Robust Model Predictive Control

Robust variants of Model Predictive Control (MPC) are able to account for set bounded disturbance while still ensuring state constraints are met. There are three main approaches to robust MPC:

Min-max MPC. In this formulation, the optimization is performed with respect to all possible evolutions of the disturbance.^[1] This is the optimal solution to linear robust control problems, however it caries a high computational cost.
Constraint Tightening MPC. Here the state constraints are enlarged by a given margin so that a trajectory can be guaranteed to be found under any evolution of disturbance.^[2]
Tube MPC. This uses an independent nominal model of the system, and uses a feedback controller to ensure the actual state converges to the nominal state.^[3] The amount of separation required from the state constraints is determined by the robust positively invariant (RPI) set, which is the set of all possible state deviations that may be introduced by disturbance with the feedback controller.

^ Scokaert, P. O. (1998). "Min-max feedback model predictive control for constrained linear systems". IEEE Transactions on Automatic Control. 43 (8): 1136–1142. doi:10.1109/9.704989. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
^ Richards, A. (2006). "Robust stable model predictive control with constraint tightening". Proceedings of the American Control Conference. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
^ Langson, W. (2004). "Robust model predictive control using tubes". Automatica. 40 (1): 125–133. doi:10.1016/j.automatica.2003.08.009. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)

[1] Scokaert, P. O. (1998). "Min-max feedback model predictive control for constrained linear systems". IEEE Transactions on Automatic Control. 43 (8): 1136–1142. doi:10.1109/9.704989. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)

[2] Richards, A. (2006). "Robust stable model predictive control with constraint tightening". Proceedings of the American Control Conference. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)

[3] Langson, W. (2004). "Robust model predictive control using tubes". Automatica. 40 (1): 125–133. doi:10.1016/j.automatica.2003.08.009. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)

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