| Control Theory and its applications span a broad spectrum of disciplines, Electrical Engineering at one end to Life Sciences at the other end. In this doctoral dissertation, research problems in Overhead Power Transmission Lines and HIV/AIDS (Human Immunodeficiency Virus /Acquired Immune Deficiency Syndrome) infection are chosen, from these vastly varied domains, for synthesizing and developing Advanced Control Strategies. This research aims to provide optimum solutions through the application of Singular Perturbation and Time Scale (SPaTS) methods, specifically, Time Scale Analysis and Synthesis. Measles, another infectious disease in Life Sciences, is briefly investigated for the application of SPaTS methods. These methods achieve model order reduction by a time scale separation procedure that guarantees excellent eigenvalue approximations of the original system. Moreover, decoupling of dynamics facilitates simple, lower order, slow and fast controllers designs, thereby enhancing the reliability of controllers and significant reduction in real-time computations. The model approximation, using this methodology does not impair the system dynamics in any way. The analysis and synthesis is carried out for deterministic optimal control problems with the objective of, mitigating perturbations in the transmission line, and developing a feasible long term HIV treatment plan with minimum side effects. The proposed control strategies are validated through extensive simulations. The results of the simulations and research provide valuable insights into the development of closed-loop, real-time, optimal controllers that are computationally more efficient and feasible for Smart Grid /Dynamic Line Rating technology and long term treatments of HIV infection. |