Semi-infinite methods for robust optimization and control
File(s)
Author(s)
Wehbeh, Jad
Type
Thesis or dissertation
Abstract
Robust optimization and optimal control problems require finding decision variables that guarantee constraint satisfaction and performance for all admissible uncertainties. Exact formulations naturally lead to optimization problems with finitely many decision variables but infinitely many constraints, known as semi-infinite programs. Although highly expressive, semi-infinite formulations, particularly those involving existence constraints or decision-dependent uncertainties, remain computationally challenging.
This thesis develops a novel framework for formulating and solving a broad class of robust optimal control problems through advances in continuous logic representations and semi-infinite programming methods. First, it introduces an exact binary-free reformulation of logical constraints in nonlinear optimization and optimal control. Discrete logic is represented using continuous auxiliary variables and smooth nonlinear constraints whose feasible sets exactly match those of the original mixed-integer formulations, enabling the use of continuous optimization solvers without sacrificing correctness.
Building on this foundation, the thesis extends local reduction techniques for semi-infinite programming to handle existence-constrained and generalized semi-infinite programs. These extensions enable efficient solution of problems in which constraint satisfaction depends on auxiliary decisions or where the uncertainty set depends on the optimization variables. Convergence properties are established under regularity assumptions, and the resulting algorithms demonstrate strong computational performance on nonlinear benchmark problems.
The proposed methods are applied to several challenging robust optimal control settings, including open-loop robust control with logic constraints and state- and control-dependent uncertainty, robust optimal output feedback under bounded measurement and model uncertainty, and robust model predictive control (MPC) for nonlinear systems. In particular, an update-aware robust MPC algorithm is developed that explicitly accounts for future control updates, yielding provably improved worst-case performance guarantees compared to traditional robust MPC formulations.
Through theoretical analysis and numerical examples, this thesis demonstrates that combining exact continuous logic reformulations with semi-infinite programming methods enables tractable solution approaches for robust optimal control problems previously beyond practical reach.
This thesis develops a novel framework for formulating and solving a broad class of robust optimal control problems through advances in continuous logic representations and semi-infinite programming methods. First, it introduces an exact binary-free reformulation of logical constraints in nonlinear optimization and optimal control. Discrete logic is represented using continuous auxiliary variables and smooth nonlinear constraints whose feasible sets exactly match those of the original mixed-integer formulations, enabling the use of continuous optimization solvers without sacrificing correctness.
Building on this foundation, the thesis extends local reduction techniques for semi-infinite programming to handle existence-constrained and generalized semi-infinite programs. These extensions enable efficient solution of problems in which constraint satisfaction depends on auxiliary decisions or where the uncertainty set depends on the optimization variables. Convergence properties are established under regularity assumptions, and the resulting algorithms demonstrate strong computational performance on nonlinear benchmark problems.
The proposed methods are applied to several challenging robust optimal control settings, including open-loop robust control with logic constraints and state- and control-dependent uncertainty, robust optimal output feedback under bounded measurement and model uncertainty, and robust model predictive control (MPC) for nonlinear systems. In particular, an update-aware robust MPC algorithm is developed that explicitly accounts for future control updates, yielding provably improved worst-case performance guarantees compared to traditional robust MPC formulations.
Through theoretical analysis and numerical examples, this thesis demonstrates that combining exact continuous logic reformulations with semi-infinite programming methods enables tractable solution approaches for robust optimal control problems previously beyond practical reach.
Version
Open Access
Date Issued
2026-01-17
Date Awarded
2026-07-01
Copyright Statement
Attribution-NonCommercial-ShareAlike 4.0 International Licence (CC BY NC-SA)
Advisor
Kerrigan, Eric C.
Sponsor
Natural Sciences and Engineering Research Council of Canada
Publisher Department
Department of Electrical and Electronic Engineering
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)