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Converse optimality theory addresses an optimal control problem conversely where the system is unknown and the value function is chosen. Previous work treated this problem both in continuous and discrete time and non-extensively considered…
In this review, we present a survey of the Lyapunov Error and Reversibility Error (\cite{Faranda2012}), and we propose a generalization to make them invariant to the choice of initial conditions. We first define a process as the evolution…
Several results regarding the stability and the stabilization of linear impulsive positive systems under arbitrary, constant, minimum, maximum and range dwell-time are obtained. The proposed stability conditions characterize the pointwise…
Since batch algorithms suffer from lack of proficiency in confronting model mismatches and disturbances, this contribution proposes an adaptive scheme based on continuous Lyapunov function for online robot dynamic identification. This paper…
Recently, many machine learning optimizers have been analysed considering them as the asymptotic limit of some differential equations when the step size goes to zero. In other words, the optimizers can be seen as a finite difference scheme…
System identification in control theory aims to approximate dynamical systems from trajectory data. While neural networks have demonstrated strong predictive accuracy, they often fail to preserve critical physical properties such as…
Linear Parameter-Varying (LPV) systems with jumps and piecewise differentiable parameters is a class of hybrid LPV systems for which no tailored stability analysis and stabilization conditions have been obtained so far. We fill this gap…
Adaptive control strategies usually are designed based on gradient methods for the sake of simplicity in Lyapunov analysis. However, least squares (LS)-based parameter identifiers, with proper selection of design parameters, exhibit better…
In a recent paper we have shown how to learn controllers for unknown linear systems using finite-sized noisy data by solving linear matrix inequalities. In this note we extend this approach to deal with unknown nonlinear polynomial systems…
Identification of the parameters of stable linear dynamical systems is a well-studied problem in the literature, both in the low and high-dimensional settings. However, there are hardly any results for the unstable case, especially…
We discuss the irreversibility, nonlocality, and fluctuations, as well as the Lyapunov and hydrodynamic instabilities characterizing atomistic, smooth-particle, and finite-difference solutions of the two-dimensional Rayleigh-B\'enard…
The dynamics of transitional flows are governed by an interplay between the non-normal linear dynamics and quadratic nonlinearity in the incompressible Navier-Stokes equations. In this work, we propose a framework for nonlinear stability…
In the design and operation of complex dynamical systems, it is essential to ensure that all state trajectories of the dynamical system converge to a desired equilibrium within a guaranteed stability region. Yet, for many practical systems…
Accurate approximations of the change of system's output and its statistics with respect to the input are highly desired in computational dynamics. Ruelle's linear response theory provides breakthrough mathematical machinery for computing…
Sequential algorithms for the Stable Matching Problem are often too slow in the context of some large scale applications like switch scheduling. Parallel architectures can offer a notable decrease in runtime complexity. We propose a stable…
Growing penetration of renewable generation in power systems brings more challenges in transient stability assessment using direct methods. One of the reasons is the inability to assess the risk of instability brought by tripping of a large…
This paper is concerned with stability analysis of nonlinear time-varying systems by using Lyapunov function based approach. The classical Lyapunov stability theorems are generalized in the sense that the time-derivative of the Lyapunov…
This paper presents novel stabilizability conditions for switched linear systems with arbitrary and uncontrollable underlying switching signals. We distinguish and study two particular settings: i) the \emph{robust} case, in which the…
Numerical solutions for the optimal feedback stabilization of discrete time dynamical systems is the focus of this paper. Set-theoretic notion of almost everywhere stability introduced by the Lyapunov measure, weaker than conventional…
Given a family of systems, identifying stabilizing switching signals in terms of infinite walks constructed by concatenating cycles on the underlying directed graph of a switched system that satisfy certain conditions, is a well-known…