In this paper, we propose a new heuristic algorithm for the Input-Output Scheduling Problem (IOSP) at large scale automated warehouses. The proposed method separates IOSP into two subproblems, the one is to arrange all given tasks into a good partition, and the other is to generate a good tour for each group. It searches the best grouping of tasks by variable depth neighborhood local search, generating the optimum tour for each test group by enumeration. The small group size in IOSP makes it possible to enumerate tours. The results of numerical experiments on the same instances that some existing method solved show that the proposed method well competes with existing one under the criterion that considers both schedule length and solution time.
A stochastic ellipsoid method with multiple cuts is proposed for a class of robust feasibility problems which is to find a solution satisfying a set of parameter-dependent convex constraints for all possible parameter values. In particular, a new update rule is presented for constructing a smaller ellipsoid which contains the intersection of a previous ellipsoid and strips determined by given multiple gradients. A quantitative analysis of the volume of the updated ellipsoid is also provided, which leads to a further modification of the algorithm achieving fast convergence.
This paper presents a robust controller design method for linear time-invariant SISO systems based on an optimization approach. The task is to enlarge real stability radius to counter plant parameter perturbations by using extra degree of freedom of the controller parameters in the pole placement scheme. The formula for the real stability radius is known as an infimum of a certain function and that makes its gradients discontinuous. It is shown that by some manipulations, the considered problem can be converted to a nonlinear optimization problem, to which a gradient-based optimization method becomes applicable. The case of complex stability radius is also considered, which is less sharp as a robust stability index than the real counterpart, but has a much simpler form. Numerical examples for both cases are presented to show that they actually work, and some comparisons are discussed, leading to a suggestion on the effective uses of these two stability radius computation methods.
In this paper, we consider a blocking zero placement problem for closed-loop systems by state feedback. As a solution to the problem, we derive a dynamic state feedback controller which can be designed by solving a stabilization problem by constant state feedback. Moreover, we apply the proposed blocking zero placement method to a periodic disturbance rejection problem. Since a transfer function with blocking zeros can eliminate input signals corresponding to these blocking zeros, the periodic disturbance can be rejected if closed-loop systems have corresponding blocking zeros with the period on the imaginary axis.