Robust Model Predictive Control Using Tube
这个知识库包括管道模型预测控制（tube MPC）[1]以及用MATLAB编写的通用模型预测控制（MPC）的示例。

This repository includes examples for the tube model predictive control (tube-MPC)[1] as well as the generic model predictive control (MPC) written in MATLAB.

Requirement
optimization_toolbox (matlab)

control_toolbox (matlab)

Multi-Parametric Toolbox 3 (open-source and freely available at http://people.ee.ethz.ch/~mpt/3/)

Feedback, bug reports, contributions
If you find this package helpful, giving a “star” to this repositry will be a happy feedback for me! If you find a bug, or have more broader kind of quession about tube MPC,please post that in the issue page. I will try hard to respond to questions via e-mail but, I strongly recommend do it in the issue page. It’s much easier for me to keep myself on track.

Usage
See example/example_tubeMPC.m and example/example_MPC.m for the tube-MPC and generic MPC, respectively. Note that every inequality constraint here is expressed as a convex set. For example, the constraints on the state Xc is specified as a rectangular, which is constructed with 4 vertexes. When considering a 1-dim input Uc, Uc will be specified by min and max value (i.e. u∊[u_min, u_max]), so it will be constructed by 2 vertexes. For more detail, please see the example codes.

参考文献：

[1] Mayne, David Q., María M. Seron, and S. V. Raković. “Robust model predictive control of constrained linear systems with bounded disturbances.” Automatica 41.2 (2005): 219-224.

[2] Rakovic, Sasa V., et al. “Invariant approximations of the minimal robust positively invariant set.” IEEE Transactions on Automatic Control 50.3 (2005): 406-410.

[3] Kouvaritakis, Basil, and Mark Cannon. “Model predictive control.” Switzerland: Springer International Publishing (2016).

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