Scalable Control Approximations for Resource Constrained Environments

Introduction

This project aims at making a breakthrough contribution in optimal control and decision making for nonlinear processes that take place on network structures and are dynamic in time and/or space.

Applicability

The setting has a wide range of potential domains of applicability, comprising:

• Thermal dynamics in energy networks
• Electric dynamics in energy networks
• Fluid dynamics in energy networks
• Logistics
• Disease spreading dynamics
• Cell signalling in biomedicine

Objectives

The project will pursue the following objectives:

1. To contribute new theory
2. To develop numerical approximation methods
3. To implement algorithmic methods in software
4. To conduct proof-of-concept studies

Research Context

Research in the young field of mixed-integer optimal control (MIOC) has recently seen increased momentum together with numerical approximation algorithms and control theory. Despite initial successes, key questions remain unsolved because of:

• A lack of analytical understanding
• A lack of tractable formulations
• The unavailability of efficient solvers
• The insufficiency of existing implementations

Focus Areas

This project focuses on pivotal but poorly understood topics:

• Decomposition, relaxation, and approximation
• Domains admitting homogenization and limiting processes using weak topologies
• Tractable approximations of direct costs of decisions
• Efficient distributed and parallel nonlinear solvers
• Robustness of approximate nonlinear decision policies under uncertainty

These key issues appear systematically in a wide range of control tasks of high societal relevance.

Contribution to the Field

By addressing them, the project helps to bridge a persistent and pronounced gap in simulation & optimization practice. Due to non-trivial interactions emerging in theory and the unavailability of comprehensive algorithms, these topics cannot be suitably handled by merely combining the respective states of the art.

Conclusion

A focused effort to decisively extend MIOC to optimal decisions for dynamics on networks is therefore a timely endeavour that will help to address the challenging demands of practitioners.