Data-driven distributionally robust model predictive control
File(s)
Author(s)
Zhong, Zhengang
Type
Thesis
Abstract
To mitigate the detrimental effects of uncertainty and disturbances, two main model predictive control (MPC) frameworks have been developed to explicitly incorporate uncertainty into controller synthesis: robust MPC (RMPC) and stochastic MPC (SMPC). RMPC determines control actions that are optimal under the worst-case realization of uncertainty within a deterministic set, while SMPC assumes or estimates the probability distribution of uncertainty and optimizes a probabilistic objective under probabilistic constraints. Although probabilistic constraints can reduce the conservativeness of RMPC by incorporating distributional information, obtaining the true distribution of uncertainty in real-world systems is often infeasible. Moreover, the high computational burden of SMPC and its sensitivity to distributional discrepancy limit its practical performance.
To address the challenges mentioned above, this thesis considers data-driven distributionally robust MPC (DRMPC) problems. Instead of requiring exact knowledge of the disturbance distribution, DRMPC constructs an ambiguity set using samples of disturbance realizations. This set represents the family of distributions consistent with the observed data, and control actions are determined based on the worst-case distribution within it, achieving robustness to sampling and modeling errors.
Chapters 1–2 motivate the integration of distributional robustness into MPC and present the mathematical foundations of DRMPC.
Chapters 3–5 focus on linear systems. Chapter 3 presents a general DRMPC framework ensuring stability and recursive feasibility. Chapter 4 introduces a Wasserstein-based DRMPC for stochastic linear systems, ensuring tractability and constraint satisfaction. Chapter 5 integrates Wasserstein and moment-based ambiguity sets into the DRMPC framework, ensuring recursive feasibility and stochastic input-to-state practical stability.
Chapters 6–8 extend DRMPC to nonlinear systems. Chapter 6 introduces two linearization-based methods and incorporates an offset-free approach to address model mismatch. Chapter 7 proposes dynamic ambiguity propagation via iterative LQR. Chapter 8 presents a Koopman-based stochastic DRMPC ensuring regulation and constraint satisfaction with finite-sample guarantees.
To address the challenges mentioned above, this thesis considers data-driven distributionally robust MPC (DRMPC) problems. Instead of requiring exact knowledge of the disturbance distribution, DRMPC constructs an ambiguity set using samples of disturbance realizations. This set represents the family of distributions consistent with the observed data, and control actions are determined based on the worst-case distribution within it, achieving robustness to sampling and modeling errors.
Chapters 1–2 motivate the integration of distributional robustness into MPC and present the mathematical foundations of DRMPC.
Chapters 3–5 focus on linear systems. Chapter 3 presents a general DRMPC framework ensuring stability and recursive feasibility. Chapter 4 introduces a Wasserstein-based DRMPC for stochastic linear systems, ensuring tractability and constraint satisfaction. Chapter 5 integrates Wasserstein and moment-based ambiguity sets into the DRMPC framework, ensuring recursive feasibility and stochastic input-to-state practical stability.
Chapters 6–8 extend DRMPC to nonlinear systems. Chapter 6 introduces two linearization-based methods and incorporates an offset-free approach to address model mismatch. Chapter 7 proposes dynamic ambiguity propagation via iterative LQR. Chapter 8 presents a Koopman-based stochastic DRMPC ensuring regulation and constraint satisfaction with finite-sample guarantees.
Version
Open Access
Date Issued
2024-12-31
Date Awarded
01/11/2025
License URL
Advisor
del Rio Chanona, Antonio
Petsagkourakis, Panagiotis
Publisher Department
Department of Chemical Engineering
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)