Viewed as approximations to quantum mechanics, classical evolutions can violate the positive semidefiniteness of the density matrix. The nature of the violation suggests a classification of dynamical systems based on classical-quantum correspondence; we show that this can be used to identify when environmental interaction (decoherence) will be unsuccessful in inducing the quantum-classical tran...

This paper is concerned with the stabilisation of a general class of nonlinear systems via the associated angular approach. In this method, the system is converted into two subsystems the so called radial and spherical systems. The spherical system is a nonlinear equation on a sphere and the radial system is a scalar differential equation. A stabilising control can be designed based on the one-...

In order to bring contraction analysis into the very fruitful and topical fields of stochastic and Bayesian systems, we extend here the theory describes in [Lohmiller and Slotine, 1998] to random differential equations. We propose new definitions of contraction (almost sure contraction and contraction in mean square) which allow to master the evolution of a stochastic system in two manners. The...

In terms of functional dependence, the description of observable functions in nonlinear dynamical systems, which are analytic with respect to phase variables, is obtained. For processing of measurements, integral operators are used, which provide certain noise stability of operation of phase state reconstruction. The analogue of the duality theory known for linear problems of observation and co...

We investigate in this work the validity of linear stochastic models for nonlinear dynamical systems. We exploit as our basic tool a previously proposed Rayleigh-Ritz approximation for the effective action of nonlinear dynamical systems started from random initial conditions. The present paper discusses only the case where the PDF-Ansatz employed in the variational calculation is “Markovian”, i...

This paper presents a simple methodology for obtaining the entire set of continuous controllers that cause a nonlinear dynamical system to exactly track a given trajectory. The trajectory is provided as a set of algebraic and/or differential equations that may or may not be explicitly dependent on time. Closed-form results are also provided for the realtime optimal control of such systems when ...

41 kx 0 k < 0:4, it becomes unstable for larger initial conditions. The response of the of the system for the initial condition x 0 = (0:15; 00:25;0:35), shown in Figure 8, indicates that the trajectory becomes very large after 10 units of time. Simulation 2 reveals how the method proposed using a nonlinear controller may increase the region of attraction substantially. 5 Conclusion A general a...

Recently, Horváth, Song, and Terlaky [A novel unified approach to invariance condition of dynamical system, submitted to Applied Mathematics and Computation] proposed a novel unified approach to study, i.e., invariance conditions, sufficient and necessary conditions, under which some convex sets are invariant sets for linear dynamical systems. In this paper, by utilizing analogous methodology, ...

We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium (related to driving velocity fields which are generically bound to obey suitable local conservation laws) can be reconciled with the notion of dispersion due to a...