Robust Constrained Optimization via Sliding Mode Control

TL;DR

This paper introduces a robust sliding mode control framework for equality constrained optimization, ensuring exact constraint satisfaction, finite-time convergence, and robustness to disturbances.

Contribution

It reformulates KKT conditions as a control affine system, integrating sliding mode control to improve robustness and convergence in constrained optimization.

Findings

Guarantees exact constraint enforcement with finite time convergence.

Demonstrates robustness to disturbances, uncertainties, and noise.

Shows superior accuracy and robustness in numerical benchmarks.

Abstract

This paper develops a sliding mode control based frame work for equality constrained optimization by reformulation the first order Karush Kuhn Tucker conditions as control affine dynamical system. The optimization variables are treated as states and the Lagrange multipliers as control input, with equality constraints defined as sliding manifold. The resulting design guarantees exact constraint enforcement with finite time convergence, independent of objective convexity, and exhibits robustness to matched disturbance, structural uncertainty and bounded measurement noise. To accelerate the convergence, a nonsingular terminal sliding mode based normed gradient flow is introduced, ensuring both finite time convergence to optimal solution and constraint satisfaction. Rigorous Lyapunov analysis establishes closed loop stability and convergence. Numerical studies across diverse benchmark problems demonstrate superior accuracy and robustness over classical continuous time optimization method, highlighting effectiveness under disturbance.