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With the use of the general variational principle of self-organization ofsystems with varying constraints, namely the principle of dynamicalharmonization of systems presented in the first work of the cycle, we advancean approach to the control over the evolution of systems of many particles. Thegeometric nature of this principle is analyzed. On the basis of the deBroglie--Bohm representation of the Schr\"odinger equation, we establish aconnection of the nonlocality and the coherence of the systems of manyparticles with mass entropic forces. The defining role of a coherentacceleration and a space-time curvature in the control over the synthesis ofnew structures in systems with varying constraints is demonstrated. The basiccriteria for electromagnetic fields to initiate the processes ofself-organizing synthesis and for the quantum properties of a nonlocality onmacroscopic scales, which are necessary for the self-organizing synthesis, areformulated.

Control over multiscale systems with constraints. 3. Geometrodynamics of the evolution of systems with varying constraints