arXiv subjects

Samuel Coogan

Publications and source records attributed to Samuel Coogan.

At least 55 records · Page 3Linked to original sources

arXiv2023

A Contracting Dynamical System Perspective toward Interval Markov Decision Processes

Interval Markov decision processes are a class of Markov models where the transition probabilities between the states belong to intervals. In this paper, we study the problem of efficient estimation of the optimal policies in Interval Markov Decision Processes (IMDPs) with continuous action-space. Given an IMDP, we show that the pessimistic (resp. the optimistic) value iterations, i.e., the value iterations under the assumption of a competitive adversary (resp. cooperative agent), are monotone dynamical systems and are contracting with respect to the $\ell_{\infty}$-norm. Inspired by this dynamical system viewpoint, we introduce another IMDP, called the action-space relaxation IMDP. We show that the action-space relaxation IMDP has two key features: (i) its optimal value is an upper bound for the optimal value of the original IMDP, and (ii) its value iterations can be efficiently solved using tools and techniques from convex optimization. We then consider the policy optimization problems at each step of the value iterations as a feedback controller of the value function. Using this system-theoretic perspective, we propose an iteration-distributed implementation of the value iterations for approximating the optimal value of the action-space relaxation IMDP.

eess.SY↗

arXiv2023

Interval Reachability of Nonlinear Dynamical Systems with Neural Network Controllers

This paper proposes a computationally efficient framework, based on interval analysis, for rigorous verification of nonlinear continuous-time dynamical systems with neural network controllers. Given a neural network, we use an existing verification algorithm to construct inclusion functions for its input-output behavior. Inspired by mixed monotone theory, we embed the closed-loop dynamics into a larger system using an inclusion function of the neural network and a decomposition function of the open-loop system. This embedding provides a scalable approach for safety analysis of the neural control loop while preserving the nonlinear structure of the system. We show that one can efficiently compute hyper-rectangular over-approximations of the reachable sets using a single trajectory of the embedding system. We design an algorithm to leverage this computational advantage through partitioning strategies, improving our reachable set estimates while balancing its runtime with tunable parameters. We demonstrate the performance of this algorithm through two case studies. First, we demonstrate this method's strength in complex nonlinear environments. Then, we show that our approach matches the performance of the state-of-the art verification algorithm for linear discretized systems.

eess.SY↗

arXiv2023

A Toolbox for Fast Interval Arithmetic in numpy with an Application to Formal Verification of Neural Network Controlled Systems

In this paper, we present a toolbox for interval analysis in numpy, with an application to formal verification of neural network controlled systems. Using the notion of natural inclusion functions, we systematically construct interval bounds for a general class of mappings. The toolbox offers efficient computation of natural inclusion functions using compiled C code, as well as a familiar interface in numpy with its canonical features, such as n-dimensional arrays, matrix/vector operations, and vectorization. We then use this toolbox in formal verification of dynamical systems with neural network controllers, through the composition of their inclusion functions.

eess.SY↗

arXiv2023

GreenEVT: Greensboro Electric Vehicle Testbed

The ongoing electrification of the transportation fleet will increase the load on the electric power grid. Since both the transportation network and the power grid already experience periods of significant stress, joint analyses of both infrastructures will most likely be necessary to ensure acceptable operation in the future. To enable such analyses, this paper presents an open-source testbed that jointly simulates high-fidelity models of both the electric distribution system and the transportation network. The testbed utilizes two open-source simulators, OpenDSS to simulate the electric distribution system and the microscopic traffic simulator SUMO to simulate the traffic dynamics. Electric vehicle charging links the electric distribution system and the transportation network models at vehicle locations determined using publicly available parcel data. Leveraging high-fidelity synthetic electric distribution system data from the SMART-DS project and transportation system data from OpenStreetMap, this testbed models the city of Greensboro, NC down to the household level. Moreover, the methodology and the supporting scripts released with the testbed allow adaption to other areas where high-fidelity geolocated OpenDSS datasets are available. After describing the components and usage of the testbed, we exemplify applications enabled by the testbed via two scenarios modeling the extreme stresses encountered during evacuations.

eess.SY↗

arXiv2022

Model Free Barrier Functions via Implicit Evading Maneuvers

This paper demonstrates that the safety override arising from the use of a barrier function can in some cases be needlessly restrictive. In particular, we examine the case of fixed-wing collision avoidance and show that when using a barrier function, there are cases where two fixed-wing aircraft can come closer to colliding than if there were no barrier function at all. In addition, we construct cases where the barrier function labels the system as unsafe even when the vehicles start arbitrarily far apart. In other words, the barrier function ensures safety but with unnecessary costs to performance. We therefore introduce model-free barrier functions which take a data driven approach to creating a barrier function. We demonstrate the effectiveness of model-free barrier functions in a collision avoidance simulation of two fixed-wing aircraft.

cs.LG↗

arXiv2022

Leveraging Heterogeneous Capabilities in Multi-Agent Systems for Environmental Conflict Resolution

In this paper, we introduce a high-level controller synthesis framework that enables teams of heterogeneous agents to assist each other in resolving environmental conflicts that appear at runtime. This conflict resolution method is built upon temporal-logic-based reactive synthesis to guarantee safety and task completion under specific environment assumptions. In heterogeneous multi-agent systems, every agent is expected to complete its own tasks in service of a global team objective. However, at runtime, an agent may encounter un-modeled obstacles (e.g., doors or walls) that prevent it from achieving its own task. To address this problem, we employ the capabilities of other heterogeneous agents to resolve the obstacle. A controller framework is proposed to redirect agents with the capability of resolving the appropriate obstacles to the required target when such a situation is detected. Three case studies involving a bipedal robot Digit and a quadcopter are used to evaluate the controller performance in action. Additionally, we implement the proposed framework on a physical multi-agent robotic system to demonstrate its viability for real world applications.

cs.RO↗

arXiv2022

Robust Training and Verification of Implicit Neural Networks: A Non-Euclidean Contractive Approach

This paper proposes a theoretical and computational framework for training and robustness verification of implicit neural networks based upon non-Euclidean contraction theory. The basic idea is to cast the robustness analysis of a neural network as a reachability problem and use (i) the $\ell_{\infty}$-norm input-output Lipschitz constant and (ii) the tight inclusion function of the network to over-approximate its reachable sets. First, for a given implicit neural network, we use $\ell_{\infty}$-matrix measures to propose sufficient conditions for its well-posedness, design an iterative algorithm to compute its fixed points, and provide upper bounds for its $\ell_\infty$-norm input-output Lipschitz constant. Second, we introduce a related embedded network and show that the embedded network can be used to provide an $\ell_\infty$-norm box over-approximation of the reachable sets of the original network. Moreover, we use the embedded network to design an iterative algorithm for computing the upper bounds of the original system's tight inclusion function. Third, we use the upper bounds of the Lipschitz constants and the upper bounds of the tight inclusion functions to design two algorithms for the training and robustness verification of implicit neural networks. Finally, we apply our algorithms to train implicit neural networks on the MNIST dataset and compare the robustness of our models with the models trained via existing approaches in the literature.

cs.LG↗

arXiv2022

Safe Schedule Verification for Urban Air Mobility Networks with Node Closures

In Urban Air Mobility (UAM) networks, takeoff and landing sites, called vertiports, are likely to experience intermittent closures due to, e.g., adverse weather. To ensure safety, all in-flight Urban Air Vehicles (UAVs) in a UAM network must therefore have alternative landing sites with sufficient landing capacity in the event of a vertiport closure. In this paper, we study the problem of safety verification of UAM schedules in the face of vertiport closures. We first provide necessary and sufficient conditions for a given UAM schedule to be safe in the sense that, if a vertiport closure occurs, then all UAVs will be able to safely land at a backup landing site. Next, we convert these conditions to an efficient algorithm for verifying safety of a UAM schedule via a linear program by using properties of totally unimodular matrices. Our algorithm allows for uncertain travel time between UAM vertiports and scales quadratically with the number of scheduled UAVs. We demonstrate our algorithm on a UAM network with up to 1,000 UAVs.

eess.SY↗

arXiv2022

Run Time Assurance for Safety-Critical Systems: An Introduction to Safety Filtering Approaches for Complex Control Systems

Run Time Assurance (RTA) Systems are online verification mechanisms that filter an unverified primary controller output to ensure system safety. The primary control may come from a human operator, an advanced control approach, or an autonomous control approach that cannot be verified to the same level as simpler control systems designs. The critical feature of RTA systems is their ability to alter unsafe control inputs explicitly to assure safety. In many cases, RTA systems can functionally be described as containing a monitor that watches the state of the system and output of a primary controller, and a backup controller that replaces or modifies control input when necessary to assure safety. An important quality of an RTA system is that the assurance mechanism is constructed in a way that is entirely agnostic to the underlying structure of the primary controller. By effectively decoupling the enforcement of safety constraints from performance-related objectives, RTA offers a number of useful advantages over traditional (offline) verification. This article provides a tutorial on developing RTA systems.

eess.SY↗

arXiv2022

Safe Learning for Uncertainty-Aware Planning via Interval MDP Abstraction

We study the problem of refining satisfiability bounds for partially-known stochastic systems against planning specifications defined using syntactically co-safe Linear Temporal Logic (scLTL). We propose an abstraction-based approach that iteratively generates high-confidence Interval Markov Decision Process (IMDP) abstractions of the system from high-confidence bounds on the unknown component of the dynamics obtained via Gaussian process regression. In particular, we develop a synthesis strategy to sample the unknown dynamics by finding paths which avoid specification-violating states using a product IMDP. We further provide a heuristic to choose among various candidate paths to maximize the information gain. Finally, we propose an iterative algorithm to synthesize a satisfying control policy for the product IMDP system. We demonstrate our work with a case study on mobile robot navigation.

eess.SY↗

arXiv2022

Comparative Analysis of Interval Reachability for Robust Implicit and Feedforward Neural Networks

We use interval reachability analysis to obtain robustness guarantees for implicit neural networks (INNs). INNs are a class of implicit learning models that use implicit equations as layers and have been shown to exhibit several notable benefits over traditional deep neural networks. We first establish that tight inclusion functions of neural networks, which provide the tightest rectangular over-approximation of an input-output map, lead to sharper robustness guarantees than the well-studied robustness measures of local Lipschitz constants. Like Lipschitz constants, tight inclusions functions are computationally challenging to obtain, and we thus propose using mixed monotonicity and contraction theory to obtain computationally efficient estimates of tight inclusion functions for INNs. We show that our approach performs at least as well as, and generally better than, applying state-of-the-art interval bound propagation methods to INNs. We design a novel optimization problem for training robust INNs and we provide empirical evidence that suitably-trained INNs can be more robust than comparably-trained feedforward networks.

cs.LG↗

arXiv2022

Resilience of Input Metering in Dynamic Flow Networks

In this paper, we study robustness of input metering policies in dynamic flow networks in the presence of transient disturbances and attacks. We consider a compartmental model for dynamic flow networks with a First-In-First-Out (FIFO) routing rule as found in, e.g., transportation networks. We model the effect of the transient disturbance as an abrupt change to the state of the network and use the notion of the region of attraction to measure the resilience of the network to these changes. For constant and periodic input metering, we introduce the notion of monotone-invariant points to establish inner-estimates for the regions of attraction of free-flow equilibrium points and free-flow periodic orbits using monotone systems theory. These results are applicable to, e.g., networks with cycles, which have not been considered in prior literature on dynamic flow networks with FIFO routing. Finally, we propose two approaches for finding suitable monotone-invariant points in the flow networks with FIFO rules.

math.OC↗

arXiv2021

Robustness Certificates for Implicit Neural Networks: A Mixed Monotone Contractive Approach

Implicit neural networks are a general class of learning models that replace the layers in traditional feedforward models with implicit algebraic equations. Compared to traditional learning models, implicit networks offer competitive performance and reduced memory consumption. However, they can remain brittle with respect to input adversarial perturbations. This paper proposes a theoretical and computational framework for robustness verification of implicit neural networks; our framework blends together mixed monotone systems theory and contraction theory. First, given an implicit neural network, we introduce a related embedded network and show that, given an $\ell_\infty$-norm box constraint on the input, the embedded network provides an $\ell_\infty$-norm box overapproximation for the output of the given network. Second, using $\ell_{\infty}$-matrix measures, we propose sufficient conditions for well-posedness of both the original and embedded system and design an iterative algorithm to compute the $\ell_{\infty}$-norm box robustness margins for reachability and classification problems. Third, of independent value, we propose a novel relative classifier variable that leads to tighter bounds on the certified adversarial robustness in classification problems. Finally, we perform numerical simulations on a Non-Euclidean Monotone Operator Network (NEMON) trained on the MNIST dataset. In these simulations, we compare the accuracy and run time of our mixed monotone contractive approach with the existing robustness verification approaches in the literature for estimating the certified adversarial robustness.

cs.LG↗

arXiv2021

Sensitivity to User Mischaracterizations in Electric Vehicle Charging

In this paper, we consider electric vehicle charging facilities that offer various levels of service for varying prices such that rational users choose a level of service that minimizes the total cost to themselves including an opportunity cost that incorporates users' value of time. In this setting, we study the sensitivity of the expected occupancy at the facility to mischaracterizations of user profiles and uncharacterized heterogeneity. For user profile mischaracterizations, we first provide a fundamental upper bound for the difference between the expected occupancy under any two different distributions on a user's impatience (i.e., value of time) that only depends on the minimum and maximum charging rate offered by the charging facility. Next, we consider the case when a user's impatience is a discrete random variable and study the sensitivity of the expected occupancy to the probability masses and attained values of the random variable. We show that the expected occupancy varies linearly with respect to the probability masses and is piecewise constant with respect to the attained values. Furthermore, we study the effects on the expected occupancy from the occurrence of heterogeneous user populations. In particular, we quantify the effect on the expected occupancy from the existence of sub-populations that may only select a subset of the offered service levels. Lastly, we quantify the variability of early departures on the expected occupancy. These results demonstrate how the facility operator might design prices such that the expected occupancy does not vary much under small changes in the distribution of a user's impatience, variable and limited user service needs, or uncharacterized early departure, quantities which are generally difficult to characterize accurately from data. We further demonstrate our results via examples.

eess.SY↗

arXiv2021

The Strong Integral Input-to-State Stability Property in Dynamical Flow Networks

Dynamical flow networks serve as macroscopic models for, e.g., transportation networks, queuing networks, and distribution networks. While the flow dynamics in such networks follow the conservation of mass on the links, the outflow from each link is often non-linear due to, e.g., flow capacity constraints and simultaneous service rate constraints. Such non-linear constraints imply a limit on the magnitude of exogenous inflow that is able to be accommodated by the network before it becomes overloaded and its state trajectory diverges. This paper shows how the Strong integral Input-to-State Stability (Strong iISS) property allows for quantifying the effects of the exogenous inflow on the flow dynamics. The Strong iISS property enables a unified stability analysis of classes of dynamical flow networks that were only partly analyzable before, such as networks with cycles, multi-commodity flow networks and networks with non-monotone flow dynamics. We present sufficient conditions on the maximum magnitude of exogenous inflow to guarantee input-to-state stability for a dynamical flow network, and we also present cases when this sufficient condition is necessary. The conditions are exemplified on a few existing dynamical flow network models, specifically, fluid queuing models with time-varying exogenous inflows and multi-commodity flow models.

eess.SY↗

arXiv2021

Composition of Safety Constraints For Fixed-Wing Collision Avoidance Amidst Limited Communications

This paper considers how to ensure that a system of fixed wing Unmanned Aerial Vehicles (UAVs) can avoid collisions. To do so we develop a novel method for creating a barrier function, which is similar to a Lyapunov function and can be used to ensure that a system can stay safe for all future times. After introducing the general approach, it is shown how to ensure that collision avoidance for two vehicles can be guaranteed for all future times. The construction is then extended to the case of arbitrarily many vehicles by addressing how to satisfy multiple safety objectives simultaneously. We do this while ensuring output actuator commands are within specified limits. Because this formulation requires communication of control values and may therefore reduce throughput of other important messages, we then show how to reformulate the solution without this significant communication overhead while still ensuring safety is maintained and actuator limits are respected. We validate the theoretical developments of this paper in the simulator SCRIMMAGE with a simulation of 20 UAVs that maintain safe distances from each other even though their nominal paths would otherwise cause a collision.

cs.RO↗

arXiv2021

Capacity-Constrained Urban Air Mobility Scheduling

This paper studies the problem of scheduling urban air mobility trips when travel times are uncertain and capacity at destinations is limited. Urban air mobility, in which air transportation is used for relatively short trips within a city or region, is emerging as a possible component in future transportation networks. Destinations in urban air mobility networks, called vertiports or vertistops, typically have limited landing capacity, and, for safety, it must be guaranteed that an air vehicle will be able to land before it can be allowed to take off. We first present a tractable model of urban air mobility networks that accounts for limited landing capacity and uncertain travel times between destinations with lower and upper travel time bounds. We then establish theoretical bounds on the achievable throughput of the network. Next, we present a tractable algorithm for scheduling trips to satisfy safety constraints and arrival deadlines. The algorithm allows for dynamically updating the schedule to accommodate, e.g., new demands over time. The paper concludes with case studies that demonstrate the algorithm on two networks.

math.OC↗

arXiv2021

On the Impact of the Capacity Drop Phenomenon for Freeway Traffic Flow Control

Capacity drop is an empirically observed phenomenon in vehicular traffic flow on freeways whereby, after a critical density is reached, a state of congestion sets in, but the freeway does not become decongested again until the density drops well below the critical density. This introduces a hysteresis effect so that it is easier to enter the congested state than to leave it. However, many existing first-order models of traffic flow, particularly those used for control design, ignore capacity drop, leading to suboptimal controllers. In this paper, we consider a cell transmission model of traffic flow that incorporates capacity drop to study the problem of optimal freeway ramp metering. We show that, if capacity drop is ignored in the control design, then the resulting controller, obtained via a convex program, may be significantly suboptimal. We then propose an alternative model predictive controller that accounts for capacity drop via a mixed integer linear program and show that, for sufficiently large rollout horizon, this controller is optimal. We also compare these approaches to a heuristic hand-crafted controller that is viewed as a modification of an integral feedback controller to account for capacity drop. This heuristic controller outperforms the controller that ignores capacity drop but underperforms compared to the proposed alternative model predictive controller. These results suggest that it is generally important to include capacity drop in the controller design process, and we demonstrate this insight on several case studies.

eess.SY↗