Tools for the analysis, design and decentralized control of complex systems: from decomposition-aggregations to mean field control

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With the increasing level of interdependencies and interconnection of systems, be they energy or communication systems, and their interconnection into envisioned smart grids, be they manufacturing systems and their supply chains, financial systems, or environmental systems, there is a great need for effective tools to help the understanding, the design, and for scalability, the synthesis of decentralized controls. Such interconnected systems are termed complex in this research proposal. Within the spectrum of possible complex systems, we consider two relatively extreme cases: type (i) systems, such as manufacturing transfer lines, or cascaded hydraulic dams which exhibit sparse and highly localized connections; type (ii) systems which on the contrary exhibit a dense network of interconnections with components exerting influence on and subject to the influence of most other system components. A typical man made example of type (ii) systems is economies and markets, or traffic systems where individual decisions influence and are in turn influenced by the mass of other decisions; in nature, an archetypal example is the collective motion of herds, fish schools, and birds. For type (i) systems, we propose the exploration of decomposition-aggregation methods with our main engineering paradigm being manufacturing systems. For inspiration, we also look towards successful biological systems structures such as metabolic networks, in an effort to abstract out good control architectures and good design principles later to be justified on theoretical grounds. As for type (ii) systems, we propose to use a methodology that we coinvented. It results from a blend of game theory initially developed for economics applications, and another very successful body of ideas in physics known as statistical physics constructed to provide effective macroscopic descriptions of large systems of interacting particles. The methodology is applied to the study of collective dynamics in fish schools and herds, with envisioned engineering applications in robotics and communications.