  This paper addresses the inverse optimal control for the linear quadratic
tracking problem with a fixed but unknown target state, which aims to estimate
the possible triplets comprising the target state, the state weight matrix, and
the input weight matrix from observed optimal control input and the
corresponding state trajectories. Sufficient conditions have been provided for
the unique determination of both the linear quadratic cost function as well as
the target state. A computationally efficient and numerically reliable
parameter identification algorithm is proposed by equating optimal control
strategies with a system of linear equations, and the associated relative error
upper bound is derived in terms of data volume and signal-to-noise ratio.
Moreover, the proposed inverse optimal control algorithm is applied for the
joint cluster coordination and intent identification of a multi-agent system.
By incorporating the structural constraint of the Laplace matrix, the relative
error upper bound can be reduced accordingly. Finally, the algorithm's
efficiency and accuracy are validated by a vehicle-on-a-lever example and a
multi-agent formation control example.
