Abstract
Linear-Rate Multi-Mode Systems is a model that can be seen both as a subclass of switched linear systems with imposed global safety constraints and as hybrid automata with no guards on transitions. We study the existence and design of a controller for this model that keeps at all times the state of the system within a given safe set. A sufficient and necessary condition is given for such a controller to exist as well as an algorithm that finds one in polynomial time. We further generalise the model by adding costs on modes and present an algorithm that constructs a safe controller which minimises the peak cost, the average-cost or any cost expressed as a weighted sum of these two. Finally, we present numerical simulation results based on our implementation of these algorithms.
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Albadi, M.H., El-Saadany, E.F.: Demand response in electricity markets: An overview. In: Proc. of IEEE Power Engineering Society General Meeting, pp. 1–5 (June 2007)
Alur, R., Trivedi, A., Wojtczak, D.: Optimal scheduling for constant-rate mulit-mode systems. In: Proc. of Hybrid Systems: Computation and Control 2012 (2012)
Alur, R.: Formal verification of hybrid systems. In: Proc. of International Conference on Embedded Software 2011, pp. 273–278 (2011)
Alur, R., Courcoubetis, C., Henzinger, T.A., Ho, P.-H.: Hybrid automata: An algorithmic approach to the specification and verification of hybrid systems. In: Grossman, R.L., Ravn, A.P., Rischel, H., Nerode, A. (eds.) HS 1991 and HS 1992. LNCS, vol. 736, pp. 209–229. Springer, Heidelberg (1993)
Camacho, E.F., Bordons, C., Camacho, E.F., Bordons, C.: Model predictive control, vol. 303. Springer, Berlin (1999)
Giua, A., Seatzu, C., Van der Mee, C.: Optimal control of switched autonomous linear systems. In: Proc. of the 40th Conference on Decision and Control, pp. 2472–2477 (2001)
Henzinger, T.A.: The theory of hybrid automata. In: Proc. of the 11th LICS Symposium (1996)
Henzinger, T.A., Kopke, P.W., Puri, A., Varaiya, P.: What’s decidable about hybrid automata? Journal of Comp. and Sys. Sciences 57, 94–124 (1998)
Ma, Y., Borrelli, F., Hencey, B., Coffey, B., Bengea, S., Haves, P.: Model predictive control for the operation of building cooling systems. In: Proc. of American Control Conference, pp. 5106–5111 (2010)
Nghiem, T.X., Behl, M., Mangharam, R., Pappas, G.J.: Green scheduling of control systems for peak demand reduction. In: Proc. of Conference on Decision and Control (2011)
Nghiem, T.X., Behl, M., Pappas, G.J., Mangharam, R.: Green scheduling for radiant systems in buildings. In: Proc. of Conference on Decision and Control (2012)
Oldewurtel, F., Ulbig, A., Parisio, A., Andersson, G., Morari, M.: Reducing peak electricity demand in building climate control using real-time pricing and model predictive control. In: Proc. of 49th IEEE Conference on Decision and Control, pp. 1927–1932 (2010)
Shuzhi, S., Sun Ge, Z.: Switched linear systems: Control and design. Springer (2005)
Schrijver, A.: Theory of linear and integer programming. John Wiley & Sons, Inc., New York (1986)
TRFund Energy Study. Understanding PECO’s general service tariff
Wojtczak, D.: Optimal scheduling for linear-rate multi-mode systems. CoRR, abs/1302.4406 (2013)
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Wojtczak, D. (2013). Optimal Control for Linear-Rate Multi-mode Systems. In: Braberman, V., Fribourg, L. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2013. Lecture Notes in Computer Science, vol 8053. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40229-6_18
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DOI: https://doi.org/10.1007/978-3-642-40229-6_18
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