<p>  </p> <p>The development of an increasingly interconnected infrastructure and its rapid evolution demands engineering testing solutions capable of investigating realistically and with high accuracy the interactions among the different components of the problem to study. The examination of any of these components without losing the interaction of the other surroundings components is not only realistic, but also desirable. The more interconnected the whole system is, the greater the dependencies. Real-time Hybrid Simulation (RTHS) is a disruptive technology that has the potential to address this type of complex interactions or internal couplings by partitioning the system into numerical (better understood) substructures and experimental (unknown) substructures, which are built physically in the laboratory. These two types of substructures are connected through a transfer system (e.g., hydraulic actuators) to enforce boundary conditions in their common interfaces creating a synchronized cyber-physical system. However, despite the RTHS community has been improving these hybrid techniques, there are still important barriers in their core methodologies. Current control approaches developed for RTHS were validated mainly for linear applications with limited capabilities to deal with high uncertainties, hard nonlinearities, or extensive damage of structural elements due to plasticity. Furthermore, capturing the realistic dynamics of a structural system requires the description of the motion using more than one degree of freedom, which increases the number of hydraulic actuators needed to enforce additional degrees of freedom at boundary condition interface. As these requirements escalate for larger or more complex problems, the computational cost can turn into a prohibitive constraint. </p> <p>In this dissertation, the main research goal is to develop and validate a nonlinear controller with capabilities to control highly uncertain nonlinear physical substructures with complex boundary conditions and its parallel computational implementation for accurate and realistic RTHS. The validation of the proposed control system is achieved through a set of real-time tracking control and RTHS experiments that explore robustness, accuracy performance, and their trade-off </p>