We consider the general problem of analysis and design of control systems in the presence of uncertainties. We treat uncertainties that affect a control system as random variables. The performance of the system is measured by the expectation of some derived random variables, which are typically bounded. We develop adaptive sequential randomized algorithms for estimating and optimizing the expectation of such bounded random variables with guaranteed accuracy and confidence level. These algorithms can be applied to overcome the conservatism and computational complexity in the analysis and design of controllers to be used in uncertain environments. We develop methods for investigating the optimality and computational complexity of such algorithms.