Optimal and Robust Control

Assigned (compulsory) reading

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Recommended (not compulsory) further reading

The core topic of this lecture - model predictive control - has already been described in a number of dedicated monographs:

1. J. Maciejowski. Predictive control with constraints, Prentice Hall, 2000.
2. J. B. Rawlings, D. Q. Mayne, M. M. Diehl. Model predictive control: theory, computation and design, 2nd ed., Nob Hill Pub, 2019. Electronic version freely (and legally) available at http://www.nobhillpublishing.com/mpc-paperback/index-mpc.html.
   
3. E. F. Camacho and C. Bordons. Model predictive control, Springer, 2nd ed., 2008.
4. G. Goodwin and M. M. Seron and J. A. de Doná. Constrained control and estimation - an optimisation approach. Springer, 2005.
5. F. Borrelli, A. Bemporad, and M. Morari, Predictive Control for Linear and Hybrid Systems, 1 edition. Cambridge, New York: Cambridge University Press, 2017. Electronic version freely available from the authors at http://cse.lab.imtlucca.it/~bemporad/publications/papers/BBMbook.pdf.
   
6. S. V. Raković and W. S. Levine, Eds., Handbook of Model Predictive Control. Birkhäuser Basel, 2019.
   
   

In particular, [5] and, the new edition of [2], which is freely downloadable, are up to date recommendable textbooks written by the leaders in the field..

Although these books may be useful to consult occassionally, for a dynamically evolving discipline such as MPC, there are a wealth of decent resources available online:

1. F. Borrelli, A. Bemporad, M. Morari. Predictive control for linear and hybrid systems. 2015. Available [ONLINE] at http://www.mpc.berkeley.edu/mpc-course-material.
2. A. Bemporad. Model predictive control - course material. Slides available [ONLINE] at http://cse.lab.imtlucca.it/~bemporad/mpc_course.html.
3. M. Cannon. Model predictive control - lecture notes. Available [ONLINE] at http://www.eng.ox.ac.uk/~conmrc/mpc/notes.html.
4. S. Boyd. Model predictive control (withing EE364b) - lecture slides. Available [ONLINE] at https://stanford.edu/class/ee364b/lectures/mpc_slides.pdf.
5. A. Bemporad - A recording of a lecture "Recent Advances in Embedded Model Predictive Control". Available [ONLINE] at 
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In particular, the topic of a projected gradient method for (online) MPC is discussed in the section 3.1 of the slides OptimizationMethods_handouts.pdf linked from the Borrelli's course web page given above (and also in his book). Numerous practical details such as eleaborate analysis of various stoppic criteria can be found in

• S. Richter, “Computational complexity certification of gradient methods for real-time model predictive control,” Ph.D. Thesis, ETH, Zurich, Switzerland, 2012. Available [ONLINE] at https://www.research-collection.ethz.ch/bitstream/handle/20.500.11850/60443/eth-6362-02.pdf.
• S. Richter, C. N. Jones, and M. Morari, “Real-time input-constrained MPC using fast gradient methods,” in Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference, 2009, pp. 7387–7393
  

Projected gradient method can be regarded a generalization of a powerful idea of proximal algorithms, which is described thoroughly in

• N. Parikh and S. Boyd, “Proximal Algorithms,” Found. Trends Optim., vol. 1, no. 3, pp. 127–239, Jan. 2014. Available [ONLINE] at http://web.stanford.edu/~boyd/papers/prox_algs.html.