PROGRAMMING
Guslitser, E. (2002) · Cited by 49
Kerrigan, E. C., & Maciejowski, J. M. (2003) · European Control Conference (ECC) · doi:10.23919/ecc.2003.7085166 · Cited by 36
Self-citationRobust stability of min-max MPC controllers for nonlinear systems with bounded uncertainties
Limón, D., Álamo, T., & Camacho, E. F. (2004) · Cited by 11
Input-to-state stabilizing MPC for neutrally stable linear systems subject to input constraints
Kim, J., Yoon, T.-W., Jadbabaie, A., & Persis, C. D. (2004) · IEEE Conference on Decision and Control (CDC) · doi:10.1109/cdc.2004.1429605 · Cited by 9
Cited by
(2013) · Dynamic Modelling and Predictive Control in Solid Oxide Fuel Cells: First Principle and Data‐Based Approaches · doi:10.1002/9781118501054.ch6 · Cited by 1,047
Theory and applications of robust optimization
Bertsimas, D., Brown, D. B., & Caramanis, C. (2011) · SIAM Review · doi:10.1137/080734510 · Cited by 134
Robust MPC with data-driven demand forecasting for frequency regulation with heat pumps
Bünning, F., Warrington, J., Heer, P., Smith, R. S., & Lygeros, J. (2022) · Control Engineering Practice · doi:10.1016/j.conengprac.2022.105101 · Cited by 47
Metadata
- Authors
- Goulart, P. J., Kerrigan, E. C., & Maciejowski, J. M.
- Venue
- Automatica
- Publisher
- Elsevier BV
- Published
- 2006-04
- Volume
- 42
- Issue
- 4
- Pages
- 523-533
- ISSN
- 0005-1098 (ISSN-L)
- OpenAlex
- W2110349823
- Cited by
- 580
- References
- 36
- FWCI
- 39.63
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
