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This is a very naive implementation that author played in the graduate school.
The goal is to minimize the cost of stablizing the double integrator (2DOF) under the constraints.
To implement the mpc.m file, you need to install a free MATLAB package MPT3(https://www.mpt3.org) in advance. This is a very powerful package used for MPC.
You can see the report (pdf file) for my conclusion.
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course project: a simple implementation of Q learning and MPC