Emergent Behaviour and Adaptivity
This work package has the goal of extending classical mean field results to deal with specific features of CAS, like their multi-scale nature and their intrinsic uncertainty. We will also exploit mean field to provide algorithms to design suitable control policies. We will also lift those results to the language level, to make their application as much automatic as possible. Finally, we will apply and validate the theory on the smart grids case study.
- The first task in this work package is concerned with Identification of emergent behaviour in multi-scale systems and will deal with two crucial features of collective adaptive systems in a mean field setting. One issue is that of detecting and managing the emergence of multiple temporal (like fast and slow dynamics) and organisational scales (like centralised and decentralised controlling mechanisms). We will tackle it exploiting hybrid mean field limits (in which the limit is an hybrid system rather than a ODE) and techniques for time scale decomposition coming from biophysics, like Quasi-Steady-State and Quasi-Equilibrium. Another feature of CAS is their intrinsic uncertainty, mainly caused by the human-in-the-loop. To deal with it, we will consider stochastic models based on interval probabilities and develop mean field limits in terms of differential inclusions.
- The second task in this work package deals with Control and adaptivity of emergent behaviour and will focus on the design of control algorithms for collective adaptive systems. We will build on the results of the previous task and consider a multiple scale approach. We will use mean field approximation techniques and the multi-scale structure to build decentralized control algorithms. A key application of these results will be in the development of robust methods for the control of smart energy systems. The classical techniques to guarantee the stability of these systems is to explicitly reserve a large quantity of energy. A large penetration of renewable energy sources (solar PV, wind turbines) requires to rethink these paradigm and go from centralized to distributed control. Our aim is to use a composable approach (using distributed control and aggregating into abstract models) that can compensate for the volatility and prediction uncertainties. Mean field techniques will help developing mechanisms to predict where and when will be the electricity needed. We also plan to lift these results in a more abstract framework and interface them with the other case studies. For example, to study incentives mechanisms in bike-sharing systems or smart buses.
- The final task in this work package is concerned with Linking language and mean field approximations. We will reconsider all the theoretical advances obtained in the work package from the point of view of usability, trying to define language primitives and static analysis routines that can help users of the language certify their applicability for a given model, without the need to work directly with complex mathematical machinery. These primitives and algorithms will then be integrated in the language CAS-SCEL.