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Register a new userRun-Time Safety Monitoring of Neural-Network-Enabled Dynamical Systems
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Weiming Xiang
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Complex dynamical systems rely on the correct deployment and operation of numerous components, with state-of-the-art methods relying on learning-enabled components in various stages of modeling, sensing, and control at both offline and online levels. This paper addresses the run-time safety monitoring problem of dynamical systems embedded with neural network components. A run-time safety state estimator in the form of an interval observer is developed to construct lower-bound and upper-bound of system state trajectories in run time. The developed run-time safety state estimator consists of two auxiliary neural networks derived from the neural network embedded in dynamical systems, and observer gains to ensure the positivity, namely the ability of estimator to bound the system state in run time, and the convergence of the corresponding error dynamics. The design procedure is formulated in terms of a family of linear programming feasibility problems. The developed method is illustrated by a numerical example and is validated with evaluations on an adaptive cruise control system.
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The deployment of autonomous systems that operate in unstructured environments necessitates algorithms to verify their safety. This can be challenging due to, e.g., black-box components in the control software, or undermodelled dynamics that prevent model-based verification. We present a novel verification framework for an unknown dynamical system from a given set of noisy observations of the dynamics. Using Gaussian processes trained on this data set, the framework abstracts the system as an uncertain Markov process with discrete states defined over the safe set. The transition bounds of the abstraction are derived from the probabilistic error bounds between the regression and underlying system. An existing approach for verifying safety properties over uncertain Markov processes then generates safety guarantees. We demonstrate the versatility of the framework on several examples, including switched and nonlinear systems.
Given a stochastic dynamical system modelled via stochastic differential equations (SDEs), we evaluate the safety of the system through characterisations of its exit time moments. We lift the (possibly nonlinear) dynamics into the space of the occupation and exit measures to obtain a set of linear evolution equations which depend on the infinitesimal generator of the SDE. Coupled with appropriate semidefinite positive matrix constraints, this yields a moment-based approach for the computation of exit time moments of SDEs with polynomial drift and diffusion dynamics. To extend the capability of the moment approach, we propose a state augmentation method which allows us to generate the evolution equations for a broader class of nonlinear stochastic systems and apply the moment method to previously unsupported dynamics. In particular, we show a general augmentation strategy for sinusoidal dynamics which can be found in most physical systems. We employ the methodology on an Ornstein-Uhlenbeck process and stochastic spring-mass-damper model to characterise their safety via their expected exit times and show the additional exit distribution insights that are afforded through higher order moments.
In this paper, we study the robustness of safety properties of a linear dynamical system with respect to model uncertainties. Our paper involves three parts. In the first part, we provide symbolic (analytical) and numerical (representation based) techniques for computing the reachable set of uncertain linear systems. We further prove a relationship between the reachable set of a linear uncertain system and the maximum singular value of the uncertain dynamics matrix. Finally, we propose two heuristics to compute the robustness threshold of the system -- the maximum uncertainty that can be introduced to the system without violating the safety property. We evaluate the reachable set computation techniques, effects of singular values, and estimation of robustness threshold on two case studies from varied domains, illustrating the applicability, practicality and scalability of the artifacts, proposed in this paper, on real-world examples. We further evaluate our artifacts on several linear dynamical system benchmarks. To the best of the authors knowledge, this is the first work to: (i) extend perturbation theory to compute reachable sets of linear uncertain systems, (ii) leverage the relationship between the reachable set of a linear system and the maximum singular values to determine the effect of uncertainties and (3) estimate the threshold of robustness that can be tolerated by the system while remaining safe.
Neural networks have been increasingly applied for control in learning-enabled cyber-physical systems (LE-CPSs) and demonstrated great promises in improving system performance and efficiency, as well as reducing the need for complex physical models. However, the lack of safety guarantees for such neural network based controllers has significantly impeded their adoption in safety-critical CPSs. In this work, we propose a controller adaptation approach that automatically switches among multiple controllers, including neural network controllers, to guarantee system safety and improve energy efficiency. Our approach includes two key components based on formal methods and machine learning. First, we approximate each controller with a Bernstein-polynomial based hybrid system model under bounded disturbance, and compute a safe invariant set for each controller based on its corresponding hybrid system. Intuitively, the invariant set of a controller defines the state space where the system can always remain safe under its control. The union of the controllers invariants sets then define a safe adaptation space that is larger than (or equal to) that of each controller. Second, we develop a deep reinforcement learning method to learn a controller switching strategy for reducing the control/actuation energy cost, while with the help of a safety guard rule, ensuring that the system stays within the safe space. Experiments on a linear adaptive cruise control system and a non-linear Van der Pols oscillator demonstrate the effectiveness of our approach on energy saving and safety enhancement.
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