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Min-max control of constrained uncertain discrete-time linear systems
Abstract
For discrete-time uncertain linear systems with constraints on inputs and states, we develop an approach to determine state feedback controllers based on a min-max control formulation. Robustness is achieved against additive norm-bounded input disturbances and/or polyhedral parametric uncertainties in the state-space matrices. We show that the finite-horizon robust optimal control law is a continuous piecewise affine function of the state vector and can be calculated by solving a sequence of multiparametric linear programs. When the optimal control law is implemented in a receding horizon scheme, only a piecewise affine function needs to be evaluated on line at each time step. The technique computes the robust optimal feedback controller for a rather general class of systems with modest computational effort without needing to resort to gridding of the state-space.
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Cites
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
Cited by
Optimization over state feedback policies for robust control with constraints
Goulart, P. J., Kerrigan, E. C., & Maciejowski, J. M. (2006) · Automatica · doi:10.1016/j.automatica.2005.08.023 · Cited by 580
Dynamic modeling and control of supply chain systems: A review
Sarimveis, H., Patrinos, P., Tarantilis, C. D., & Kiranoudis, C. T. (2008) · Computers & Operations Research · doi:10.1016/j.cor.2007.01.017 · Cited by 458
Rubagotti, M., Raimondo, D. M., Ferrara, A., & Magni, L. (2011) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2010.2074590 · Cited by 196
Action robust reinforcement learning and applications in continuous control
Tessler, C., Efroni, Y., & Mannor, S. (2019) · arXiv · doi:10.48550/arxiv.1901.09184 · Cited by 108
Metadata
- Authors
- Bemporad, A., Borrelli, F., & Morari, M.
- Venue
- IEEE Transactions on Automatic Control
- Published
- 2003-09
- Volume
- 48
- Issue
- 9
- Pages
- 1600-1606
- ISSN
- 0018-9286 (ISSN-L)
- OpenAlex
- W2134702196
- Cited by
- 518
- References
- 1
- FWCI
- 57.12
- Type
- journal article
- Language
- en
- Open access
- closed
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- Bemporad, A., Borrelli, F., & Morari, M. (2003). Min-max control of constrained uncertain discrete-time linear systems. IEEE Transactions on Automatic Control. https://doi.org/10.1109/tac.2003.816984
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