Optimal Control for Simple Linear Hybrid Systems

This paper studies optimal time-bounded control in a simple subclass of linear hybrid systems, which consists of one continuous variable and global constraints. Each state has a continuous cost attached to it, which is linear in the sojourn time, while a discrete cost is attached to each transition taken. We show the corresponding decision problem to be NP-complete and develop an FPTAS for finding an approximate solution. We have implemented a small prototype to compare the performance of these approximate and precise algorithms for this problem. Our results indicate that the proposed approximation schemes scale. Furthermore, we show that the same problem with infinite time horizon is in LOGSPACE.

[1]  Kim G. Larsen,et al.  Uppaal Stratego , 2015, TACAS.

[2]  Patricia Bouyer,et al.  Weighted Timed Automata: Model-Checking and Games , 2006, MFPS.

[3]  George J. Pappas,et al.  Event-based Green scheduling of radiant systems in buildings , 2013, 2013 American Control Conference.

[4]  Thomas A. Henzinger,et al.  The Algorithmic Analysis of Hybrid Systems , 1995, Theor. Comput. Sci..

[5]  Eduardo F. Camacho,et al.  Introduction to Model Based Predictive Control , 1999 .

[6]  Dominik Wojtczak,et al.  Optimal Control for Linear-Rate Multi-mode Systems , 2013, FORMATS.

[7]  Kim G. Larsen,et al.  Optimizing Control Strategy Using Statistical Model Checking , 2013, NASA Formal Methods.

[8]  George J. Pappas,et al.  Green scheduling of control systems for peak demand reduction , 2011, IEEE Conference on Decision and Control and European Control Conference.

[9]  Philippe Schnoebelen,et al.  Model Checking Timed Automata with One or Two Clocks , 2004, CONCUR.

[10]  Patricia Bouyer,et al.  Average-Price and Reachability-Price Games on Hybrid Automata with Strong Resets , 2008, FORMATS.

[11]  Andrew Chiu,et al.  Division in logspace-uniform NC1 , 2001, RAIRO Theor. Informatics Appl..

[12]  Amir Pnueli,et al.  Low dimensional hybrid systems - decidable, undecidable, don't know , 2012, Inf. Comput..

[13]  Manfred Morari,et al.  Reducing peak electricity demand in building climate control using real-time pricing and model predictive control , 2010, 49th IEEE Conference on Decision and Control (CDC).

[14]  Rajeev Alur,et al.  A Theory of Timed Automata , 1994, Theor. Comput. Sci..

[15]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[16]  Thomas A. Henzinger,et al.  Hybrid Automata: An Algorithmic Approach to the Specification and Verification of Hybrid Systems , 1992, Hybrid Systems.

[17]  Bin Li,et al.  Optimal on-off control of an air conditioning and refrigeration system , 2010, Proceedings of the 2010 American Control Conference.

[18]  Philip Haves,et al.  Model predictive control for the operation of building cooling systems , 2010, Proceedings of the 2010 American Control Conference.

[19]  Kim G. Larsen,et al.  Time for Statistical Model Checking of Real-Time Systems , 2011, CAV.

[20]  Luis Pérez-Lombard,et al.  A review on buildings energy consumption information , 2008 .

[21]  Rajeev Alur,et al.  Optimal scheduling for constant-rate multi-mode systems , 2012, HSCC '12.

[22]  Thomas A. Henzinger,et al.  The theory of hybrid automata , 1996, Proceedings 11th Annual IEEE Symposium on Logic in Computer Science.