Statistical learning theory and randomized algorithms for control

The topic of the present article is the use of randomized algorithms to solve some problems in control system designs that are perceived to be "difficult". A brief introduction is given to the notions of computational complexity that are pertinent to the present discussion, and then some problems in control system analysis and synthesis that are difficult in a complexity-theoretic sense are described. Some of the elements of statistical learning theory, which forms the basis of the randomized approach, are briefly described. Finally, these two sets of ideas are brought together to show that it is possible to construct efficient randomized algorithms for each of the difficult problems discussed by using the ideas of statistical learning theory. A real-life design example of synthesizing a first-order controller for the longitudinal stabilization of an unstable fighter aircraft is then presented to show that the randomized approach can be quite successful in tackling a practical problem.