arXiv subjects

Taylor T. Johnson

Publications and source records attributed to Taylor T. Johnson.

At least 55 records · Page 3Linked to original sources

arXiv2022

An Empirical Analysis of the Use of Real-Time Reachability for the Safety Assurance of Autonomous Vehicles

Recent advances in machine learning technologies and sensing have paved the way for the belief that safe, accessible, and convenient autonomous vehicles may be realized in the near future. Despite tremendous advances within this context, fundamental challenges around safety and reliability are limiting their arrival and comprehensive adoption. Autonomous vehicles are often tasked with operating in dynamic and uncertain environments. As a result, they often make use of highly complex components, such as machine learning approaches, to handle the nuances of sensing, actuation, and control. While these methods are highly effective, they are notoriously difficult to assure. Moreover, within uncertain and dynamic environments, design time assurance analyses may not be sufficient to guarantee safety. Thus, it is critical to monitor the correctness of these systems at runtime. One approach for providing runtime assurance of systems with components that may not be amenable to formal analysis is the simplex architecture, where an unverified component is wrapped with a safety controller and a switching logic designed to prevent dangerous behavior. In this paper, we propose using a real-time reachability algorithm for the implementation of the simplex architecture to assure the safety of a 1/10 scale open source autonomous vehicle platform known as F1/10. The reachability algorithm that we leverage (a) provides provable guarantees of safety, and (b) is used to detect potentially unsafe scenarios. In our approach, the need to analyze an underlying controller is abstracted away, instead focusing on the effects of the controller's decisions on the system's future states. We demonstrate the efficacy of our architecture through a vast set of experiments conducted both in simulation and on an embedded hardware platform.

cs.RO↗

arXiv2021

The Occupation Kernel Method for Nonlinear System Identification

This manuscript presents a novel approach to nonlinear system identification leveraging densely defined Liouville operators and a new "kernel" function that represents an integration functional over a reproducing kernel Hilbert space (RKHS) dubbed an occupation kernel. The manuscript thoroughly explores the concept of occupation kernels in the contexts of RKHSs of continuous functions, and establishes Liouville operators over RKHS where several dense domains are found for specific examples of this unbounded operator. The combination of these two concepts allow for the embedding of a dynamical system into a RKHS, where function theoretic tools may be leveraged for the examination of such systems. This framework allows for trajectories of a nonlinear dynamical system to be treated as a fundamental unit of data for nonlinear system identification routine. The approach to nonlinear system identification is demonstrated to identify parameters of a dynamical system accurately, while also exhibiting a certain robustness to noise.

math.OC↗

arXiv2021

Dynamic Mode Decomposition for Continuous Time Systems with the Liouville Operator

Dynamic Mode Decomposition (DMD) has become synonymous with the Koopman operator, where continuous time dynamics are examined through a discrete time proxy determined by a fixed timestep using Koopman (i.e. composition) operators. Using the newly introduced "occupation kernels," the present manuscript develops an approach to DMD that treats continuous time dynamics directly through the Liouville operator, which can include Koopman generators. This manuscript outlines the technical and theoretical differences between Koopman based DMD for discrete time systems and Liouville based DMD for continuous time systems, which includes an examination of these operators over several reproducing kernel Hilbert spaces (RKHSs). While Liouville operators are modally unbounded, this manuscript introduces the concept of a scaled Liouville operator, which for many dynamical systems yields a compact operator over the exponential dot product kernel's native space. Hence, norm convergence of the DMD procedure is established when using scaled Liouville operators, which is a decided advantage over Koopman based DMD methods.

math.DS↗

arXiv2020

Verification of Deep Convolutional Neural Networks Using ImageStars

Convolutional Neural Networks (CNN) have redefined the state-of-the-art in many real-world applications, such as facial recognition, image classification, human pose estimation, and semantic segmentation. Despite their success, CNNs are vulnerable to adversarial attacks, where slight changes to their inputs may lead to sharp changes in their output in even well-trained networks. Set-based analysis methods can detect or prove the absence of bounded adversarial attacks, which can then be used to evaluate the effectiveness of neural network training methodology. Unfortunately, existing verification approaches have limited scalability in terms of the size of networks that can be analyzed. In this paper, we describe a set-based framework that successfully deals with real-world CNNs, such as VGG16 and VGG19, that have high accuracy on ImageNet. Our approach is based on a new set representation called the ImageStar, which enables efficient exact and over-approximative analysis of CNNs. ImageStars perform efficient set-based analysis by combining operations on concrete images with linear programming (LP). Our approach is implemented in a tool called NNV, and can verify the robustness of VGG networks with respect to a small set of input states, derived from adversarial attacks, such as the DeepFool attack. The experimental results show that our approach is less conservative and faster than existing zonotope methods, such as those used in DeepZ, and the polytope method used in DeepPoly.

cs.LG↗

arXiv2020

Reachable Set Estimation for Neural Network Control Systems: A Simulation-Guided Approach

The vulnerability of artificial intelligence (AI) and machine learning (ML) against adversarial disturbances and attacks significantly restricts their applicability in safety-critical systems including cyber-physical systems (CPS) equipped with neural network components at various stages of sensing and control. This paper addresses the reachable set estimation and safety verification problems for dynamical systems embedded with neural network components serving as feedback controllers. The closed-loop system can be abstracted in the form of a continuous-time sampled-data system under the control of a neural network controller. First, a novel reachable set computation method in adaptation to simulations generated out of neural networks is developed. The reachability analysis of a class of feedforward neural networks called multilayer perceptrons (MLP) with general activation functions is performed in the framework of interval arithmetic. Then, in combination with reachability methods developed for various dynamical system classes modeled by ordinary differential equations, a recursive algorithm is developed for over-approximating the reachable set of the closed-loop system. The safety verification for neural network control systems can be performed by examining the emptiness of the intersection between the over-approximation of reachable sets and unsafe sets. The effectiveness of the proposed approach has been validated with evaluations on a robotic arm model and an adaptive cruise control system.

eess.SY↗

arXiv2020

NNV: The Neural Network Verification Tool for Deep Neural Networks and Learning-Enabled Cyber-Physical Systems

This paper presents the Neural Network Verification (NNV) software tool, a set-based verification framework for deep neural networks (DNNs) and learning-enabled cyber-physical systems (CPS). The crux of NNV is a collection of reachability algorithms that make use of a variety of set representations, such as polyhedra, star sets, zonotopes, and abstract-domain representations. NNV supports both exact (sound and complete) and over-approximate (sound) reachability algorithms for verifying safety and robustness properties of feed-forward neural networks (FFNNs) with various activation functions. For learning-enabled CPS, such as closed-loop control systems incorporating neural networks, NNV provides exact and over-approximate reachability analysis schemes for linear plant models and FFNN controllers with piecewise-linear activation functions, such as ReLUs. For similar neural network control systems (NNCS) that instead have nonlinear plant models, NNV supports over-approximate analysis by combining the star set analysis used for FFNN controllers with zonotope-based analysis for nonlinear plant dynamics building on CORA. We evaluate NNV using two real-world case studies: the first is safety verification of ACAS Xu networks and the second deals with the safety verification of a deep learning-based adaptive cruise control system.

eess.SY↗

arXiv2019

Real-Time Verification for Distributed Cyber-Physical Systems

Safety-critical distributed cyber-physical systems (CPSs) have been found in a wide range of applications. Notably, they have displayed a great deal of utility in intelligent transportation, where autonomous vehicles communicate and cooperate with each other via a high-speed communication network. Such systems require an ability to identify maneuvers in real-time that cause dangerous circumstances and ensure the implementation always meets safety-critical requirements. In this paper, we propose a real-time decentralized reachability approach for safety verification of a distributed multi-agent CPS with the underlying assumption that all agents are time-synchronized with a low degree of error. In the proposed approach, each agent periodically computes its local reachable set and exchanges this reachable set with the other agents with the goal of verifying the system safety. Our method, implemented in Java, takes advantages of the timing information and the reachable set information that are available in the exchanged messages to reason about the safety of the whole system in a decentralized manner. Any particular agent can also perform local safety verification tasks based on their local clocks by analyzing the messages it receives. We applied the proposed method to verify, in real-time, the safety properties of a group of quadcopters performing a distributed search mission.

cs.MA↗

arXiv2019

Numerical Verification of Affine Systems with up to a Billion Dimensions

Affine systems reachability is the basis of many verification methods. With further computation, methods exist to reason about richer models with inputs, nonlinear differential equations, and hybrid dynamics. As such, the scalability of affine systems verification is a prerequisite to scalable analysis for more complex systems. In this paper, we improve the scalability of affine systems verification, in terms of the number of dimensions (variables) in the system. The reachable states of affine systems can be written in terms of the matrix exponential, and safety checking can be performed at specific time steps with linear programming. Unfortunately, for large systems with many state variables, this direct approach requires an intractable amount of memory while using an intractable amount of computation time. We overcome these challenges by combining several methods that leverage common problem structure. Memory is reduced by exploiting initial states that are not full-dimensional and safety properties (outputs) over a few linear projections of the state variables. Computation time is saved by using numerical simulations to compute only projections of the matrix exponential relevant for the verification problem. Since large systems often have sparse dynamics, we use Krylov-subspace simulation approaches based on the Arnoldi or Lanczos iterations. Our method produces accurate counter-examples when properties are violated and, in the extreme case with sufficient problem structure, can analyze a system with one billion real-valued state variables.

math.NA↗

arXiv2018

Specification-Guided Safety Verification for Feedforward Neural Networks

This paper presents a specification-guided safety verification method for feedforward neural networks with general activation functions. As such feedforward networks are memoryless, they can be abstractly represented as mathematical functions, and the reachability analysis of the neural network amounts to interval analysis problems. In the framework of interval analysis, a computationally efficient formula which can quickly compute the output interval sets of a neural network is developed. Then, a specification-guided reachability algorithm is developed. Specifically, the bisection process in the verification algorithm is completely guided by a given safety specification. Due to the employment of the safety specification, unnecessary computations are avoided and thus the computational cost can be reduced significantly. Experiments show that the proposed method enjoys much more efficiency in safety verification with significantly less computational cost.

cs.LG↗

arXiv2018

Verification for Machine Learning, Autonomy, and Neural Networks Survey

This survey presents an overview of verification techniques for autonomous systems, with a focus on safety-critical autonomous cyber-physical systems (CPS) and subcomponents thereof. Autonomy in CPS is enabling by recent advances in artificial intelligence (AI) and machine learning (ML) through approaches such as deep neural networks (DNNs), embedded in so-called learning enabled components (LECs) that accomplish tasks from classification to control. Recently, the formal methods and formal verification community has developed methods to characterize behaviors in these LECs with eventual goals of formally verifying specifications for LECs, and this article presents a survey of many of these recent approaches.

cs.AI↗

arXiv2018

Cyber-Physical Specification Mismatches

Embedded systems use increasingly complex software and are evolving into cyber-physical systems (CPS) with sophisticated interaction and coupling between physical and computational processes. Many CPS operate in safety-critical environments and have stringent certification, reliability, and correctness requirements. These systems undergo changes throughout their lifetimes, where either the software or physical hardware is updated in subsequent design iterations. One source of failure in safety-critical CPS is when there are unstated assumptions in either the physical or cyber parts of the system, and new components do not match those assumptions. In this work, we present an automated method towards identifying unstated assumptions in CPS. Dynamic specifications in the form of candidate invariants of both the software and physical components are identified using dynamic analysis (executing and/or simulating the system implementation or model thereof). A prototype tool called Hynger (for HYbrid iNvariant GEneratoR) was developed that instruments Simulink/Stateflow (SLSF) model diagrams to generate traces in the input format compatible with the Daikon invariant inference tool, which has been extensively applied to software systems. Hynger, in conjunction with Daikon, is able to detect candidate invariants of several CPS case studies. We use the running example of a DC-to-DC power converter, and demonstrate that Hynger can detect a specification mismatch where a tolerance assumed by the software is violated due to a plant change. Another case study of an automotive control system is also introduced to illustrate the power of Hynger and Daikon in automatically identifying cyber-physical specification mismatches.

eess.SY↗

arXiv2018

Reachability Analysis and Safety Verification for Neural Network Control Systems

Autonomous cyber-physical systems (CPS) rely on the correct operation of numerous components, with state-of-the-art methods relying on machine learning (ML) and artificial intelligence (AI) components in various stages of sensing and control. This paper develops methods for estimating the reachable set and verifying safety properties of dynamical systems under control of neural network-based controllers that may be implemented in embedded software. The neural network controllers we consider are feedforward neural networks called multilayer perceptrons (MLP) with general activation functions. As such feedforward networks are memoryless, they may be abstractly represented as mathematical functions, and the reachability analysis of the network amounts to range (image) estimation of this function provided a set of inputs. By discretizing the input set of the MLP into a finite number of hyper-rectangular cells, our approach develops a linear programming (LP) based algorithm for over-approximating the output set of the MLP with its input set as a union of hyper-rectangular cells. Combining the over-approximation for the output set of an MLP based controller and reachable set computation routines for ordinary difference/differential equation (ODE) models, an algorithm is developed to estimate the reachable set of the closed-loop system. Finally, safety verification for neural network control systems can be performed by checking the existence of intersections between the estimated reachable set and unsafe regions. The approach is implemented in a computational software prototype and evaluated on numerical examples.

eess.SY↗

arXiv2018

Simulation-Based Reachability Analysis for High-Index Large Linear Differential Algebraic Equations

Reachability analysis is a fundamental problem for safety verification and falsification of Cyber-Physical Systems (CPS) whose dynamics follow physical laws usually represented as differential equations. In the last two decades, numerous reachability analysis methods and tools have been proposed for a common class of dynamics in CPS known as ordinary differential equations (ODE). However, there is lack of methods dealing with differential algebraic equations (DAE) which is a more general class of dynamics that is widely used to describe a variety of problems from engineering and science such as multibody mechanics, electrical cicuit design, incompressible fluids, molecular dynamics and chemcial process control. Reachability analysis for DAE systems is more complex than ODE systems, especially for high-index DAEs because they contain both a differential part (i.e., ODE) and algebraic constraints (AC). In this paper, we extend the recent scalable simulation-based reachability analysis in combination with decoupling techniques for a class of high-index large linear DAEs. In particular, a high-index linear DAE is first decoupled into one ODE and one or several AC subsystems based on the well-known Marz decoupling method ultilizing admissible projectors. Then, the discrete reachable set of the DAE, represented as a list of star-sets, is computed using simulation. Unlike ODE reachability analysis where the initial condition is freely defined by a user, in DAE cases, the consistency of the inititial condition is an essential requirement to guarantee a feasible solution. Therefore, a thorough check for the consistency is invoked before computing the discrete reachable set. Our approach sucessfully verifies (or falsifies) a wide range of practical, high-index linear DAE systems in which the number of state variables varies from several to thousands.

cs.SC↗

arXiv2018

Output Reachable Set Estimation and Verification for Multi-Layer Neural Networks

In this paper, the output reachable estimation and safety verification problems for multi-layer perceptron neural networks are addressed. First, a conception called maximum sensitivity in introduced and, for a class of multi-layer perceptrons whose activation functions are monotonic functions, the maximum sensitivity can be computed via solving convex optimization problems. Then, using a simulation-based method, the output reachable set estimation problem for neural networks is formulated into a chain of optimization problems. Finally, an automated safety verification is developed based on the output reachable set estimation result. An application to the safety verification for a robotic arm model with two joints is presented to show the effectiveness of proposed approaches.

cs.LG↗

arXiv2018

Reachable Set Estimation and Safety Verification for Piecewise Linear Systems with Neural Network Controllers

In this work, the reachable set estimation and safety verification problems for a class of piecewise linear systems equipped with neural network controllers are addressed. The neural network is considered to consist of Rectified Linear Unit (ReLU) activation functions. A layer-by-layer approach is developed for the output reachable set computation of ReLU neural networks. The computation is formulated in the form of a set of manipulations for a union of polytopes. Based on the output reachable set for neural network controllers, the output reachable set for a piecewise linear feedback control system can be estimated iteratively for a given finite-time interval. With the estimated output reachable set, the safety verification for piecewise linear systems with neural network controllers can be performed by checking the existence of intersections of unsafe regions and output reach set. A numerical example is presented to illustrate the effectiveness of our approach.

eess.SY↗

arXiv2018

Reachable Set Estimation and Verification for Neural Network Models of Nonlinear Dynamic Systems

Neural networks have been widely used to solve complex real-world problems. Due to the complicate, nonlinear, non-convex nature of neural networks, formal safety guarantees for the behaviors of neural network systems will be crucial for their applications in safety-critical systems. In this paper, the reachable set estimation and verification problems for Nonlinear Autoregressive-Moving Average (NARMA) models in the forms of neural networks are addressed. The neural network involved in the model is a class of feed-forward neural networks called Multi-Layer Perceptron (MLP). By partitioning the input set of an MLP into a finite number of cells, a layer-by-layer computation algorithm is developed for reachable set estimation for each individual cell. The union of estimated reachable sets of all cells forms an over-approximation of reachable set of the MLP. Furthermore, an iterative reachable set estimation algorithm based on reachable set estimation for MLPs is developed for NARMA models. The safety verification can be performed by checking the existence of intersections of unsafe regions and estimated reachable set. Several numerical examples are provided to illustrate our approach.

eess.SY↗

arXiv2017

Reachable Set Computation and Safety Verification for Neural Networks with ReLU Activations

Neural networks have been widely used to solve complex real-world problems. Due to the complicate, nonlinear, non-convex nature of neural networks, formal safety guarantees for the output behaviors of neural networks will be crucial for their applications in safety-critical systems.In this paper, the output reachable set computation and safety verification problems for a class of neural networks consisting of Rectified Linear Unit (ReLU) activation functions are addressed. A layer-by-layer approach is developed to compute output reachable set. The computation is formulated in the form of a set of manipulations for a union of polyhedra, which can be efficiently applied with the aid of polyhedron computation tools. Based on the output reachable set computation results, the safety verification for a ReLU neural network can be performed by checking the intersections of unsafe regions and output reachable set described by a union of polyhedra. A numerical example of a randomly generated ReLU neural network is provided to show the effectiveness of the approach developed in this paper.

cs.LG↗

arXiv2016

Order-Reduction Abstractions for Safety Verification of High-Dimensional Linear Systems

Order-reduction is a standard automated approximation technique for computer-aided design, analysis, and simulation of many classes of systems, from circuits to buildings. For a given system, these methods produce a reduced-order system where the dimension of the state-space is smaller, while attempting to preserve behaviors similar to those of the full-order original system. To be used as a sound abstraction for formal verification, a measure of the similarity of behavior must be formalized and computed, which we develop in a computational way for a class of linear systems and periodically-switched systems as the main contributions of this paper. We have implemented the order-reduction as a sound abstraction process through a source-to-source model transformation in the HyST tool and use SpaceEx to compute sets of reachable states to verify properties of the full-order system through analysis of the reduced-order system. Our experimental results suggest systems with on the order of a thousand state variables can be reduced to systems with tens of state variables such that the order-reduction overapproximation error is small enough to prove or disprove safety properties of interest using current reachability analysis tools. Our results illustrate this approach is effective to alleviate the state-space explosion problem for verification of high-dimensional linear systems.

eess.SY↗