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We propose an algorithm to actively estimate the parameters of a linear dynamical system. Given complete control over the system's input, our algorithm adaptively chooses the inputs to accelerate estimation. We show a finite time bound…
A method is presented to analyze the stability of feedback systems with neural network controllers. Two stability theorems are given to prove asymptotic stability and to compute an ellipsoidal inner-approximation to the region of attraction…
Dynamic games arise when multiple agents with differing objectives choose control inputs to a dynamic system. Dynamic games model a wide variety of applications in economics, defense, and energy systems. However, compared to single-agent…
The nonlinear dynamics of a system with periodic structure can be analyzed using a square matrix. We show that because the special property of the square matrix constructed for nonlinear dynamics, we can reduce the dimension of the matrix…
We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both…
This paper introduces coordinate-independent methods for analysing multiscale dynamical systems using numerical techniques based on the transfer operator and its adjoint. In particular, we present a method for testing whether an arbitrary…
The data-driven techniques have been developed to deal with the output regulation problem of unknown linear systems by various approaches. In this paper, we first extend an existing algorithm from single-input single-output linear systems…
This article describes a numerical procedure designed to tune the parameters of periodically-driven dynamical systems to a state in which they exhibit rich dynamical behavior. This is achieved by maximizing the diversity of subharmonic…
Nonlinear dynamic models are widely used for characterizing functional forms of processes that govern complex biological pathway systems. Over the past decade, validation and further development of these models became possible due to data…
Nonlinear systems with model uncertainty are often described by stochastic differential equations. Some techniques from random dynamical systems are discussed. They are relevant to better understanding of solution processes of stochastic…
We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…
We present a framework for constructing a structured realization of a linear time-invariant dynamical system solely from a discrete sampling of an input and output trajectory of the system. We estimate the transfer function of the original…
This paper is a preliminary work to address the problem of dynamical systems with parameters varying in time. An idea to predict their behaviour is proposed. These systems are called \emph{transient systems}, and are distinguished from…
The aim of this section is to present programs allowing to high- light the slow-fast evolution of the solutions of nonlinear and chaotic dynamical systems such as: Van der Pol, Chua and Lorenz models. These programs provide animated phase…
Iterative optimization algorithms depend on access to information about the objective function. In a differentiable programming framework, this information, such as gradients, can be automatically derived from the computational graph. We…
An artificial neural network architecture, parameterization networks, is proposed for simulating extrapolated dynamics beyond observed data in dynamical systems. Parameterization networks are used to ensure the long term integrity of…
In this paper we consider a population consisting of two species, dynamics of which is defined by a quadratic stochastic operator with variable coefficients, making it discontinuous operator at two points. This operator depends on three…
We explore the promising performance of a transformer model in predicting outputs of parametric dynamical systems with external time-varying input signals. The outputs of such systems vary not only with physical parameters but also with…
In the paper, we study behavior of discrete dynamical systems (automata) w.r.t. transitivity; that is, speaking loosely, we consider how diverse may be behavior of the system w.r.t. variety of word transformations performed by the system:…
This work focuses on developing a data-driven framework using Koopman operator theory for system identification and linearization of nonlinear systems for control. Our proposed method presents a deep learning framework with recursive…