Discrete-time inverse linear quadratic optimal control over finite time-horizon under noisy output measurements

Abstract In this paper, the problem of inverse quadratic optimal control over finite time-horizon for discrete-time linear systems is considered. Our goal to recover corresponding objective function using noisy observations. First, identifiability model structure analyzed under relative degree assumption and we show strictly globally identifiable. Next, study whose initial state distribution observation noise are unknown, yet exact observations on states available. We formulate as a risk minimization approximate empirical average. It further shown that solution approximated statistically consistent degrees. then case where not available, noises known be white Gaussian distributed also (with unknown mean covariance). EM-algorithm used estimate parameters in function. The effectiveness our results demonstrated by numerical examples.