An application of randomized algorithm in robust controller design

Both H∞ optimization techniques and eigenstructure assignment have their unique significances in control engineering. The first one is an effective method to ensure the robust stability of the closed loop system whereas the second one is very useful in shaping the transient response of the closed loop system by placing the eigenvalues and eigenvectors in the desired locations. Hence, to design a controller which not only ensures the robust stability of the closed loop system but also shapes the closed loop transient response very well, these two methods are combined by minimizing a mixed time and frequency domain performance index. A directed search based method already exists in the literature to solve such an optimization problem. But such a directed search based method is computationally tedious as it requires gradient calculation of the objective function and does not guarantee to yield the global minimum of the objective function. The present work proposes a randomized algorithm based solution to the aforementioned optimization problem. This randomized algorithm based method is computationally easier than the directed search based method and gives improved results due to the increased chance of reaching the global minimum of the objective function.