Here we obtain the optimal

quadratic performance index consisting of tracking errors and control input.

We introduce the

quadratic performance index function for system (1):

Then the state-dependent Riccati equation was presented for an affine nonlinear system and finite horizon quadratic performance index.

In this case assuming that all state variables are available for feedback the aim of using SDRE controller is to find control law with gain feedback k(x) as u k (x)x such that the finite horizon quadratic performance index is minimized:

A unique tuning strategy that makes use of a weighted quadratic performance index to compute controller output change is used to help achieve improved control performance.

A set of future control signals is generally computed to minimize a quadratic performance index over a fixed control horizon.

The design process was simplified by introducing a quadratic performance index with corresponding input delay in [24].

This is a preview control problem in which the system is described as (16), the quadratic performance index is described as (17), and [DELTA]r(k) is previewable.