Unified Control Framework: A Novel Perspective on Constrained Optimization, Optimization-based Control, and Parameter Estimation

A common theme in all the above areas is designing a dynamical system to accomplish desired objectives, possibly in some predefined optimal way. Since control theory advances the idea of suitably modifying the behavior of a dynamical system, this paper explores the role of control theory in designing efficient algorithms (or dynamical systems) related to problems surrounding the optimization framework, including constrained optimization, optimization-based control, and parameter estimation. This amalgamation of control theory with the above-mentioned areas has been made possible by the recently introduced paradigm of Passivity and Immersion (P\&I) based control. The generality and working of P\&I, as compared to the existing approaches in control theory, are best introduced through the example presented below.