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

TL;DR

This paper explores how control theory, especially Passivity and Immersion (P&I), can unify and improve the design of algorithms for constrained optimization, control, and parameter estimation by viewing them as dynamical systems.

Contribution

It introduces a unified control framework leveraging P&I control to connect and enhance constrained optimization, control, and parameter estimation methods.

Findings

Demonstrates the effectiveness of P&I-based control in optimization tasks

Provides a unified dynamical systems perspective for various control problems

Shows improved convergence properties through the proposed framework

Abstract

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.