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The smoothing distribution is the conditional distribution of the diffusion process in the space of trajectories given noisy observations made continuously in time. It is generally difficult to sample from this distribution. We use the…
Stochastic processes are commonly used models to describe dynamics of a wide variety of nonequilibrium phenomena ranging from electrical transport to biological motion. The transition matrix describing a stochastic process can be regarded…
The spatial distribution of interacting chemical fields is investigated in the non-diffusive limit. The evolution of fluid parcels is described by independent dynamical systems driven by chaotic advection. The distribution can be filamental…
In an effort to understand the glass transition, the kinetics of a spin model with frustration but no quenched randomness has been analyzed. The phenomenology of the spin model is remarkably similiar to that of structural glasses. Analysis…
In this paper, the scattering/transmission inside a step-modulated subwavelength metal slit is investigated in detail. We firstly investigate the scattering in a junction structure by two types of structural changes. The variation of…
This paper investigates the stability properties and performance of super-twisting sliding-mode control loops subject to periodic perturbations. Although there exist conditions on the control gains that guarantee finite-time stability of…
It is shown that a spin system with long range interactions can be converted into a chaotic dynamical system that is differentiable and low-dimensional. The thermodynamic limit of the spin system is then equivalent to studying the long term…
The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…
This paper proposes a sliding mode controller with smooth control effort for a class of nonlinear plants. The proposed controller is created by allowing some constant parameters of the earlier smooth sliding control (SSC) to vary as a…
This study shows that typical pendulum dynamics is far from the simple equation of motion presented in textbooks. A reasonably complete damping model must use nonlinear terms in addition to the common linear viscous expression. In some…
Spin-dynamics techniques can now be used to study the deterministic time-dependent behavior of magnetic systems containing over 10^5 spins with quite good accuracy. This approach will be introduced, including the theoretical foundations of…
The main objective of this paper is to propose an alternative procedure to carry out one of the key steps of immersion and invariance stabilising controller design. Namely, the one that ensures attractivity of the manifold whose internal…
In this article we discuss several aspects of the stochastic dynamics of spin models. The paper has two independent parts. Firstly, we explore a few properties of the multi-point correlations and responses of generic systems evolving in…
Hamilton's equations with noise and friction possess a hidden supersymmetry, valid for time-independent as well as periodically time-dependent systems. It is used to derive topological properties of critical points and periodic trajectories…
Simulink is widely used in industrial design processes to model increasingly complex embedded control systems. Thus, their formal analysis is highly desirable. However, this comes with two major challenges: First, Simulink models often…
The decoupling of spin and density dynamics is a remarkable feature of quantum one-dimensional many-body systems. In a few-body regime, however, little is known about this phenomenon. To address this problem, we study the time evolution of…
This work deals with planar dynamical systems with and without noise. In the first part, we seek to gain a refined understanding of such systems by studying their differential-geometric transformation properties under an arbitrary smooth…
We study the smoothness properties of a global and nonautonomous topological conjugacy between a linear system and a quasilinear perturbation. The linear system exhibits a nonuniform exponential dichotomy with a nontrivial projector and…
We consider kinetic systems and prove their stability working in weighted spaces in which the systems are symmetric. We prove stability for various explicit and implicit semi-discrete and fully discrete schemes. The applications include…
This paper presents an approach to systematically design sliding mode control and manifold to stabilize nonlinear uncertain systems. The objective is also accomplished to enlarge the inner bound of region of attraction for closed-loop…