The Adaptive LQ Regulator

2019/01/14 by Omar Hijab, Hijab, Omar
Engineering · #34H15 #49L25 (Secondary) #60G35 (Primary) #93E20 #93E35 #Advanced Algorithms and Applications #Advanced Control Systems Design #Elevator Systems and Control #FOS: Mathematics #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.1901.04574

openalex publication_date 2019/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The optimal adaptive control of a linear system in a signal-plus-noise setting with infinite horizon LQ regulator cost is studied. The class of partially observed linear systems for which the certainty equivalence property holds is identified. It is also shown that a linear system is adaptively stabilizable if and only if it is uniformly stabilizable, and the class of partially observed linear systems for which the certainty equivalence value function is a supersolution of the Bellman equation is identified.

Related

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• Finite Time Adaptive Stabilization of LQ Systems
• Adaptive Control and Regret Minimization in Linear Quadratic Gaussian\n (LQG) Setting
• The Power of Linear Controllers in LQR Control
• Adaptive Certainty-Equivalence Control With Regulation-Triggered Finite-Time Least-Squares Identification, Part II: Analysis