On the Solvability of the Regular Linear Quadratic Regulation: Stabilizable Case
Abstract
Abstract. This paper investigates the solvability of the regular free-endpoint indefinite linear quadratic regulation problem, an open issue in optimal control. The problem can be decomposed into two core aspects: strong well-posedness and attainability. In this paper, we establish both sufficient and necessary conditions for strong well-posedness, with a small gap between them, and importantly, these conditions do not rely on the typical assumption that a negative semidefinite solution to a certain linear matrix inequality exists. Building on the established sufficient conditions for well-posedness, we also provide necessary and sufficient conditions for attainability, along with a characterization of the value function and the optimal control.
Fields of Study & Subjects
Stability and Controllability of Differential Equations
Advanced Control Systems Optimization
Optimization and Variational Analysis
Publication details
- Journal / source
- SIAM Journal on Control and Optimization
- Volume
- 64
- Issue
- 1
- Pages
- 211–235
- Publication date
- 12 January 2026
- Language
- EN