Automated Synthesis of Safe and Robust PID Controllers for Stochastic Hybrid Systems Article Swipe

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Fedor Shmarov , Nicola Paoletti , Ezio Bartocci , Shan Lin , Scott A. Smolka , Paolo Zuliani ·

YOU? · · 2017 · Open Access · · DOI: https://doi.org/10.48550/arxiv.1707.05229

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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PID controller Control theory (sociology) Nonlinear system Computer science Lipschitz continuity Reachability Probabilistic logic Hybrid system Bounded function Controller (irrigation) Mathematical optimization Control engineering Mathematics Control (management) Engineering Algorithm Artificial intelligence Agronomy Physics Mathematical analysis Temperature control Quantum mechanics Biology Machine learning

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/1707.05229
PDF: https://arxiv.org/pdf/1707.05229
OA Status: green
Cited By: 2
References: 25
Related Works: 10
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DOI: https://doi.org/10.48550/arxiv.1707.05229

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Title: Automated Synthesis of Safe and Robust PID Controllers for Stochastic Hybrid Systems

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Type: preprint

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Language: en

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Publication year: 2017

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Publication date: 2017-07-17

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Authors: Fedor Shmarov, Nicola Paoletti, Ezio Bartocci, Shan Lin, Scott A. Smolka, Paolo Zuliani

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Landing page: https://arxiv.org/abs/1707.05229

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Concepts: PID controller, Control theory (sociology), Nonlinear system, Computer science, Lipschitz continuity, Reachability, Probabilistic logic, Hybrid system, Bounded function, Controller (irrigation), Mathematical optimization, Control engineering, Mathematics, Control (management), Engineering, Algorithm, Artificial intelligence, Agronomy, Physics, Mathematical analysis, Temperature control, Quantum mechanics, Biology, Machine learning

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Cited by: 2

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citation_normalized_percentile