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Models Predictive Control For A Finite Time Horizon

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4. Model predictive control
MPC is a general term for computer control algorithms [10] that uses an outright process model to predict future response of the plant.
An optimized input is determined by solving an open-loop optimal control problem over a finite time horizon. The number of samples one looks forward is called the prediction horizon Np. While, number of samples that the optimal input is computed for is called the control horizon Nu. The complexity of the problem can be decreased by selecting a shorter control horizon than prediction horizon. From the calculated input signal only the first element is applied to the system.
This can allows solving online the optimized control problem, where prediction error action and control input are minimized through a future horizon, possibility of subject to constraints on the manipulated inputs, outputs and states. Then, the optimization returns an optimal control sequence as input and the first input only from the sequence is used as input to the system. By the next sample interval, the total optimization approach repeated and the horizon shifted. This approach is used to allow indemnity for modeling error and future disturbance. Basic structure of model predictive control is shown in Fig. 2. Fig. 2 Basic structure of model predictive control

In an MPC-algorithm there are four important elements:

4.1. Model used for prediction
The model is in most MPC-formulations today given on discrete time state space form:

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