Abstract: At the core of modern autonomous engineering lies the challenge of solving time-varying nonlinear programs in real time, where traditional tracking methods fail to guarantee that the system remains feasible for all time. To bridge this gap, this work introduces a safety-critical dynamical systems framework that uses control barrier functions (CBFs) to enforce forward invariance of the constraint set. For equality-constrained time-varying problems, we develop a continuous-time architecture that embeds a control Lyapunov tracking objective and a CBF safety condition into a unified quadratic program (QP), proving local uniform ultimate boundedness and exponential stability. To tackle inequality-constrained time-varying problem—where abrupt active-set changes typically disrupt standard CBF behavior—we regularize the problem using the Fischer-Burmeister complementarity function to maintain strict safety guarantees. We also design a safe heavy-ball dynamical system utilizing exponential CBFs, offering enhanced robust filtering against noisy gradients and adversarial uncertainties across complex, non-convex domains, for solving static nonlinear programs. The proposed techniques are validated on various path planning problems in robotics.

Event Details
Title: A Safety-Critical Dynamical Systems Framework for Solving Time-Varying Nonlinear Programs (PhD Viva Voce)
Date: July 13, 2026 at 12:30 PM
Venue: Google Meet (https://meet.google.com/nod-mjhm-sfy)
Speaker: Mr. Karthik Shenoy (EE21D405)
Guide: Dr. Arunkumar D Mahindrakar
Type: PHD seminar

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