The Logical Path to Autonomous Cyber-Physical Systems

Autonomous cyber-physical systems are systems that combine the physics of motion with advanced cyber algorithms to act on their own without close human supervision. The present consensus is that reasonable levels of autonomy, such as for self-driving cars or autonomous drones, can only be reached with the help of artificial intelligence and machine learning algorithms that cope with the uncertainties of the real world. That makes safety assurance even more challenging than it already is in cyber-physical systems (CPSs) with classically programmed control, precisely because AI techniques are lauded for their flexibility in handling unpredictable situations, but are themselves harder to predict. This paper identifies the logical path toward autonomous cyber-physical systems in multiple steps. First, differential dynamic logic ( Open image in new window ) provides a logical foundation for developing cyber-physical system models with the mathematical rigor that their safety-critical nature demands. Then, its ModelPlex technique provides a logically correct way to tame the subtle relationship of CPS models to CPS implementations. Finally, the resulting logical monitor conditions can then be exploited to safeguard the decisions of learning agents, guide the optimization of learning processes, and resolve the nondeterminism frequently found in verification models. Overall, logic leads the way in combining the best of both worlds: the strong predictions that formal verification techniques provide alongside the strong flexibility that the use of AI provides.

[1]  Stefan Mitsch,et al.  A Formal Safety Net for Waypoint-Following in Ground Robots , 2019, IEEE Robotics and Automation Letters.

[2]  João Leite,et al.  Dynamic Doxastic Differential Dynamic Logic for Belief-Aware Cyber-Physical Systems , 2019, TABLEAUX.

[3]  Nathan Fulton,et al.  Safe AI for CPS (Invited Paper) , 2018, 2018 IEEE International Test Conference (ITC).

[4]  Claire J. Tomlin,et al.  Guaranteed Safe Online Learning via Reachability: tracking a ground target using a quadrotor , 2012, 2012 IEEE International Conference on Robotics and Automation.

[5]  Pushmeet Kohli,et al.  Training verified learners with learned verifiers , 2018, ArXiv.

[6]  A. Platzer,et al.  ModelPlex: verified runtime validation of verified cyber-physical system models , 2016, Formal Methods Syst. Des..

[7]  Andrew W. Moore,et al.  Reinforcement Learning: A Survey , 1996, J. Artif. Intell. Res..

[8]  Ashish Tiwari,et al.  Logic in Software, Dynamical and Biological Systems , 2011, 2011 IEEE 26th Annual Symposium on Logic in Computer Science.

[9]  George J. Pappas,et al.  Verification of Hybrid Systems , 2018, Handbook of Model Checking.

[10]  André Platzer,et al.  ModelPlex: verified runtime validation of verified cyber-physical system models , 2014, Formal Methods in System Design.

[11]  Nathan Fulton,et al.  Safe Reinforcement Learning via Formal Methods: Toward Safe Control Through Proof and Learning , 2018, AAAI.

[12]  André Platzer,et al.  Differential Dynamic Logic for Hybrid Systems , 2008, Journal of Automated Reasoning.

[13]  Junfeng Yang,et al.  Towards Practical Verification of Machine Learning: The Case of Computer Vision Systems , 2017, ArXiv.

[14]  André Platzer,et al.  How to model and prove hybrid systems with KeYmaera: a tutorial on safety , 2015, International Journal on Software Tools for Technology Transfer.

[15]  André Platzer,et al.  Verified Runtime Validation for Partially Observable Hybrid Systems , 2018, ArXiv.

[16]  André Platzer,et al.  VeriPhy: verified controller executables from verified cyber-physical system models , 2018, PLDI.

[17]  André Platzer,et al.  A Complete Uniform Substitution Calculus for Differential Dynamic Logic , 2016, Journal of Automated Reasoning.

[18]  Rajeev Alur,et al.  Formal verification of hybrid systems , 2011, 2011 Proceedings of the Ninth ACM International Conference on Embedded Software (EMSOFT).

[19]  Antoine Girard,et al.  SpaceEx: Scalable Verification of Hybrid Systems , 2011, CAV.

[20]  Nathan Fulton,et al.  Verifiably Safe Off-Model Reinforcement Learning , 2019, TACAS.

[21]  André Platzer,et al.  Logical Analysis of Hybrid Systems - Proving Theorems for Complex Dynamics , 2010 .

[22]  Thomas A. Henzinger,et al.  The Discipline of Embedded Systems Design , 2007, Computer.

[23]  André Platzer Logic & Proofs for Cyber-Physical Systems , 2016, IJCAR.

[24]  Kim G. Larsen,et al.  Verification and Performance Analysis for Embedded Systems , 2009, 2009 Third IEEE International Symposium on Theoretical Aspects of Software Engineering.

[25]  André Platzer,et al.  The Complete Proof Theory of Hybrid Systems , 2012, 2012 27th Annual IEEE Symposium on Logic in Computer Science.

[26]  Edmund M. Clarke,et al.  Bayesian statistical model checking with application to Stateflow/Simulink verification , 2013, Formal Methods Syst. Des..

[27]  Anil Nerode Logic and Control , 2007, CiE.

[28]  André Platzer,et al.  Formally verified differential dynamic logic , 2017, CPP.

[29]  Osbert Bastani,et al.  Safe Reinforcement Learning via Online Shielding , 2019, ArXiv.

[30]  George J. Pappas Wireless control networks: modeling, synthesis, robustness,security , 2011, HSCC '11.

[31]  Jean-Baptiste Jeannin,et al.  A formally verified hybrid system for safe advisories in the next-generation airborne collision avoidance system , 2016, International Journal on Software Tools for Technology Transfer.

[32]  Nathan Fulton,et al.  KeYmaera X: An Axiomatic Tactical Theorem Prover for Hybrid Systems , 2015, CADE.

[33]  André Platzer,et al.  Logics of Dynamical Systems , 2012, 2012 27th Annual IEEE Symposium on Logic in Computer Science.

[34]  Edmund M. Clarke,et al.  The Image Computation Problem in Hybrid Systems Model Checking , 2007, HSCC.

[35]  Sanjit A. Seshia,et al.  Compositional Falsification of Cyber-Physical Systems with Machine Learning Components , 2017, NFM.

[36]  André Platzer,et al.  Formal verification of obstacle avoidance and navigation of ground robots , 2016, Int. J. Robotics Res..

[37]  Edmund M. Clarke,et al.  Bayesian statistical model checking with application to Stateflow/Simulink verification , 2010, Formal Methods in System Design.

[38]  André Platzer,et al.  Logical Foundations of Cyber-Physical Systems , 2018, Springer International Publishing.

[39]  Pieter Collins Optimal Semicomputable Approximations to Reachable and Invariant Sets , 2006, Theory of Computing Systems.

[40]  Emilio Frazzoli,et al.  A Survey of Motion Planning and Control Techniques for Self-Driving Urban Vehicles , 2016, IEEE Transactions on Intelligent Vehicles.

[41]  Richard S. Sutton,et al.  Dimensions of Reinforcement Learning , 1998 .