An incremental input-to-state stability condition for a generic class of recurrent neural networks

This paper proposes a novel sufficient condition for the incremental input-to-state stability of a generic class of recurrent neural networks (RNNs). The established condition is compared with others available in the literature, showing to be less conservative. Moreover, it can be applied for the design of incremental input-to-state stable RNN-based control systems, resulting in a linear matrix inequality constraint for some specific RNN architectures. The formulation of nonlinear observers for the considered system class, as well as the design of control schemes with explicit integral action, are also investigated. The theoretical results are validated through simulation on a referenced nonlinear system

Convex Equilibrium-Free Stability and Performance Analysis of Discrete-Time Nonlinear Systems

This paper considers the equilibrium-free stability and performance analysis of discrete-time nonlinear systems. We consider two types of equilibrium-free notions. Namely, the universal shifted concept, which considers stability and performance w.r.t. all equilibrium points of the system, and the incremental concept, which considers stability and performance between trajectories of the system. In this paper, we show how universal shifted stability and performance of discrete-time systems can be analyzed by making use of the time-difference dynamics. Moreover, we extend the existing results for incremental dissipativity for discrete-time systems based on dissipativity analysis of the differential dynamics to more general state-dependent storage functions for less conservative results. Finally, we show how both these equilibrium-free notions can be cast as a convex analysis problem by making use of the linear parameter-varying framework, which is also demonstrated by means of an example.Comment: Submitted to IET Control Theory & Application

Data-Driven Safety-Critical Control: Synthesizing Control Barrier Functions With Koopman Operators

Control barrier functions (CBFs) are a powerful tool to guarantee safety of autonomous systems, yet they rely on the computation of control invariant sets, which is notoriously difficult. A backup strategy employs an implicit control invariant set computed by forward integrating the system dynamics. However, this integration is prohibitively expensive for high dimensional systems, and inaccurate in the presence of unmodelled dynamics. We propose to learn discrete-time Koopman operators of the closed-loop dynamics under a backup strategy. This approach replaces forward integration by a simple matrix multiplication, which can mostly be computed offline. We also derive an error bound on the unmodeled dynamics in order to robustify the CBF controller. Our approach extends to multi-agent systems, and we demonstrate the method on collision avoidance for wheeled robots and quadrotors