Related papers: Stability-Certified Learning of Control Systems wi…
Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…
In this paper we address the issue of output instability of deep neural networks: small perturbations in the visual input can significantly distort the feature embeddings and output of a neural network. Such instability affects many deep…
The stabilization of nonlinear systems under zero-state-detectability assumption or its analogues is considered. The proposed supervisory control provides a finite time practical stabilization of output and it is based on uniting local and…
Constraint tightening to non-conservatively guarantee recursive feasibility and stability in Stochastic Model Predictive Control is addressed. Stability and feasibility requirements are considered separately, highlighting the difference…
This paper studies exponential stability properties of a class of two-dimensional (2D) systems called differential repetitive processes (DRPs). Since a distinguishing feature of DRPs is that the problem domain is bounded in the "time"…
We study the control of networked systems with the goal of optimizing both transient and steady-state performances while providing stability guarantees. Linear proportional-integral (PI) controllers are almost always used in practice, but…
Stability certification and identifying a safe and stabilizing initial set are two important concerns in ensuring operational safety, stability, and robustness of dynamical systems. With the advent of machine-learning tools, these issues…
We develop a dynamic model of cascading failures in a financial network whereby cross-holdings are viewed as feedback, external assets investments as inputs and failure penalties as static nonlinearities. We provide sufficient milder and…
We introduce a method for learning provably stable deep neural network based dynamic models from observed data. Specifically, we consider discrete-time stochastic dynamic models, as they are of particular interest in practical applications…
Empirical modelling often aims for the simplest model consistent with the data. A new technique is presented which quantifies the consistency of the model dynamics as a function of location in state space. As is well-known, traditional…
Mathematical modeling is an essential step, for example, to analyze the transient behavior of a dynamical process and to perform engineering studies such as optimization and control. With the help of first-principles and expert knowledge, a…
Learning stabilizing controllers from data is an important task in engineering applications; however, collecting informative data is challenging because unstable systems often lead to rapidly growing or erratic trajectories. In this work,…
The input/output stability of an interconnected system composed of an ordinary differential equation and a damped string equation is studied. Issued from the literature on time-delay systems, an exact stability result is firstly derived…
For networked systems, the control law is typically subject to network flaws such as delays and packet dropouts. Hence, the time in between updates of the control law varies unexpectedly. Here, we present a stability theorem for nonlinear…
This paper presents the analysis of the stability properties of PID controllers for dynamical systems with multiple state delays, focusing on the mathematical characterization of the potential sensitivity of stability with respect to…
Linear systems of neutral type are considered using the infinite dimensional approach. The main problems are asymptotic, non-exponential stability, exact controllability and regular asymptotic stabilizability. The main tools are the moment…
Learning-based optimal control algorithms control unknown systems using past trajectory data and a learned model of the system dynamics. These controllers use either a linear approximation of the learned dynamics, trading performance for…
The recently introduced structured input-output analysis is a powerful method for capturing nonlinear phenomena associated with incompressible flows, and this paper extends that method to the compressible regime. The proposed method relies…
We consider the adaptive control problem for discrete-time, nonlinear stochastic systems with linearly parameterised uncertainty. Assuming access to a parameterised family of controllers that can stabilise the system in a bounded set within…
Chaos is a fundamental feature of many complex dynamical systems, including weather systems and fluid turbulence. These systems are inherently difficult to predict due to their extreme sensitivity to initial conditions. Many chaotic systems…