Solution of multicriteria control problems in certain types of linear distributed-parameter systems by a multicriteria simplex method

Considerable attention has been given in the past decade to the optimal control problems by applying linear programming techniques and linear programming has proved to be a very efficient tool for linear lumped-parameter systems Ia For linear distributed-parameter systems, there are only two known papers where particular examples of optimal control of distributed-parameter systems were solved by linear programming techniques [3, 61. However, these papers only consider a single objective as a consequence of the application of traditional linear programming techniques. On the other hand, in 1973, M. Zeleny introduced a Multicriteria Simplex Method, which is a simple generalization of the conventional single-objective simplex method [9, 10, 111. He developed theory and algorithms which can be applied to linear programming problems involving multiple, noncommensurable objective functions. Nowadays, a multicriteria simplex method seems to be most powerful and attractive method for linear multiobjective programming problems. In previous papers, we have considered multicriteria linear continuous optimal control problems of lumped-parameter systems through the application of multicriteria simplex method and indicated the efficiency of the proposed method [4, 51. In this paper, we discuss the problems of optimal control of one dimensional linear stationary distributed parameter systems with several cost functionals by means of a multicriteria simplex method.