M16 OXFORD

Current operations in energy and transportation are experiencing a transition to new operational paradigms that exhibit certain complexity features. Complexity involves challenges associated with: (i) coordinating operations among heterogenous interacting entities without sharing information considered as private; (ii) robustness against uncertainty; (iii) the ability to deal with an interplay of continuous and discrete scheduling decisions. This course provides a theoretical and computational framework for coordination and optimal operation of complex systems, addressing the aforementioned features of complexity. We first draw motivation from the energy sector, formalizing several of the current operational challenges as multi-agent optimal control and optimization problems. We then introduce and analyze a portfolio of algorithms capable to deal with the three main complexity pillars, with emphasis on distributed optimization over networks, addressing also the case where both continuous and discrete decisions are involved. Finally, we consider the case where uncertainty affects the underlying systems and show how data-driven algorithms based on statistical learning theory and randomized optimization can be extended to a multi-agent setting. Course outline 1. Motivation of decision making in complex systems • Energy systems operations: Aggregation of distributed energy resources; demand response; electric vehicle scheduling; building energy management 2. Mathematical preliminaries on optimization and iterative algorithms 3. Distributed algorithms for multi-agent decision making • Continuous domains: Primal-based algorithms (proximal methods; projected sub-gradient methods) and primal-dual algorithms (distributed alternating direction method of multipliers; distributed dual decomposition) for constrained optimization over networks. • Discrete domains: Primal-dual algorithms for resource sharing problems 4. Data-driven algorithms for optimization under uncertainty • The scenario approach to optimization under a learning theoretic lens • Probabilistic robustness in multi-agent decision making problems 5. Research vistas