Narrow Results

We introduce a continuous version of the contact model which is well known and widely studied in the lattice case. Under certain general assumptions on the infection spreading characteristics, we construct the contact process as a Markov process in the configuration space of the system.

We construct a new equilibrium dynamics of infinite particle systems in a Riemannian manifold X. This dynamics is an analog of the Kawasaki dynamics of lattice spin systems. The Kawasaki dynamics now is a process where interacting particles randomly hop over X. We establish conditions on the a priori explicitly given symmetrizing measure and the generator of this dynamics, under which a corresponding conservative Markov processes exists. We also outline two types of scaling limit of the equilibrium Kawasaki dynamics: one leading to an equilibrium Glauber dynamics in continuum (a birth-and-death process), and the other leading to a diffusion dynamics of interacting particles (in particular, the gradient stochastic dynamics).

A design method of an optimal preview controller for a class of linear continuous time-varying systems is presented in this paper. By differentiating both the output error signal and the two sides of the state equation, an augmented error system is constructed, which contains the error signal, the state vector and the derivative of the state vector. Then the performance index function is introduced and the control problem is solved by optimal control theory. Thus the optimal preview control input for the original time-varying system is found. The proposed controller includes the previewable future signal, so the response speed is accelerated. Meanwhile, the integrators in the controller make the output vector track the target signal better. The numerical simulations illustrate the validity of the proposed method.