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Assessment of the degree of boundedness/stability of multidimensional nonlinear systems with time-dependent and nonperiodic coefficients is an important problem in various applied areas which has no adequate resolution yet. Most of the…
We describe methods for proving bounds on infinite-time averages in differential dynamical systems. The methods rely on the construction of nonnegative polynomials with certain properties, similarly to the way nonlinear stability can be…
Tight estimation of the Lipschitz constant for deep neural networks (DNNs) is useful in many applications ranging from robustness certification of classifiers to stability analysis of closed-loop systems with reinforcement learning…
This work is concerned with robust filtering of nonlinear sampled-data systems with and without exact discrete-time models. A linear matrix inequality (LMI) based approach is proposed for the design of robust $H_{\infty}$ observers for a…
Optimal sensing nodes selection (SNS) in dynamic systems is a combinatorial optimization problem that has been thoroughly studied in the recent literature. This problem can be formulated within the context of set optimization. For…
In this paper we address the challenging problem of designing globally convergent estimators for the parameters of nonlinear systems containing a non-separable exponential nonlinearity. This class of terms appears in many practical…
Techniques known as Nonlinear Set Membership prediction, Kinky Inference or Lipschitz Interpolation are fast and numerically robust approaches to nonparametric machine learning that have been proposed to be utilised in the context of system…
In this paper, we propose fixed-order set-valued (in the form of l2-norm hyperballs) observers for some classes of nonlinear bounded-error dynamical systems with unknown input signals that simultaneously find bounded hyperballs of states…
We investigate the effect of explicitly enforcing the Lipschitz continuity of neural networks with respect to their inputs. To this end, we provide a simple technique for computing an upper bound to the Lipschitz constant---for multiple…
Obtaining predictive low-order models is a central challenge in fluid dynamics. Data-driven frameworks have been widely used to obtain low-order models of aerodynamic systems; yet, resulting models tend to yield predictions that grow…
This paper focuses on the model-free synthesis of state observers for nonlinear autonomous systems without knowing the governing equations. Specifically, the Kazantzis-Kravaris/Luenberger (KKL) observer structure is leveraged, where the…
The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems…
Nonlinear systems play a significant role in numerous scientific and engineering disciplines, and comprehending their behavior is crucial for the development of effective control and prediction strategies. This paper introduces a novel…
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…
We address the problem of designing simultaneous input and state interval observers for Lipschitz continuous nonlinear systems with rank-deficient feedthrough, unknown inputs and bounded noise signals. Benefiting from the existence of…
To improve the robustness of deep classifiers against adversarial perturbations, many approaches have been proposed, such as designing new architectures with better robustness properties (e.g., Lipschitz-capped networks), or modifying the…
In this paper we present a general tool to handle the presence of zero dynamics which are asymptotically but not locally exponentially stable in problems of robust nonlinear stabilization by output feedback. We show how it is possible to…
In the paper, the global optimization problem of a multidimensional "black-box" function satisfying the Lipschitz condition over a hyperinterval with an unknown Lipschitz constant is considered. A new efficient algorithm for solving this…
Transient instability in nonlinear stochastic dynamical systems is a fundamental limitation in safety-critical aerospace applications, particularly during powered descent and landing where failure is driven by finite-time excursions rather…
In this article, we present a brief overview of some of the recent progress made in identifying and generating finite dimensional integrable nonlinear dynamical systems, exhibiting interesting oscillatory and other solution properties,…