Nested Optimized Adaptive Linear Control

Optimal control theory was formulated with the implicit assumption that the system under investigation possesses inherent stabilizability. In this framework, the derived optimal control strategy not only stabilizes the system but also concurrently ensures the optimization of the designated cost function without the need for explicit separation of these two aspects. This approach is theoretically elegant and has demonstrated considerable success in various applications. However, here are some hidden dangers due to the uncertainties introduced. Particularly in the context of increasingly complex large-scale systems, this approach poses challenges. In this paper, the aspects of stabilization and optimization will be explicitly addressed in a separate manner in an endeavor to strike a balance between ensuring stability and achieving optimal control. Specifically, the nested optimized adaptive linear control framework builds upon the classical linear optimized control. This framework leverages the advantages of optimal control while also effectively addressing stability concerns. Central to these advancements is the introduction of a nested structural framework that facilitates explicit handling of the stabilization aspect. To underscore the merits of our approach, we provide illustrative examples that highlight its advantages in comparison to recent approaches of a similar nature.