Structure of Optimal Control in Optimal Shaping of the Steel Arch

Abstract The paper presents the problem of optimal shaping of the H-bar cross-section of a steel arch that ensures minimal mass. Nineteen combinations of nine basic load states are considered simultaneously in the problem formulation. The optimal shaping task is formulated as a control theory problem within the formal structure of the maximum Pontriagin’s principle. Since the ranges of constraint activity defining the control structure are a priori unknown and must be determined numerically, assuming the proper control structure plays a key role in the task solution. The main achievement of the present work is the determination of a solution of the multi-decision and multi-constraint optimization problem of the arch constituting a primary structural system of the existing building assuring the reduction of the structure mass up to 42%. In addition, the impact of the assumed state constraint value on the solution structure is examined.