Hydrodynamics of stationary non-equilibrium states for some stochastic lattice gas models
We consider discrete lattice gas models in a finite interval with stochastic jump dynamics in the interior, which conserve the particle number, and with stochastic dynamics at the boundaries chosen to model infinite particle reservoirs at fixed chemical potentials. The unique stationary measures of these processes support a steady particle current from the reservoir of higher chemical potential into the lower and are non-reversible. We study the structure of the stationary measure in the hydrodynamic limit, as the microscopic lattice size goes to infinity. In particular, we prove as a law of large numbers that the empirical density field converges to a deterministic limit which is the solution of the stationary transport equation and the empirical current converges to the deterministic limit given by Fick's law.
This paper deals with the stabilization problem of the free-floating space manipulator system. Using the underactuated property and the conservation of angular momentum, a stabilization controller based on passivity concept is designed for this system. Associated proof shows that global stability of the angles of the manipulator joints is guaranteed. Moreover, for any kind of underactuated mechanism system, if the conservations of angular momentum property are satisfied, this kind of control strategy can be implemented to stabilize the actuated degree of freedom, which shows practical merit of the approach. Finally, numerical simulation of a simplified free-floating space robot system is conducted to prove the feasibility and effectiveness of the proposed control strategy.