Robust Tube Linear MPC with Artificial Reference

This repository contains a simulation demonstration for the paper:

Limón, Daniel, et al.
"MPC for tracking piecewise constant references for constrained linear systems."
Automatica, vol. 44, no. 9, 2008, pp. 2382-2387.

Recommended References

For a deeper understanding of robust tube-based MPC and related concepts, the following papers are recommended:

1. Limon, D., et al.
   "On the design of robust tube-based MPC for tracking."
   IFAC Proceedings Volumes, vol. 41, no. 2, 2008, pp. 15333-15338.

2. Mayne, David Q., María M. Seron, and Saša V. Raković.
   "Robust model predictive control of constrained linear systems with bounded disturbances."
   Automatica, vol. 41, no. 2, 2005, pp. 219-224.

3. Gilbert, Elmer G., and K. Tin Tan.
   "Linear systems with state and control constraints: The theory and application of maximal output admissible sets."
   IEEE Transactions on Automatic Control, vol. 36, no. 9, 1991, pp. 1008-1020.

4. Rakovic, Sasa V., et al. "Invariant approximations of the minimal robust positively invariant set." IEEE Transactions on automatic control 50.3 (2005): 406-410.

Required Toolboxes

The following MATLAB toolboxes are required to run the simulations:

1. MPT3 – for set operations.
2. MATLAB Optimization Toolbox – for fmincon.
3. YALMIP – for solving LMIs (included in MPT3 if installed properly).

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