Abstract: Based on the theory of analogy, the parametricvariational principle derived from plastic mechanics and contact mechanicsis developed and applied to the theory of optimal control. New coupledequations of Hamilton canonical equation and linear complementarity equationare established for the problem of LQ optimal control with constrainedcontrol input. By dividing the continuous time into a series of equidistantintervals, a new numerical algorithm based on the parametric quadraticprogramming method for solving the coupled-equations is proposed in thediscrete time domain. Numerical simulations show that the algorithm given inthis paper is effective for the problem of LQ optimal control withconstrained control input and the convergence speed and accuracy of thealgorithm is satisfactory.