In the present dissertation, displacement control systems for large span structures using cablenets are herein proposed. The system is based on cable supported beam nets with additional prestressing control of the support cables such as to optimize the structural behavior of the system: the passive control design problem leads to an optimal control problem for structures governed by variational inequalities. The optimal shape of a prestressing support cable in many cases leads to a Form-Finding problem of the structure. The analysis is based on the two-nodes-curved-cable-element where large displacements and large rotations occur. Therefore, a multi-span cable is a non-linear and flexible structure since every loading case defines a new equilibrium configuration for the system. Using a prestressing strategy, the configuration of the cable structure due to the permanent loading is final. The novel passive control system is based on prestressing cables mechanism where permanent loads are relieved by a first level prestressing cables set named (a) and moving loads together with excessive displacements are taken by an additional cablenet (b) depending on the form and the use of the structure. Several variations of these passive control systems using prestressing cables are herein proposed: 1) A combination of a horizontal straight beams and external prestressing supported cable connecting with vertical rods where sliding contacts occur between rods and the cable. 2) A set of cables named (β) is used. This set has the same form with the cables of set (α), they also fastened at the same points while freely sliding bearings are used as connection joints with the vertical rods of the structure. The peculiarity of the cables of the latter set in that they are not homogenous. They are composed of n number of initially prestressed rods surrounded with the cracked unilateral stiffness rod elements with different initial prestresses at each face of the polygonal line. The prestressed cable elements are connected with nonprestressed of small length cable elements of the same set (β), where are not activated during permanent loading because of the set (α) supported cables, but is only activated under the moving loading action. 3) A prestress strategy when set (α) cables supported a horizontal straight beam structure, such as the reactions of the cable at the sliding contacts with the vertical rods due to prestress are bigger than the action forces of the permanent loading at the upper side of the same vertical rods. The result of this strategy is a new equilibrium configuration of the beam structure in opposite direction of the moving loading action. 4) The unilateral Form-Finding of arch beam structures using cable configuration due to the nodal permanent loading, but with negative shape form. 5) Introduction of diagonal cable element with no contact at the middle of their length, to connect nodes of the upper beam structure and the corresponding (in diagonal direction) node of the set (α) cable. The diagonal cables are not prestressed, but in the case of moving loading action the one them is stretched and the other has no action due to no press occur in cable elements. 6) The use of small displacements at the moving end of beam or arch structure supported with set (α) cable, due to moving loading action. 7) In floating bodies model, the compulsion overtopping of natural waterline of the body by the use of stable anchorage to the bottom by four prestressed cable (or chain) elements. 8) A combination between several of the above systems to the same model. The proposed models for large space structures with several passive systems on it, such as the above eight cases, aim with the purpose to minimize the effects of moving loading action. In any case the proposed model has been fully numerically examined, by the use (2-D) or (3-D) linear and non-linear finite element models. Many examples of them are bridge structures with several free length spans and with different passive control systems of displacements against moving loads according DIN1072 & Eurocode-1. In the case of (3-D) models some of the examples have been checked successfully with wind loading models. Additionally checks with excellent results gave the basic examples for bridge structures against seismic action with dynamic spectra analysis according Greek National Rules. The study presents new techniques for the design and construction of large span structures (such as bridges, long cover structures and as an extension of the passive prestress control method using cables and applications on floating bodies and structures). The scope of this work is to develop new models of large space structures where unilateral conditions occur minimizing moments action and respectively the necessary sections of the structural members. These type of structure minimize the seismic action on the bridge. The proposed models of large span structures lead to a safer and more economical method of construction with small disturbance to the natural environment.