Linearize model at each step in the prediction horizon (MPC)

Hello

I trying to implement an MPC scheme where the (nonlinear) model will be linearized at each step in the prediction horizon.

My idea is that at the first step of the prediction horizon the model will be linearized using the current operating points. Then we do only one step of the prediction horizon with the model that has just been linearized, take that control signal "u" which the optimisation solver gives for that current step of the prediction, simulate one step of the nonlinear model with that "u" and integrate the result in order to achieve the new operating point (approximately), linearize the model around this new operating point and repeat until the full horizon is covered.

Is this feasible? and achieveable in Matlab using for example quadprog? I usually use quadprog with linear MPC with model that stays the same during the horizon so forgive me if my "strategy" above is faulty.