Abstract
A controller design method based on a quantitative model checking technique is proposed. Controllers have been designed to shape the closed-loop system’s responses to meet certain requirements. We use Linear Temporal Logic for Control (LTLC) [16] to formally describe complex requirements and design a controller to meet the requirements with guidance from model checking results. The technique can help design a controller robust against errors systematically hampering the controller’s efforts. To demonstrate the usefulness of the proposed technique, we exercised several controller design examples with different types of errors.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
We use the term LTI systems for both continuous-time LTI systems and discrete-time LTI systems when the usage is clear from the context.
- 2.
We use the term propositional formula because the semantics of LTLC is interpreted over each computation path where all the variables are assigned with a value.
- 3.
To check the ternary satisfaction relation \(\models \), LTLC model checker has to find accepting runs ending with a loop and examine the feasibility of the runs generated by the Cartesian product of the accepting runs and computation paths ending with a loop of all possible periods.
References
LTLC-Checker. https://sites.google.com/site/youngminkwon
Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126, 183–235 (1994)
Biere, A., Cimatti, A., Clarke, E., Zhu, Y.: Symbolic model checking without BDDs. In: Cleaveland, W.R. (ed.) TACAS 1999. LNCS, vol. 1579, pp. 193–207. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-49059-0_14
Bu, L., Li, Y., Wang, L., Li, X.: BACH: bounded reachability checker for linear hybrid automata. In: Formal Methods in Computer Aided Design, pp. 65–68. IEEE Computer Society (2008)
Clarke, E., Grumberg, O., Peled, D.: Model Checking. MIT Press, Cambridge (2000)
Franklin, G.F., Powell, J.D., Emami-Naeini, A.: Feedback Control of Dynamic Systems, 3rd edn. Addison Wesley, Reading (1994)
Fränzle, M., Herde, C.: HySAT: an efficient proof engine for bounded model checking of hybrid systems. Formal Methods Syst. Des. 30, 179–198 (2007)
Frehse, G., Le Guernic, C., Donzé, A., Cotton, S., Ray, R., Lebeltel, O., Ripado, R., Girard, A., Dang, T., Maler, O.: SpaceEx: scalable verification of hybrid systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 379–395. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22110-1_30
Girard, A., Pola, G., Tabuada, P.: Approximately bisimilar symbolic models for incrementally stable switched systems. Trans. Autom. Control 55, 116–126 (2010)
Henzinger, T.A.: The theory of hybrid automata. In: Annual Symposium on Logic in Computer Science, pp. 278–292. IEEE Computer Society (1996)
Henzinger, T.A., Ho, P.-H., Wong-Toi, H.: HyTech: a model checker for hybrid systems. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 460–463. Springer, Heidelberg (1997). https://doi.org/10.1007/3-540-63166-6_48
Holzmann, G.J.: The model checker spin. IEEE Trans. Softw. Eng. 23, 279–295 (1997)
Kloetzer, M., Belta, C.: A fully automated framework for control of linear systems from temporal logic specifications. Trans. Autom. Control 53, 287–297 (2008)
Kress-Gazit, H., Fainekos, G.E., Pappas, G.J.: Temporal-logic-based reactive mission and motion planning. Trans. Robot. 25, 1370–1381 (2009)
Kwon, Y.M., Agha, G.: LTLC: linear temporal logic for control. In: Egerstedt, M., Mishra, B. (eds.) HSCC 2008. LNCS, vol. 4981, pp. 316–329. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78929-1_23
Kwon, Y., Kim, E.: Bounded model checking of hybrid systems for control. IEEE Trans. Autom. Control 60, 2961–2976 (2015)
Kwon, Y., Kim, E., Jeong, S., Lee, A.: Quantitative model checking for a smart grid pricing. In: International Conference on the Quantitative Evaluation of Systems (QEST), pp. 55–71. IEEE (2017)
Larsen, K.G., Pettersson, P., Yi, W.: UPPAAL in a nutshell. Int. J. Softw. Tools Technol. Transf. 1, 134–152 (1997)
Liu, J., Ozay, N., Topcu, U., Murray, R.M.: Synthesis of reactive switching protocols from temporal logic specifications. IEEE Trans. Autom. Control 58, 1771–1785 (2013)
Luenberger, D.G.: Linear and Nonlinear Programming, 2nd edn. Addison Wesley, Reading (1989)
Oppenheim, A.V., Willsky, A.S.: Signals and Systems. Prentice-Hall, Englewood Cliffs (1983)
Start, H., Woods, J.W.: Probability and Random Processes with Applications to Signal Processing, 3rd edn. Prentice-Hall, Upper Saddle River (2002)
Tabuada, P., Pappas, G.J.: Linear time logic control of discrete-time linear systems. Trans. Autom. Control 51, 1862–1877 (2006)
Acknowledgement
The authors thank the anonymous referees for their helpful comments. This work was supported by MSIP, Korea under the ICTCCP program (IITP-2017-R0346-16-1007) and by KEIT under the GATC program (10077300).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Kwon, Y., Kim, E. (2018). Quantitative Model Checking for a Controller Design. In: Gallardo, M., Merino, P. (eds) Model Checking Software. SPIN 2018. Lecture Notes in Computer Science(), vol 10869. Springer, Cham. https://doi.org/10.1007/978-3-319-94111-0_17
Download citation
DOI: https://doi.org/10.1007/978-3-319-94111-0_17
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-94110-3
Online ISBN: 978-3-319-94111-0
eBook Packages: Computer ScienceComputer Science (R0)