A Study On The Applications Of Learning Theory To Robust Control

In this dissertation some important results from learning theory and probability theory are applied to some robust control problems. Polynomial-time randomized algorithms based on learning theory are constructed to solve approximately some NP-hard or intractable robust control problems in probabilistic sense. It is shown that the randomized algorithms here are efficient and have low computational complexity through a lot of examples.The main contents and results are as follows: First, randomized algorithms based on UCEP property are designed to deal with robust stabilization controller synthesis problems in which parametric uncertainties are extended to more general forms. Moreover, the approach is generalized in several aspects such as stability regions, MIMO systems, discrete systems and composite systems;Second, randomized algorithms based on UCEM property are developed to solve optimal robust performance controller design problems in probabilistic sense;Third, empirical risk minimization (ERM) and structural risk minimization (SRM) principles are first applied to solve robust controller synthesis problems in probabilistic sense;Fourth, some robustness analysis problems for systems with mixed perturbations and systems with simultaneous perturbations in plants and controllers are settled approximately using randomized approaches;Fifth, a probabilistic approach is presented to design controller in robust stabilization problems, and similar methods are applied to the simultaneous stabilization problems of several plants;Sixth, probabilistic robustness margin analysis problems are studied, it is shown that remarkable amplifications of classical margins can often be obtained while keeping the risk level very small;Finally, randomized algorithms based on UCEP property are designed to deal with a class of NP-hard matrix problems in probabilistic sense.