Continuous-time inverse quadratic optimal control problem

In this paper, the problem of finite horizon inverse optimal control (IOC) is investigated, where the quadratic cost function of a dynamic process is required to be recovered based on the observation of optimal control sequences. We propose the first complete result of the necessary and sufficient c...

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Bibliographic Details
Published in:	Automatica (Oxford) Vol. 117; p. 108977
Main Authors:	Li, Yibei, Yao, Yu, Hu, Xiaoming
Format:	Journal Article
Language:	English
Published:	Elsevier Ltd 01.07.2020
Subjects:	Inverse dynamic problem Linear matrix inequality Linear quadratic regulators Optimal control Linear matrix inequality Inverse dynamic problem Linear quadratic regulators Optimal control
ISSN:	0005-1098, 1873-2836
Online Access:	Get full text
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Summary:	In this paper, the problem of finite horizon inverse optimal control (IOC) is investigated, where the quadratic cost function of a dynamic process is required to be recovered based on the observation of optimal control sequences. We propose the first complete result of the necessary and sufficient condition for the existence of corresponding standard linear quadratic (LQ) cost functions. Under feasible cases, the analytic expression of the whole solution space is derived and the equivalence of weighting matrices in LQ problems is discussed. For infeasible problems, an infinite dimensional convex problem is formulated to obtain a best-fit approximate solution with minimal control residual. And the optimality condition is solved under a static quadratic programming framework to facilitate the computation. Finally, numerical simulations are used to demonstrate the effectiveness and feasibility of the proposed methods.
ISSN:	0005-1098 1873-2836
DOI:	10.1016/j.automatica.2020.108977