The thesis presents comparative study of modern control methods for regulating under-actuates systems. The classical pendulum on a cart system, a 2-DOF under-actuated system was utilized as a benchmark system for analyzing controllers' performances. The work includes analysis, controller design and swing-up control simulation for the following three methods: Nonlinear state-space control The mathematical model based on the Lie theoretic approach with nonlinear output injection was developed. The controller accomplishes both swing-up and stabilization of the pendulum. The feasibility of the implementation is limited due to physical constraints (length of the cart rail). Fuzzy logic control A Sugeno type fuzzy inference engine implementing the control strategy was built over the system fuzzy model. The simulations showed successful controller behavior but the generated system control input exhibited some non-smoothness that could cause increase on the actuator demand. Method of embedded artificial constraints (EAC). The analysis reveals dependence between the pendulum motion and the cart acceleration. Using this artificial constraint a state link was developed and the nonlinear control problem was reduced to a linear controller design. A stabilizing linear state-space controller has been developed and methods for arbitrary pole placement and optimal linear quadratic regulator design were compared. A reduced order current estimator for velocity estimation has been studied and implemented. A software client/server controller application running on a QNX Neutrino 6.1 platform was developed. The real-time experiments conducted with the EAC/linear state-space controller confirmed good swing-up and stabilization system performance.