It is important to determine the control horizon for transforming the input constrained infinite horizon linear quadratic regulation problem into the finite horizon model predictive control problem. There isn’t an efficient algorithm to get the small conservative control horizon quickly. A fast algorithm to estimate the control horizon is presented. The null controllable region and its vertex are computed and the initial state is projected into one facet of the null controllable region. The initial state is expressed as the convex combination of the vertexes. The minimal cost value can be obtained by solving a linear programming problem. The estimation of the control horizon can be computed quickly. From the numerical simulations, the new algorithm has the small conservation and computational complexity. http://www.sj-ce.org/paperInfo.aspx?ID=860
