Abstract
Abstraction-based control synthesis is a three-step process to solve a control problem for continuous-state system (difference equation or differential equation), by first abstracting this system into a finite transition system, solving the control problem on the abstraction, and finally refining the obtained controller to apply it to the continuous system. This chapter first provides an overview of the three steps of abstraction-based approaches and on the key role played by reachability analysis in the first step to create the finite abstraction. This approach is then illustrated on a docking problem for a marine vessel corresponding to a reach-avoid specification (reach the docking area in finite time while avoiding obstacles). This example highlights how the forward reachability analysis methods presented in this book can be used within such abstraction-based approaches to solve backward reachability problems.
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References
Baier C, Katoen JP (2008) Principles of model checking. MIT press
Belta C, Yordanov B, Gol EA (2017) Formal methods for discrete-time dynamical systems, vol 89. Springer
Boskos D, Dimarogonas DV (2019) Decentralized abstractions for multi-agent systems under coupled constraints. Eur J Control 45:1–16
Coogan S, Arcak M (2015) Efficient finite abstraction of mixed monotone systems. In: 18th international conference on hybrid systems: computation and control, pp 58–67
Coogan S, Arcak M, Belta C (2017) Formal methods for control of traffic flow: automated control synthesis from finite state transition models. IEEE Control Syst Mag 37(2):109–128
Dallal E, Tabuada P (2015) On compositional symbolic controller synthesis inspired by small-gain theorems. In: IEEE conference on decision and control, pp 6133–6138
Finucane C, Jing G, Kress-Gazit H (2010) LTLMoP: experimenting with language, temporal logic and robot control. In: IEEE/RSJ international conference on intelligent robots and systems. IEEE, pp 1988–1993
Girard A, Pola G, Tabuada P (2009) Approximately bisimilar symbolic models for incrementally stable switched systems. IEEE Trans Autom Control 55(1):116–126
Hsu K, Majumdar R, Mallik K, Schmuck AK (2018) Multi-layered abstraction-based controller synthesis for continuous-time systems. In: Proceedings of the 21st international conference on hybrid systems: computation and control, pp 120–129
Kim ES, Arcak M, Seshia SA (2015) Compositional controller synthesis for vehicular traffic networks. In: IEEE conference on decision and control, pp 6165–6171
Meyer PJ, Dimarogonas DV (2019) Hierarchical decomposition of LTL synthesis problem for nonlinear control systems. IEEE transactions on automatic control 64(11):4676–4683
Meyer PJ, Girard A, Witrant E (2017) Compositional abstraction and safety synthesis using overlapping symbolic models. IEEE Trans Autom Control 63(6):1835–1841
Meyer PJ, Yin H, Brodtkorb AH, Arcak M, Sørensen A.J (2020) Continuous and discrete abstractions for planning, applied to ship docking. In: Proceedings of the \(21^{st}\) IFAC world congress (virtual), pp 1857–1862
Mitchell IM, Bayen AM, Tomlin CJ (2005) A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games. IEEE Trans Autom Control 50(7):947–957
Moor T, Raisch J (2002) Abstraction based supervisory controller synthesis for high order monotone continuous systems. In: Modelling, analysis, and design of hybrid systems. Springer, pp 247–265
Mouelhi S, Girard A, Gössler G (2013) CoSyMA: a tool for controller synthesis using multi-scale abstractions. In: Proceedings of the 16th international conference on hybrid systems: computation and control, pp 83–88
Pola G, Pepe P, Di Benedetto MD (2016) Symbolic models for networks of control systems. IEEE Trans Autom Control 61(11):3663–3668
Reissig G (2010) Abstraction based solution of complex attainability problems for decomposable continuous plants. In: IEEE conference on decision and control, pp 5911–5917
Reissig G, Weber A, Rungger M (2016) Feedback refinement relations for the synthesis of symbolic controllers. IEEE Trans Autom Control 62(4):1781–1796
Sinyakov V, Girard A (2020) Abstraction of monotone systems based on feedback controllers. In: 21st IFAC world congress
Tabuada P (2009) Verification and control of hybrid systems: a symbolic approach. Springer Science & Business Media
Tumova J, Yordanov B, Belta C, Černá I, Barnat J (2010) A symbolic approach to controlling piecewise affine systems. In: 49th IEEE conference on decision and control. IEEE, pp 4230–4235
Wongpiromsarn T, Topcu U, Ozay N, Xu H, Murray RM (2011) TuLiP: a software toolbox for receding horizon temporal logic planning. In: Proceedings of the 14th international conference on hybrid systems: computation and control. ACM, pp 313–314
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Meyer, PJ., Devonport, A., Arcak, M. (2021). Abstraction-Based Control Synthesis. In: Interval Reachability Analysis. SpringerBriefs in Electrical and Computer Engineering(). Springer, Cham. https://doi.org/10.1007/978-3-030-65110-7_10
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DOI: https://doi.org/10.1007/978-3-030-65110-7_10
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