1. A method of predictive model control of a controlled system, comprising: using a model predictive control (MPC) model, determining an iterative, finite horizon optimization of a system model of the controlled system, in order to generate a manipulated value trajectory; at time t sampling a current state of the controlled system and computing a cost minimizing manipulated value trajectory with the MPC model for a relatively short time horizon in the future, wherein the MPC uses a quadratic programming (QP) algorithm to find the optimal solution; implementing a first step or move of the manipulated value trajectory; sampling the controlled system state again and determining the difference between the predicted and actual value of the state after the implementation of the first move; determining a correction to the manipulated value trajectory based on a first or second order approximation, using duality between the MPC model and a LQ feedback model; applying the correction to the MPC manipulated value trajectory to produce an initialized control trajectory that eliminates or reduces the need to iterate the MPC's QP algorithm to the optimal solution; repeating the control calculation starting from the now current state using the corrected manipulated value trajectory, yielding a new control and new predicted state path; and continuing the control process by continuing to shift the prediction horizon forward.