Effects of a zero-cost interval of a running cost on exercise boundaries in stochastic impulse control problems are considered. To study it, we basically use a numerical algorithm given in . However, convergences of its numerical solutions to the true solution in their algorithm under our settings here are not theoretically guaranteed, therefore we first extend their theorems related to convergences and mathematically prove it. Then using the valid algorithm, relations between the zero-cost intervals and the value function or optimal strategies are numerically studied.
In gust alleviation control synthesis, it is important how to generate the worst disturbance that has the worst effects on aviation. This paper applies the worst disturbance method based on H∞control to a linearized airplane motion model and provides new insights into the relationship between the initial condition and the worst disturbance. In addition, this paper utilizes Generic Transport Model (GTM) which is a nonlinear airplane motion model developed by NASA and discusses whether the linear model results are applicable for GTM. The first result is that the proposed worst disturbance algorithm allows us to analyze the relation between the initial conditions and short-period/Phugoid modes of longitudinal motion and especially tends to decrease the damping ration of the short period mode. The second result is to show that H∞control is applicable for GTM within the small perturbation around the trim condition and there are the same oscillation behaviors between the linear and nonlinear models.
This paper considers the problem of controlling a vibrating body's amplitude by varying the load of the vibration generator. We propose a feedback control system for a variable load whose command is the output signal of a proportional integral (PI) controller, which is driven by the deviation between the reference value and the estimated oscillation amplitude. The amplitude is estimated by using the absolute value function and a low-pass filter (LPF). An experiment is carried out with a mass-spring-damper system, which indicates the validity of the proposed method by showing that the closed-loop system becomes stable when PI gains (KP , KI) are appropriately chosen. Furthermore, this paper provides a theoretical guarantee of the closed-loop stability of the proposed system by assuming second- and forth-order plant models. The stability conditions are derived using linear approximation of the nonlinear system around the equilibrium point. The validity of the stability conditions are shown by numerical simulations. The stability condition is consistent with the experimental results: the boundary line on the KP −KI plane has a positive slope and a positive segment KI > 0 at KP =0.