Inverse linear-quadratic discrete-time finite-horizon optimal control for indistinguishable homogeneous agents: A convex optimization approach
Artikel i vetenskaplig tidskrift, 2023

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.

Convex optimization

Time-varying system matrices

Inverse optimal control

Closed-loop identification

Semidefinite programming

Linear quadratic regulator

System identification


Han Zhang

Shanghai Jiao Tong University

Axel Ringh

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Göteborgs universitet


0005-1098 (ISSN)

Vol. 148 110758






Grundläggande vetenskaper



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