.png){kind=icon}
.png){kind=icon}
Return
Benign Nonconvex Landscapes in Optimal and Robust Control, Part II: Extended Convex Lifting
.png){kind=icon}
PRE
AI
Y
C
Y
DOI：10.1109/tac.2026.3675545.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
Many optimal and robust control problems are nonconvex and potentially nonsmooth in their policy optimization forms. In Part II of this article, we introduce a new and unified extended convex lifting (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathtt {ECL}$</tex-math></inline-formula>) framework to reveal <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">hidden convexity</i> in classical optimal and robust control problems from a modern optimization perspective. Our <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathtt {ECL}$</tex-math></inline-formula> offers a bridge between nonconvex policy optimization and convex reformulations, enabling convex analysis for nonconvex problems. Despite nonconvexity and nonsmoothness, the existence of an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathtt {ECL}$</tex-math></inline-formula> not only reveals that minimizing the original function is equivalent to a convex problem but also certifies a class of first-order <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nondegenerate</i> stationary points to be globally optimal. This <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathtt {ECL}$</tex-math></inline-formula> framework can cover many benchmark control problems, including linear quadratic regulator, linear quadratic Gaussian, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_\infty$</tex-math></inline-formula> robust control. We also believe that the new <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathtt {ECL}$</tex-math></inline-formula> framework will be of independent interest for analyzing nonconvex problems beyond control.
Keywords:
Convex reformulation
global optimality
nonconvex optimization
optimal and robust control
Journal
IF:
7
Papers:
1.3W
Citations:
6.7W
Organization
Cited Papers