In this paper, trajectory tracking for discrete-time stochastic nonlinear systems is achieved by
an inverse optimal control. Additionally, the control scheme minimizes a cost functional,
which is posteriori determined. Unlike the optimal control technique, this scheme avoids to
solve the stochastic Hamilton-Jacobi-Bellman equation which is not a feasible task for this
kind of systems. The proposed optimal controller is based on a discrete-time stochastic
control Lyapunov function (DSCLF).

This paper presents an inverse optimal control approach for output tracking of discrete-time
nonlinear systems, avoiding to solve the associated Hamilton-Jacobi-Bellman (HJB)
equation, and minimizing a meaningful cost function. This stabilizing optimal controller is
based on discrete-time passivity theory. The applicability of the proposed approach is
illustrated via simulations by trajectory tracking control of a planar robot.