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SMT-based Synthesis of Safe and Robust PID Controllers for Stochastic Hybrid Systems

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Part of the book series:Lecture Notes in Computer Science ((LNPSE,volume 10629))

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Abstract

We present a new method for the automated synthesis of safe and robust Proportional-Integral-Derivative (PID) controllers for stochastic hybrid systems. Despite their widespread use in industry, no automated method currently exists for deriving a PID controller (or any other type of controller, for that matter) with safety and performance guarantees for such a general class of systems. In particular, we consider hybrid systems with nonlinear dynamics (Lipschitz-continuous ordinary differential equations) and random parameters, and we synthesize PID controllers such that the resulting closed-loop systems satisfy safety and performance constraints given as probabilistic bounded reachability properties. Our technique leverages SMT solvers over the reals and nonlinear differential equations to provide formal guarantees that the synthesized controllers satisfy such properties. These controllers are also robust by design since they minimize the probability of reaching an unsafe state in the presence of random disturbances. We apply our approach to the problem of insulin regulation for type 1 diabetes, synthesizing controllers with robust responses to large random meal disturbances, thereby enabling them to maintain blood glucose levels within healthy, safe ranges.

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Author information

Authors and Affiliations

  1. School of Computing, Newcastle University, Newcastle upon Tyne, UK

    Fedor Shmarov & Paolo Zuliani

  2. Department of Computer Science, Stony Brook University, Stony Brook, NY, USA

    Nicola Paoletti & Scott A. Smolka

  3. Faculty of Informatics, TU Wien, Wien, Austria

    Ezio Bartocci

  4. Department of Electrical and Computer Engineering, Stony Brook University, Stony Brook, NY, USA

    Shan Lin

Authors
  1. Fedor Shmarov

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  2. Nicola Paoletti

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  3. Ezio Bartocci

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  4. Shan Lin

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  5. Scott A. Smolka

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  6. Paolo Zuliani

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Corresponding author

Correspondence toPaolo Zuliani.

Editor information

Editors and Affiliations

  1. Technion - Israel Institute of Technology, Haifa, Israel

    Ofer Strichman

  2. IBM Research Lab, Haifa, Israel

    Rachel Tzoref-Brill

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Shmarov, F., Paoletti, N., Bartocci, E., Lin, S., Smolka, S.A., Zuliani, P. (2017). SMT-based Synthesis of Safe and Robust PID Controllers for Stochastic Hybrid Systems. In: Strichman, O., Tzoref-Brill, R. (eds) Hardware and Software: Verification and Testing. HVC 2017. Lecture Notes in Computer Science(), vol 10629. Springer, Cham. https://doi.org/10.1007/978-3-319-70389-3_9

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JPY 5719
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