Andrii Mironchenko

Mahdieh Zaker, Andrii Mironchenko, Amy Nejati et al.

This paper develops a direct data-driven framework for infinite networks with unknown nonlinear polynomial subsystems, enabling the synthesis of controllers that ensure the entire network is uniformly globally asymptotically stable (UGAS). To address scalability challenges arising from high dimensionality, we develop a data-driven approach to construct an input-to-state stable (ISS) Lyapunov function and its corresponding controller for each unknown subsystem using only a single set of noise-corrupted input-state trajectories collected from that subsystem. Once each subsystem admits a data-driven ISS Lyapunov function, we leverage a compositional small-gain framework for infinite-dimensional spaces to construct a global control Lyapunov function and its associated controller, thereby ensuring UGAS of the entire infinite network. The effectiveness of the proposed data-driven approach is demonstrated through three case studies, including infinite networks of spacecraft, Lorenz chaotic systems, and an academic example with a state-dependent control input matrix.

Andrii Mironchenko, Fabian Wirth, Antoine Chaillet et al.

We show that the existence of a Lyapunov-Krasovskii functional (LKF) with pointwise dissipation (i.e. dissipation in terms of the current solution norm) suffices for input-to-state stability, provided that uniform global stability can also be ensured using the same LKF. To this end, we develop a stability theory, in which the behavior of solutions is not assessed through the classical norm but rather through a specific LKF, which may provide significantly tighter estimates. We discuss the advantages of our approach by means of an example.

Andrii Mironchenko, Jan Kozlowski

We present a novel optimal allocation model for perennial plants, in which assimilates are not allocated directly to vegetative or reproductive parts but instead go first to a storage compartment from where they are then optimally redistributed. We do not restrict considerations purely to periods favourable for photosynthesis, as it was done in published models of perennial species, but analyse the whole life period of a perennial plant. As a result, we obtain the general scheme of perennial plant development, for which annual and monocarpic strategies are special cases. We not only re-derive predictions from several previous optimal allocation models, but also obtain more information about plants' strategies during transitions between favourable and unfavourable seasons. One of the model's predictions is that a plant can begin to re-establish vegetative tissues from storage, some time before the beginning of favourable conditions, which in turn allows for better production potential when conditions become better. By means of numerical examples we show that annual plants with single or multiple reproduction periods, monocarps, evergreen perennials and polycarpic perennials can be studied successfully with the help of our unified model. Finally, we build a bridge between optimal allocation models and models describing trade-offs between size and the number of seeds: a modelled plant can control the distribution of not only allocated carbohydrates but also seed size. We provide sufficient conditions for the optimality of producing the smallest and largest seeds possible.