Related papers: Discretizing stochastic dynamical systems using Ly…
The challenging problem of conducting fully Bayesian inference for the reaction rate constants governing stochastic kinetic models (SKMs) is considered. Given the challenges underlying this problem, the Markov jump process representation is…
This article proposes an approach to construct a Lyapunov function for a linear coupled impulsive system consisting of two time-invariant subsystems. In contrast to various variants of small-gain stability conditions for coupled systems,…
This paper studies the dynamic programming principle using the measurable selection method for stochastic control of continuous processes. The novelty of this work is to incorporate intermediate expectation constraints on the canonical…
The paper endeavours to solve the problem of the necessary and sufficient conditions for testing asymptotic stability of the equilibrium state without using a positive definite or semi-definite Lyapunov function for time-invariant nonlinear…
Linear dissipative differential equation is a fundamental model for a large number of physical systems, such as quantum dynamics with non-Hermitian Hamiltonian, open quantum system dynamics, diffusion process and damped system. In this…
This paper provides a self-contained ordinary differential equation solver approach for separable convex optimization problems. A novel primal-dual dynamical system with built-in time rescaling factors is introduced, and the exponential…
Proper states' representations are the key to the successful dynamics modeling of chaotic systems. Inspired by recent advances of deep representations in various areas such as natural language processing and computer vision, we propose the…
Stochastic optimal control and games have a wide range of applications, from finance and economics to social sciences, robotics, and energy management. Many real-world applications involve complex models that have driven the development of…
Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…
We present a new methodology for studying non-Hamiltonian nonlinear systems based on an information theoretic extension of a renormalization group technique using a modified maximum entropy principle. We obtain a rigorous dimensionally…
An optimal control for a dynamical system optimizes a certain objective function. Here we consider the construction of an optimal control for a stochastic dynamical system with a random structure, Poisson perturbations and random jumps,…
This paper addresses the challenge of privacy preservation for statistical inputs in dynamical systems. Motivated by an autonomous building application, we formulate a privacy preservation problem for statistical inputs in linear…
Transitions between steady dynamical regimes in diverse applications are often modelled using discontinuities, but doing so introduces problems of uniqueness. No matter how quickly a transition occurs, its inner workings can affect the…
A Lyapunov design method is used to analyze the nonlinear stability of a generic reservoir computer for both the cases of continuous-time and discrete-time dynamics. Using this method, for a given nonlinear reservoir computer, a radial…
Algorithms increasingly operate within complex physical, social, and engineering systems where they are exposed to disturbances, noise, and interconnections with other dynamical systems. This article extends known convergence guarantees of…
We study the problem of modeling a non-linear dynamical system when given a time series by deriving equations directly from the data. Despite the fact that time series data are given as input, models for dynamics and estimation algorithms…
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…
The paper is devoted to the study of a new class of optimal control problems governed by discontinuous constrained differential inclusions of the sweeping type with involving the duration of the dynamic process into optimization. We develop…
A new method for stochastic control based on neural networks and using randomisation of discrete random variables is proposed and applied to optimal stopping time problems. The method models directly the policy and does not need the…
We develop further ideas on how to construct low-dimensional models of stochastic dynamical systems. The aim is to derive a consistent and accurate model from the originally high-dimensional system. This is done with the support of centre…