• Compositional synthesis of abstractions for infinite networks (ongoing)

Complex nature of control objectives, number of participating agents, and the complexity of the problem call for methods on systematic, automated synthesis of provably correct controllers by merging ideas from computer science and control theory. In particular, correct-by-construction automated verification and synthesis, which were originally developed for specifying and verifying the correct behavior of software and hardware systems, provide a rigorous framework to efficiently address the above issues. The study of automated controller synthesis based on symbolic models has seen major advances in recent years. However, an efficient approach to the large-scale and possibly infinite-dimensional case is missing. As the computational complexity of constructing symbolic models often scales exponentially with the dimension of the state space, a brute force approach to large-scale systems is not feasible. Instead, we propose to use system structure to derive methods for large-scale systems based on dissipativity or small-gain arguments. This project aims to develop a rigorous mathematical framework for distributed symbolic control of systems composed of a countably infinite number of dynamically coupled subsystems. Our proposed methods will preserve the structure of the network in order to facilitate distributed control design. The effectiveness of the theoretical results will be verified by applications to traffic networks.

Funded by DFG, PIs: Navid Noroozi, Majid Zamani (Technische Universität München)

  • A framework for non-conservative control of dynamical networks

Trends in a wide variety of industries, including safety and reliability requirements, ease of maintenance and increasing use of renewable energy, introduce new sources of complexity in large-scale control systems. Addressing this complexity requires the introduction of new control techniques with a wider range of applicability. Moreover, the reduction of energy consumption, as set forth by the European Union, is playing an increasingly central role, thus resulting into a demand for energy efficient control strategies. Motivated by the fact that today's controllers are mostly implemented digitally, this research project proposes a framework for control of large-scale discrete-time systems via the very recent notion of non-conservative stability analysis. This framework promises to simultaneously solve the aforementioned issues by: splitting the whole system into smaller subsystems; either analytically or numerically computing a control Lyapunov-like function for each of the subsystems; verifying stability of the whole system via non-conservative stability analysis. In particular, we introduce recursive designs by the repeated application of non-conservative stability theory. Compared with their conservative counterparts, the recursive designs will not only be applicable to a wider class of large-scale systems, but also provide considerable reduction in control effort.

Funded by Alexander von Humboldt-Stiftung, PI: Navid Noroozi