With quadrotor use seeing extensive growth in recent years, the autonomous control of these Unmanned Aerial Vehicles (UAVs) is an increasing relevant and intersting field. In this paper a linear state-space approach at designing a stable hover contro
ller in the presence of disturbances is presented along with simulation of control system performance. Additionally the design of a tracking system, for linear inertial position and yaw, is presented with simulation results. The gain matrix developed for this control system is independent of the specific quadrotor parameters, meaning that this same gain matrix can be used on a wide variety of quadrotors without modification. The hover and tracking controllers designed in this paper proved to perform well in simulation under perturbation disturbances and normally distributed disturbances on the UAVs linear speeds and angular speeds.
We investigate the probabilities of large deviations for the position of the front in a stochastic model of the reaction $X+Y to 2X$ on the integer lattice in which $Y$ particles do not move while $X$ particles move as independent simple continuous t
ime random walks of total jump rate $2$. For a wide class of initial conditions, we prove that a large deviations principle holds and we show that the zero set of the rate function is the interval $[0,v]$, where $v$ is the velocity of the front given by the law of large numbers. We also give more precise estimates for the rate of decay of the slowdown probabilities. Our results indicate a gapless property of the generator of the process as seen from the front, as it happens in the context of nonlinear diffusion equations describing the propagation of a pulled front into an unstable state.
