Related papers: LaSalle Invariance Principle for Discrete-time Dyn…
We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…
This paper provides a new unified framework for second-moment stability of discrete-time linear systems with stochastic dynamics. Relations of notions of second-moment stability are studied for the systems with general stochastic dynamics,…
In this paper, we study the large deviation principle of invariant measures of stochastic reaction-diffusion lattice systems driven by multiplicative noise. We first show that any limit of a sequence of invariant measures of the stochastic…
Using any nonnegative function with a nonpositive derivative along trajectories to define a virtual output, the classic LaSalle invariance principle can be extended to switched nonlinear time-varying (NLTV) systems, by considering the weak…
Selfdual variational principles are introduced in order to construct solutions for Hamiltonian and other dynamical systems which satisfy a variety of linear and nonlinear boundary conditions including many of the standard ones. These…
We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…
While invariant measures are widely employed to analyze physical systems when a direct study of pointwise trajectories is intractable, e.g., due to chaos or noise, they cannot uniquely identify the underlying dynamics. Our first result…
Linear dynamical systems are the foundational statistical model upon which control theory is built. Both the celebrated Kalman filter and the linear quadratic regulator require knowledge of the system dynamics to provide analytic…
In this paper, we propose a novel, unified, general approach to investigate sufficient and necessary conditions under which four types of convex sets, polyhedra, polyhedral cones, ellipsoids and Lorenz cones, are invariant sets for a linear…
In this paper we study a class of \emph{self-consistent dynamical systems}, self-consistent in the sense that the discrete time dynamics is different in each step depending on current statistics. The general framework admits popular…
This paper deals with the problem of covariance stabilization for a class of linear stochastic discrete-time systems in the Stochastic Model Predictive Control (SMPC) framework. The considered systems are affected by independent and…
Many nonlinear dynamical systems can be written as Lure systems, which are described by a linear time-invariant system interconnected with a diagonal static sector-bounded nonlinearity. Sufficient conditions are derived for the global…
This work provides a framework for nonlinear model-free control of systems with unknown input-output dynamics, but outputs that can be controlled by the inputs. This framework leads to real-time control of the system such that a feasible…
Three similar convergence notions are considered. Two of them are the long established notions of convergent dynamics and incremental stability. The other is the more recent notion of contraction analysis. All three convergence notions…
This paper addresses the problem of stabilizing a part of variables for control systems described by stochastic differential equations of the Ito type. The considered problem is related to the asymptotic stability property of invariant sets…
The investigation of nonlinear dynamical systems of the type $\dot{x}=P(x,y,z),\dot{y}=Q(x,y,z),\dot{z}=R(x,y,z)$ by means of reduction to some ordinary differential equations of the second order in the form…
Continuous linear dynamical systems are used extensively in mathematics, computer science, physics, and engineering to model the evolution of a system over time. A central technique for certifying safety properties of such systems is by…
We prove some invariance principles for processes which generalize FARIMA processes, when the innovations are in the domain of attraction of a nonGaussian stable distribution. The limiting processes are extensions of the fractional L\'evy…
By one of the most fundamental principles in physics, a dynamical system will exhibit those motions which extremise an action functional. This leads to the formation of the Euler-Lagrange equations, which serve as a model of how the system…
Employing a phase space which includes the (Riemann-Liouville) fractional derivative of curves evolving on real space, we develop a restricted variational principle for Lagrangian systems yielding the so-called restricted fractional…