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

The inverse linear-quadratic optimal control problem is a system identification whose aim to recover the quadratic cost function and hence closed-loop matrices based on observations of trajectories. In this paper, discrete-time, finite-horizon case considered, where agents are also assumed be homogeneous indistinguishable. latter means that all have same dynamics objective functions in terms “snap shots” at different time instants, but what not known “which agent moved where” for consecutive observations. This absence linked trajectories makes challenging. We first show globally identifiable. Then, noiseless observations, we true matrix, matrices, can recovered as unique global solution convex optimization problem. Next, noisy formulate an estimator modified Moreover, statistical consistency shown. Finally, performance proposed method demonstrated by number numerical examples.