Exponentially Convergent Receding Horizon Strategy for Constrained Optimal Control
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Receding horizon control has been a widespread method in industrial control engineering as well as an extensively studied subject in control theory. In this work, we consider a lag L receding horizon strategy that applies the initial L optimal controls from each quadratic program to each receding horizon. We investigate a discrete-time and time-varying linear-quadratic optimal control problem that includes a nonzero reference trajectory and constraints on both state and control. We prove that, under boundedness and controllability conditions, the solution obtained by the receding horizon strategy converges to the solution of the full problem interval exponentially fast in the length of the receding horizon for some lag L. The exponential rate of convergence provides a systematic way of choosing the receding horizon length given a desired accuracy level. We illustrate our theoretical findings using a small, synthetic production cost model with real demand data.
KeywordsConstrained optimal control Receding horizon control Sensitivity analysis
Mathematics Subject Classification (2010)49N10 49N35 49Q12
We thank Prof. V. Zavala for pointing us to references about stability issues in rolling horizon control. We thank the anonymous referee of  who suggested that we look into RHC as well as the referee of this paper for important comments about our assumptions and scope relative to . This material was based upon work supported by the U.S. Department of Energy, Office of Science, under Contract DE-AC02-06CH11347. M. A. acknowledges partial NSF funding through awards FP061151-01-PR and CNS-1545046.
- 1.Bellingham, J., Richards, A., How, J.P.: Receding horizon control of autonomous aerial vehicles. In: American Control Conference, 2002. Proceedings of the 2002, vol. 5, pp. 3741–3746. IEEE (2002)Google Scholar
- 3.Bhattacharya, R., Balas, G.J., Kaya, A., Packard, A.: Nonlinear receding horizon control of F-16 aircraft. In: American Control Conference, 2001. Proceedings of the 2001, vol. 1, pp. 518–522. IEEE (2001)Google Scholar
- 8.Franz, R., Milam, M., Hauser, J.: Applied receding horizon control of the Caltech Ducted Fan. In: American Control Conference, 2002. Proceedings of the 2002, vol 5, pp. 3735–3740. IEEE (2002)Google Scholar
- 12.Interconnection, P.: Estimated hourly load data. http://www.pjm.com/markets-and-operations/energy/real-time/loadhryr.aspx. Accessed: 2017-07-23
- 18.Kwon, W.H., Han, S.H.: Receding Horizon Control: Model Predictive Control for State Models. Springer, London (2006)Google Scholar
- 29.Sideris, A., Rodriguez, L.A.: A Riccati Approach to Equality Constrained Linear Quadratic Optimal Control. In: Proceeding of the 2010 American Control Conference, pp. 5167–5172 (2010)Google Scholar