Real-time control of a dynamical system is provided by determining control variables that get as close as possible to producing a desired response. Additional consideration of physical limitations leads to a convex Quadratic Program with inequality constraints that needs to be solved in real-time. A new active set algorithm is described to solve the convex Quadratic Program efficiently that meets real-time requirements. Based on the key observation that the physical limitations of the system translate to optimal active sets that remain relatively unchanged over time (even though the actual optimal controls may be varying), starting guesses for the active set obtained from the final iterate in the previous time period greatly reduces the number of iterations and hence allows the Quadratic Programs to be solved to convergence in real-time.