Automated Synthesis of Safe Digital Controllers for Sampled-Data Stochastic Nonlinear Systems

• Published in: IEEE access Vol. 8; pp. 180825 - 180843
• Main Authors: Shmarov, Fedor, Soudjani, Sadegh, Paoletti, Nicola, Bartocci, Ezio, Lin, Shan, Smolka, Scott A., Zuliani, Paolo
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Automation; Closed loop systems; Controllers; Dynamical systems; Evaluation; Feedback control; Formal controller synthesis; Lyapunov methods; Noise measurement; Nonlinear dynamics; Nonlinear systems; Optimal control; Optimization; Pancreas; parameter synthesis; Powertrain; probabilistic guarantees; Safety; safety verification; sampled-data nonlinear systems; satisfiability modulo theories; Stability analysis; statistical model checking; Stochastic processes; Stochastic systems; Synthesis; Systems analysis
• ISSN: 2169-3536; 2169-3536
• DOI: 10.1109/ACCESS.2020.3028476

We present a new method for the automated synthesis of digital controllers with formal safety guarantees for systems with nonlinear dynamics, noisy output measurements, and stochastic disturbances. Our method derives digital controllers such that the corresponding closed-loop system, modeled as a sampled-data stochastic control system, satisfies a safety specification with probability above a given threshold. Our technique uses a fast solver and an optimization method to search for candidate controllers, which are then formally evaluated in closed-loop with the system in question by a verified solver. Unstable candidate controllers are discarded by efficiently checking a sufficient condition for Lyapunov stability of sampled-data nonlinear systems. We evaluate our technique on three case studies: an artificial pancreas model, a powertrain control model, and a quadruple-tank process.