In this paper, the authors outline the general principles behind an approach to Bayesian system identification and highlight the benefits of adopting a Bayesian framework when attempting to identify models of nonlinear dynamical systems in the presence of uncertainty. It is then described how, through a summary of some key algorithms, many of the potential difficulties associated with a Bayesia...

The stability of nonlinear stochastic dynamical system is a theoretically prominent problem, as it is of great theoretical and practical significance to many projects in reality. Firstly, the author established the basic formula. Secondly, he researches the stability theory of non-linear stochastic dynamical system, and discusses the stability criterion of null solution stability and nonlinear ...

Starting from the second order around thermal equilibrium, the response of a statistical mechanical system to an external stimulus is not only governed by dissipation and depends explicitly on dynamical details of the system. The so called frenetic contribution in the second order around equilibrium is illustrated in different physical examples, such as for non-thermodynamic aspects in the coup...

A stochastic optimal control strategy for partially observable nonlinear systems is proposed. The optimal control force consists of two parts. The first part is determined by the conditions under which the stochastic optimal control problem of a partially observable nonlinear system is converted into that of a completely observable linear system. The second part is determined by solving the dyn...

In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically co...

Reduced order models are used extensively in many areas of science and engineering for simulation, design, and control. Reduction techniques for nonlinear dynamical systems produce models that depend strongly on the nominal set of parameters for which the reduction is carried out. In this paper we address the following two questions: “What is the effect of perturbations in the problem parameter...

we establish a relationship between general constrained pseudoconvex optimization problems and globally projected dynamical systems. a corresponding novel neural network model, which is globally convergent and stable in the sense of lyapunov, is proposed. both theoretical and numerical approaches are considered. numerical simulations for three constrained nonlinear optimization problems a...

This paper discusses the application of support vector machine in the area of identification of nonlinear dynamical systems. The aim of this paper is to identify suitable model structure for nonlinear dynamic system. In this paper, Adaptive Neuro Fuzzy Inference Systems (ANFIS) and Support Vector Regression (SVR) models are applied for identification of highly nonlinear dynamic process. The res...

In this paper, we develop a thermodynamic framework for addressing consensus problems for nonlinear multiagent dynamical systems with fixed and switching topologies. Specifically, we present distributed nonlinear static and dynamic controller architectures for multiagent coordination. The proposed controller architectures are predicated on system thermodynamic notions resulting in controller ar...

Can Lyapunov exponents of infinite-dimensional dynamical systems be observed by projecting the dynamics into ℝ N using a 'typical' nonlinear projection map? We answer this question affirmatively by developing embedding theorems for compact invariant sets associated with C1 maps on Hilbert spaces. Examples of such discrete-time dynamical systems include time-T maps and Poincaré return maps gener...