Solution of one class of optimal control problems for multivariable distributed plants. I

A special problem of linear programming is considered in the functional space; the problem arises in optimal control of multivariable distributed systems. A solution procedure is developed analogous to one version of the simplex method in a finite dimensional space. The convergence of the algorithm to a solution of the problem is proved. Estimates of the proximity in the functional of the approximate solution obtained at each iteration to the optimal one are given.