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SMT-based synthesis of safe and robust PID controllers for stochastic hybrid systems

Lookup NU author(s): Dr Fedor ShmarovORCiD, Dr Paolo Zuliani



This is the authors' accepted manuscript of a conference proceedings (inc. abstract) that has been published in its final definitive form by Springer Verlag, 2017.

For re-use rights please refer to the publisher's terms and conditions.


© Springer International Publishing AG 2017. 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.

Publication metadata

Author(s): Shmarov F, Paoletti N, Bartocci E, Lin S, Smolka SA, Zuliani P, Wright DJ

Editor(s): Ofer Strichman

Publication type: Conference Proceedings (inc. Abstract)

Publication status: Published

Conference Name: HVC 2017: Hardware and Software: Verification and Testing

Year of Conference: 2017

Pages: 131-146

Print publication date: 20/01/2018

Online publication date: 12/11/2017

Acceptance date: 01/09/2017

Date deposited: 24/01/2018

ISSN: 0302-9743

Publisher: Springer Verlag


DOI: 10.1007/978-3-319-70389-3_9

Library holdings: Search Newcastle University Library for this item

Series Title: Lecture Notes in Computer Science

ISBN: 9783319703886