In this work, we propose a data-driven approach for the stability analysis of discrete-time homogeneous nonlinear systems with unknown models. The proposed framework is based on constructing Lyapunov functions via a set of data, collected from trajectories of unknown systems, while providing an a-priori guaranteed confidence on the stability of the system. In our data-driven setting, we first cast the original stability problem as a robust optimization program (ROP). Since unknown models appear in the constraint of the proposed ROP, we collect a finite number of data from trajectories of unknown systems and provide two variants of scenario optimization program (SOP) associated to the original ROP. We discuss that the proposed ROP, and its corresponding SOPs, are not convex due to having a bilinearity between decision variables. We also show that while one of the proposed SOPs is more efficient in terms of computational complexity, the other one provides Lyapunov functions with a much better performance for the original ROP. We then establish a probabilistic closeness between the optimal value of (non-convex) SOP and that of ROP, and subsequently, formally provide the stability guarantee for unknown systems with a guaranteed confidence level. We illustrate the efficacy of our proposed results by applying them to two physical case studies with unknown dynamics including (i) a DC motor and (ii) a (homogeneous) nonlinear jet engine compressor. We collect data from trajectories of unknown systems and verify their global asymptotic stability (GAS) with desirable confidence levels.@en

—The last decade has witnessed significant attention on networked control systems (NCS) due to their ubiquitous presence in industrial applications, and, in the particular case of wireless NCS, because of their architectural flexibility and
low installation and maintenance costs. In wireless NCS the communication between sensors, controllers, and actuators is supported by a communication channel that is likely to introduce variable communication delays, packet losses, limited bandwidth, and other practical non-idealities leading to numerous technical challenges. Although stability properties of NCS have been investigated
extensively in the literature, results for NCS under more complex and general objectives, and in particular results dealing with verification or controller synthesis for logical specifications, are much more limited. This work investigates how to address such complex objectives by constructively deriving symbolic models of NCS, while encompassing the mentioned network nonidealities.
The obtained abstracted (symbolic) models can then be employed to synthesize hybrid controllers enforcing rich logical specifications over the concrete NCS models. Examples of such general specifications include properties expressed as formulae in linear temporal logic (LTL) or as automata on infinite strings.
We thus provide a general synthesis framework that can be flexibly adapted to a number of NCS setups. We illustrate the effectiveness of the results over some case studies.@en