Computation of the real structured singular values μ has been known to be important for stability analysis of linear systems with structured uncertainty. The authors have proposed a method to obtain an upper bound and a lower bound of the real μ by Stability Feeler which is a tool for robust stability analysis proposed by the first author. In this paper we propose a region splitting and expanding method to reduce the conservativeness of the derived upper bound and lower bound. A numerical example show that the obtained results are nearly equal to the exact value of the real μ, which are less conservative than that derived by the other methods.
Computational fluid dynamics (CFD) simulators have recently been used for optimization in die casting and various other fields. However, solving an optimization problem with a CFD simulator (CFD optimization problem) has the issue of uncertainty in the evaluated values from the CFD simulations. Such problems are, of course, difficult to optimize compared to general problems. In this paper, we propose an optimization algorithm that can search for good solutions to CFD optimization problems. We have appliedthe algorithm to the optimization of the sprue shape for die casting at an actual plant.
This paper considers the state and parameter estimation problems for nonlinear dynamical systems by using the Unscented Kalman filter (UKF). Since unlike the extended Kalman filter (EKF), the UKF does not require Jacobians of nonlinear transformations, we show that the UKF can be used together with the higher order Runge-Kutta approximation. We then derive a Runge-Kutta based UKF algorithm for nonlinear dynamical systems. Numerical studies show that the Runge-Kutta based UKF provides better numerical results compared with EKF and UKF algorithms coupled with the Euler approximation.