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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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Authors and Affiliations
School of Computing, Newcastle University, Newcastle upon Tyne, UK
Fedor Shmarov & Paolo Zuliani
Department of Computer Science, Stony Brook University, Stony Brook, NY, USA
Nicola Paoletti & Scott A. Smolka
Faculty of Informatics, TU Wien, Wien, Austria
Ezio Bartocci
Department of Electrical and Computer Engineering, Stony Brook University, Stony Brook, NY, USA
Shan Lin
- Fedor Shmarov
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Correspondence toPaolo Zuliani.
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Technion - Israel Institute of Technology, Haifa, Israel
Ofer Strichman
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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