Inverse linear-quadratic discrete-time finite-horizon optimal control for indistinguishable homogeneous agents: A convex optimization approach

被引:5
|
作者
Zhang, Han [1 ,2 ,3 ]
Ringh, Axel [4 ,5 ,6 ]
机构
[1] Shanghai Jiao Tong Univ, Sch Elect Informat & Elect Engn, Dept Automat, Shanghai, Peoples R China
[2] Minist Educ China, Key Lab Syst Control & Informat Proc, Shanghai 200240, Peoples R China
[3] Shanghai Engn Res Ctr Intelligent Control & Manag, Shanghai 200240, Peoples R China
[4] Chalmers Univ Technol, Dept Math Sci, S-41296 Gothenburg, Sweden
[5] Univ Gothenburg, S-41296 Gothenburg, Sweden
[6] Hong Kong Univ Sci & Technol, Dept Elect & Comp Engn, Kowloon, Clear Water Bay, Hong Kong, Peoples R China
基金
中国国家自然科学基金;
关键词
Inverse optimal control; Linear quadratic regulator; System identification; Closed-loop identification; Time-varying system matrices; Convex optimization; Semidefinite programming;
D O I
10.1016/j.automatica.2022.110758
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
The inverse linear-quadratic optimal control problem is a system identification problem whose aim is to recover the quadratic cost function and hence the closed-loop system matrices based on observations of optimal trajectories. In this paper, the discrete-time, finite-horizon case is considered, where the agents are also assumed to be homogeneous and indistinguishable. The latter means that the agents all have the same dynamics and objective functions and the observations are in terms of "snap shots" of all agents at different time instants, but what is not known is "which agent moved where" for consecutive observations. This absence of linked optimal trajectories makes the problem challenging. We first show that this problem is globally identifiable. Then, for the case of noiseless observations, we show that the true cost matrix, and hence the closed-loop system matrices, can be recovered as the unique global optimal solution to a convex optimization problem. Next, for the case of noisy observations, we formulate an estimator as the unique global optimal solution to a modified convex optimization problem. Moreover, the statistical consistency of this estimator is shown. Finally, the performance of the proposed method is demonstrated by a number of numerical examples. (c) 2022 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
引用
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页数:12
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