| PhD Seminar

Name of the Speaker: Mr. Karthik Shenoy (EE21D405)
Guide: Dr. Arunkumar D Mahindrakar
Co-Guide: Dr. Vijaysekhar Chellaboina
Venue: ESB-234 (Malaviya Hall)
Date/Time: 5th January 2025 (Monday), 10:30 AM
Title: Dynamical systems approach to time-varying nonlinear programming: Safety and Stability

Abstract :

Nonlinear programming plays a central role across science, engineering, and economics, underpinning applications such as robotic motion planning and real-time power system optimization. These systems operate in dynamic environments with time-varying (TV) parameters, motivating the development of optimization frameworks capable of reliably tracking time-dependent minimizers. When decision variables represent physical states or control inputs, continuous enforcement of constraints becomes essential and is naturally interpreted in control theory as safety with respect to a prescribed constraint set. This perspective leads to the formulation of optimization algorithms as closed-loop dynamical systems that must jointly guarantee constraint invariance and stable tracking of the time-varying minimizer.

The key challenge in enforcing safety for inequality-constrained time-varying problems lies in the intrinsic non-differentiability of the minimizer trajectory, arising due to the complementary slackness. Hence, unlike the equality constrained case, we require tools from non-smooth analysis to ensure the safe tracking of the minimizer.

The seminar will begin with an overview of control barrier functions, followed by a recap of safe time-varying optimization under equality constraints. I will then address the challenges and discuss the key results associated with inequality constraints, and conclude with extensions to momentum-based optimization methods.