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updated README, added example output
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README.md

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# Model-Predictive-Control
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This repo includes the MATLAB codes for a DMC and an EPFC controller.
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This repository includes the MATLAB codes for a DMC and an EPFC controller. These two are basic types of Model-Predictive Control (MPC). The code can handle all sorts of model horizon, prediction horizon, control horizon, or gain tuning, along with mismatched model, control input limits, etc.
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Here is an example of the reference tracking and control input:
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<img width="800" height="300" alt="cart-with-spring" src="assets/images/main_output.png" />
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## DMC
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A DMC controller is implemented to control a linear system. The linear system is actually the linearized version of a nonlinear system, which as an example is considered to be a cart with a nonlinear spring, as that used for the EPFC controller in [here](#epfc).
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## EPFC
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An extended PFC controller is implemented to control a nonlinear system. The exemplar system considered is a cart with a nonlinear spring attached to it, as shown in the image:
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<img width="1000" height="800" alt="cart-with-spring" src="https://github.com/user-attachments/assets/05ea10e7-072e-4275-8c02-80a70bdfcb7c" />
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<img width="500" height="400" alt="cart-with-spring" src="assets/images/cart-with-spring.png" />
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The system state space representation is as follows:
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```

assets/figures/main.fig

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assets/images/main_output.png

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