Related papers: Discrete-Time Dynamical Systems Generated by a Qua…
This paper introduces a novel Differential Dynamic Programming (DDP) algorithm for solving discrete-time finite-horizon optimal control problems with inequality constraints. Two variants, namely Feasible- and Infeasible-IPDDP algorithms,…
The asymptotic dynamics of quantum Markov chains generated by the most general physically relevant quantum operations is investigated. It is shown that it is confined to an attractor space on which the resulting quantum Markov chain is…
We investigate the dynamical system generated by the function $\lfloor\lambda x\rfloor$ defined on $\mathbb R$ and with a parameter $\lambda\in \mathbb R$. For each given $m\in \mathbb N$ we show that there exists a region of values of…
This article presents an investigation of global properties of a class of differential operators on $\mathbb{T}^1\times\mathbb{R}$. Our approach involves the utilization of a mixed Fourier transform, incorporating both partial Fourier…
The Koopman operator allows for handling nonlinear systems through a (globally) linear representation. In general, the operator is infinite-dimensional - necessitating finite approximations - for which there is no overarching framework.…
Many applied time-dependent problems are characterized by an additive representation of the problem operator. Additive schemes are constructed using such a splitting and associated with the transition to a new time level on the basis of the…
The model is a particular case of causal set. This is a discrete model of spacetime in a microscopic level. In paper the most general properties of the model are investigated without any reference to a dynamics. The dynamics of the model is…
The main goal of this paper is to understand the formation of hexagonal patterns from the dynamical transition theory point of view. We consider the transitions from a steady state of an abstract nonlinear dissipative system. To shed light…
In this paper, we consider the inverse optimal control problem for the discrete-time linear quadratic regulator, over finite-time horizons. Given observations of the optimal trajectories, and optimal control inputs, to a linear…
This study evaluates data-driven models from a dynamical system perspective, such as unstable fixed points, periodic orbits, chaotic saddle, Lyapunov exponents, manifold structures, and statistical values. We find that these dynamical…
Reaction systems are discrete dynamical systems that model biochemical processes in living cells using finite sets of reactants, inhibitors, and products. We investigate the computational complexity of a comprehensive set of problems…
We suggest a new concept of functional-differential operators with constant delay on geometrical graphs that involves {\it global} delay parameter. Differential operators on graphs model various processes in many areas of science and…
We construct phase space localizing operators in all dimensions. These are frequency localized variants of the conditional expectation operator related to a dyadic stopping time. Our construction is an improvement over the so-called phase…
Under non-exponential discounting, we develop a dynamic theory for stopping problems in continuous time. Our framework covers discount functions that induce decreasing impatience. Due to the inherent time inconsistency, we look for…
In the present paper is devoted to the study of elliptic quadratic operator equations over the finite dimensional Euclidean space. We provide necessary and sufficient conditions for the existence of solutions of elliptic quadratic operator…
Most algorithms for solving optimization problems or finding saddle points of convex-concave functions are fixed-point algorithms. In this work we consider the generic problem of finding a fixed point of an average of operators, or an…
We show how to compute globally optimal solutions to inverse kinematics (IK) by formulating the problem as an indefinite quadratically constrained quadratic program. Our approach makes it feasible to solve IK instances of generic redundant…
Nature provides us with a restricted set of microscopic interactions. The question is whether we can synthesize out of these fundamental interactions an arbitrary unitary operator. In this paper we present a constructive algorithm for…
In this note, we consider a framework for the analysis of iterative algorithms which can described in terms of a structured set-valued operator. More precisely, at each point in the ambient space, we assume that the value of operator can be…
This paper investigates first-order variable metric backward forward dynamical systems associated with monotone inclusion and convex minimization problems in real Hilbert space. The operators are chosen so that the backward-forward…