A suboptimal control algorithm for distributed parameter systems is developed in a framework which synthesizes weighted residual methods and mathematical programming. The heat exchanger example of Koppelet al. (1968) is employed for introducing the algorithm. First, the Galerkin procedure with polynomial modes is applied to obtain a lumped ODE model for the distributed parameter system. Then the state and control variables of the lumped control problem are approximated by cubic splines on a uniform mesh. Through collocation at the knots, the ODE model is reduced to a sot of linear algebraic equations and the suboptimal control is determined from the solution of a quadratic programming problem withsparsematrices.