An off‐policy approach for model‐free stabilization of linear systems subject to input energy constraint and its application to spacecraft rendezvous

• Published in: Optimal control applications & methods Vol. 41; no. 3; pp. 948 - 959
• Main Authors: Gu, Juan, Zhou, Jianzhong
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 01.05.2020; Wiley Subscription Services, Inc
• Subjects: Computer simulation; Constraint modelling; Feedback; input energy constraint; Linear systems; low gain feedback; reinforcement learning; Riccati equation; Space rendezvous; Spacecraft; spacecraft rendezvous; System dynamics
• ISSN: 0143-2087; 1099-1514
• DOI: 10.1002/oca.2579

Summary This note is concerned with the problem of stabilizing a class of linear continuous‐time systems with completely unknown system dynamics subject to input energy constraint. To deal with this problem, a model‐based low gain feedback law is designed firstly by establishing a special algebraic Riccati equation. Such a low gain feedback law can semiglobally stabilize the linear systems subject to input energy constraint with the exact system model. In order to relax the assumption that the system model is exactly known, an off‐policy reinforcement learning approach is designed to solve the same problem without requiring the completely knowledge of the system dynamics. Finally, in order to verify the effectiveness of the proposed model‐free approach, simulation result on the spacecraft rendezvous problem is introduced.