| Robust control has been an important issue in the last two decades. Many efforts were put to develop methods which minimize some gains of the closed-loop system so that the closed-loop system attenuates the effect of some kind of noise signal. {dollar}Hsb{lcub}infty{rcub}, Hsb2,{dollar} and {dollar}lsp1{dollar} are therefore very popular research topics for many years. On the other hand, some traditional performance indices, like rise time, over-shoot, and settling time were not fully considered in the above mentioned design methods. Since performance and robustness are equally important, we address in this dissertation the robust pole assignment problem. One will see that this design considers both performance and robustness.; We first examine an existing algorithm, KNV algorithm, and relate it to an optimization problem. Next we propose several variations of KNV algorithm such that some of them are suitable for parallel machine, and some of them are suitable for sequential machine, moreover, all of them are able to assign complex eigenvalues (KNV algorithm cannot assign complex eigenvalues). We also show that the extended algorithms are globally convergent and more efficient than KNV algorithms. To verify these claims, we run thousands of examples and compare the results with the results obtained by other methods. This test shows the superiority of the proposed algorithms.; Trying to find better algorithms, we investigate some optimization techniques on Riemannian manifolds. The analysis on general problem is profitable. We propose improvement on some algorithms due to Smith, namely, we suggest using Armijo search instead of exact search scheme. We obtain the convergence and rate of convergence results for the generalized algorithms. Thereby, we obtain a unified theory for both unconstrained and constrained optimization. The new methods are particularly efficient for some special manifolds, including the manifold prescribed by pole assignment problem. We apply these techniques to pole assignment problem, and we expect that these techniques will be used for more control design problems in the future. |
