Abstract
The essential components of the classical predictive control algorithms considered in Chap. 2 also underpin the design of algorithms for robust MPC. Guarantees of closed-loop properties such as stability and convergence rely on appropriately defined terminal control laws, terminal sets and cost functions. Likewise, to ensure that constraints can be met in the future, the initial plant state must belong to a suitable controllable set. However the design of these constituents and the analysis of their effects on the performance of MPC algorithms become more complex in the case where the system dynamics are subject to uncertainty. The main difficulty is that properties such as invariance, controlled invariance (including recursive feasibility) and monotonicity of the predicted cost must be guaranteed for all possible uncertainty realizations. In many cases this leads to computation which grows rapidly with the problem size and the prediction horizon.
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- 1.
This is a simplified version of the more general inclusion condition that is considered in [20]: \(\{\varPhi s_{i|k} + B c_{i|k}\} \oplus \varPhi _e\alpha _{i|k}\mathcal {S}^0\oplus D\mathcal {W}\subseteq \{s_{i+1|k}\} \oplus \alpha _{i+1|k}\mathcal {S}^0\).
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Kouvaritakis, B., Cannon, M. (2016). Open-Loop Optimization Strategies for Additive Uncertainty. In: Model Predictive Control. Advanced Textbooks in Control and Signal Processing. Springer, Cham. https://doi.org/10.1007/978-3-319-24853-0_3
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