Abstract
In this paper, we propose an improved version of receding horizon control for systems with state delays. The proposed control guarantees closed-loop stability for a wider class of state-delay systems than the existing one. For expanded applications, a more generalized cost function, with three terminal weighting terms, is employed and minimized. Terminal weighting matrices are chosen to achieve the property that the optimal cost monotonically decreases with time. It turns out that the stability condition depends on the delay size and then it is less conservative than the existing delay-independent one. The simulation study shows that the proposed control scheme guarantees closed-loop stability even for state-delay systems that cannot be stabilized by the existing receding horizon control.
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References
Richalet, J., Rault, A., Testud, J.L., Papon, J.: Model predictive heuristic control: applications to industrial processes. Automatica 14, 413–428 (1978)
Rawlings, J.B., Muske, K.R.: The stability of constrained receding horizon control. IEEE Trans. Autom. Control 38(10), 1512–1516 (1993)
Kothare, M., Balakrishnan, V., Morari, M.: Robust constrained model predictive control using Linear Matrix Inequalities. Automatica 32, 1361–1379 (1996)
Kwon, W.H., Han, S.: Receding Horizon Control. Springer, London (2005)
Kwon, W.H., Kang, J.W., Lee, Y.S., Moon, Y.S.: Simple receding horizon control for state delayed systems with its stability. J. Process Control 13(6), 539–551 (2003)
Kwon, W.H., Lee, Y.S., Han, S.H.: General receding horizon control for linear time-delay systems. Automatica 40(9), 1603–1611 (2004)
Lee, Y.S., Han, S.H., Kwon, W.H.: Receding horizon \(H_\infty \) control for systems with a state-delay. Asian J. Control 8(1), 63–71 (2006)
Kwon, W.H., Pearson, A.E.: Feedback stabilization of linear systems with delayed control. IEEE Trans. Automat. Control 25(2), 266–269 (1980)
Park, J.H., Yoo, H.W., Han, S.H.: Receding horizon control for input-delayed systems. IEEE Trans. Automat. Control 53(7), 1746–1752 (2008)
You, H.W., Lee, Y.S., Han, S.H.: Constrained receding horizon controls for nonlinear time-delay systems. Nonlinear Dyn. 69(1–2), 149–158 (2012)
Kirk, D.E.: Optimal Control Theory. Prentice-Hall, Englewood Cliffs (1970)
Fiagbedzi, Y.A., Pearson, A.E.: Feedback stabilization of linear autonomous time lag systems. IEEE Trans. Automat. Control AC-31, 847–855 (1986)
Lee, Y.S., Moon, Y.S., Kwon, W.H., Park, P.G.: Delay-dependent robust \({H}_\infty \) control for uncertain systems with a state-delay. Automatica 40(1), 65–72 (2004)
Acknowledgments
This research was supported in part by Korea Electric Power Corporation Research Institute through Korea Electrical Engineering & Science Research Institute (grant number: 13GA04), by the MSIP (Ministry of Science, ICT and Future Planning), Korea, under the “IT Consilience creative Program” (NIPA-2014-H0201-14-1001) supervised by the NIPA (National IT Industry Promotion Agency), and by Inha Research Grant.
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Lee, Y.S., Han, S. An Improved Receding Horizon Control for Time-Delay Systems. J Optim Theory Appl 165, 627–638 (2015). https://doi.org/10.1007/s10957-014-0658-8
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DOI: https://doi.org/10.1007/s10957-014-0658-8
Keywords
- Calculus of variations and optimal control
- Receding horizon control (RHC)
- Delay-dependent controls
- Linear matrix inequality (LMI)
- State-delay systems
- Terminal weighting matrices