arXiv subjects

Andrew Clark

Publications and source records attributed to Andrew Clark.

At least 37 records · Page 2Linked to original sources

arXiv2024

Learning a Formally Verified Control Barrier Function in Stochastic Environment

Safety is a fundamental requirement of control systems. Control Barrier Functions (CBFs) are proposed to ensure the safety of the control system by constructing safety filters or synthesizing control inputs. However, the safety guarantee and performance of safe controllers rely on the construction of valid CBFs. Inspired by universal approximatability, CBFs are represented by neural networks, known as neural CBFs (NCBFs). This paper presents an algorithm for synthesizing formally verified continuous-time neural Control Barrier Functions in stochastic environments in a single step. The proposed training process ensures efficacy across the entire state space with only a finite number of data points by constructing a sample-based learning framework for Stochastic Neural CBFs (SNCBFs). Our methodology eliminates the need for post hoc verification by enforcing Lipschitz bounds on the neural network, its Jacobian, and Hessian terms. We demonstrate the effectiveness of our approach through case studies on the inverted pendulum system and obstacle avoidance in autonomous driving, showcasing larger safe regions compared to baseline methods.

cs.RO↗

arXiv2024

Fault Tolerant Neural Control Barrier Functions for Robotic Systems under Sensor Faults and Attacks

Safety is a fundamental requirement of many robotic systems. Control barrier function (CBF)-based approaches have been proposed to guarantee the safety of robotic systems. However, the effectiveness of these approaches highly relies on the choice of CBFs. Inspired by the universal approximation power of neural networks, there is a growing trend toward representing CBFs using neural networks, leading to the notion of neural CBFs (NCBFs). Current NCBFs, however, are trained and deployed in benign environments, making them ineffective for scenarios where robotic systems experience sensor faults and attacks. In this paper, we study safety-critical control synthesis for robotic systems under sensor faults and attacks. Our main contribution is the development and synthesis of a new class of CBFs that we term fault tolerant neural control barrier function (FT-NCBF). We derive the necessary and sufficient conditions for FT-NCBFs to guarantee safety, and develop a data-driven method to learn FT-NCBFs by minimizing a loss function constructed using the derived conditions. Using the learned FT-NCBF, we synthesize a control input and formally prove the safety guarantee provided by our approach. We demonstrate our proposed approach using two case studies: obstacle avoidance problem for an autonomous mobile robot and spacecraft rendezvous problem, with code available via https://github.com/HongchaoZhang-HZ/FTNCBF.

cs.RO↗

arXiv2023

Neural Lyapunov Control for Discrete-Time Systems

While ensuring stability for linear systems is well understood, it remains a major challenge for nonlinear systems. A general approach in such cases is to compute a combination of a Lyapunov function and an associated control policy. However, finding Lyapunov functions for general nonlinear systems is a challenging task. To address this challenge, several methods have been proposed that represent Lyapunov functions using neural networks. However, such approaches either focus on continuous-time systems, or highly restricted classes of nonlinear dynamics. We propose the first approach for learning neural Lyapunov control in a broad class of discrete-time systems. Three key ingredients enable us to effectively learn provably stable control policies. The first is a novel mixed-integer linear programming approach for verifying the discrete-time Lyapunov stability conditions, leveraging the particular structure of these conditions. The second is a novel approach for computing verified sublevel sets. The third is a heuristic gradient-based method for quickly finding counterexamples to significantly speed up Lyapunov function learning. Our experiments on four standard benchmarks demonstrate that our approach significantly outperforms state-of-the-art baselines. For example, on the path tracking benchmark, we outperform recent neural Lyapunov control baselines by an order of magnitude in both running time and the size of the region of attraction, and on two of the four benchmarks (cartpole and PVTOL), ours is the first automated approach to return a provably stable controller. Our code is available at: https://github.com/jlwu002/nlc_discrete.

cs.LG↗

arXiv2023

Almost-Sure Safety Guarantees of Stochastic Zero-Control Barrier Functions Do Not Hold

The 2021 paper "Control barrier functions for stochastic systems" provides theorems that give almost sure safety guarantees given stochastic zero control barrier function (ZCBF). Unfortunately, both the theorem and its proof is invalid. In this letter, we illustrate on a toy example that the almost sure safety guarantees for stochastic ZCBF do not hold and explain why the proof is flawed. Although stochastic reciprocal barrier functions (RCBF) also uses the same proof technique, we provide a different proof technique that verifies that stochastic RCBFs are indeed safe with probability one. Using the RCBF, we derive a modified ZCBF condition that guarantees safety with probability one. Finally, we provide some discussion on the role of unbounded controls in the almost-sure safety guarantees of RCBFs, and show that the rate of divergence of the ratio of the drift and diffusion is the key for whether a system has almost sure safety guarantees.

math.OC↗

arXiv2023

Exact Verification of ReLU Neural Control Barrier Functions

Control Barrier Functions (CBFs) are a popular approach for safe control of nonlinear systems. In CBF-based control, the desired safety properties of the system are mapped to nonnegativity of a CBF, and the control input is chosen to ensure that the CBF remains nonnegative for all time. Recently, machine learning methods that represent CBFs as neural networks (neural control barrier functions, or NCBFs) have shown great promise due to the universal representability of neural networks. However, verifying that a learned CBF guarantees safety remains a challenging research problem. This paper presents novel exact conditions and algorithms for verifying safety of feedforward NCBFs with ReLU activation functions. The key challenge in doing so is that, due to the piecewise linearity of the ReLU function, the NCBF will be nondifferentiable at certain points, thus invalidating traditional safety verification methods that assume a smooth barrier function. We resolve this issue by leveraging a generalization of Nagumo's theorem for proving invariance of sets with nonsmooth boundaries to derive necessary and sufficient conditions for safety. Based on this condition, we propose an algorithm for safety verification of NCBFs that first decomposes the NCBF into piecewise linear segments and then solves a nonlinear program to verify safety of each segment as well as the intersections of the linear segments. We mitigate the complexity by only considering the boundary of the safe region and by pruning the segments with Interval Bound Propagation (IBP) and linear relaxation. We evaluate our approach through numerical studies with comparison to state-of-the-art SMT-based methods. Our code is available at https://github.com/HongchaoZhang-HZ/exactverif-reluncbf-nips23.

cs.LG↗

arXiv2023

A Hybrid Submodular Optimization Approach to Controlled Islanding with Post-Disturbance Stability Guarantees

Disturbances may create cascading failures in power systems and lead to widespread blackouts. Controlled islanding is an effective approach to mitigate cascading failures by partitioning the power system into a set of disjoint islands. To retain the stability of the power system following disturbances, the islanding strategy should not only be minimally disruptive, but also guarantee post-disturbance stability. In this paper, we study the problem of synthesizing post-disturbance stability-aware controlled islanding strategies. To ensure post-disturbance stability, our computation of islanding strategies takes load-generation balance and transmission line capacity constraints into consideration, leading to a hybrid optimization problem with both discrete and continuous variables. To mitigate the computational challenge incurred when solving the hybrid optimization program, we propose the concepts of hybrid submodularity and hybrid matroid. We show that the islanding problem is equivalent to a hybrid matroid optimization program, whose objective function is hybrid supermodular. Leveraging the supermodularity property, we develop an efficient local search algorithm and show that the proposed algorithm achieves 1/2-optimality guarantee. We compare our approach with a baseline using mixed-integer linear program on IEEE 118-bus, IEEE 300-bus, ActivSg 500-bus, and Polish 2383-bus systems. Our results show that our approach outperforms the baseline in terms of the total cost incurred during islanding across all test cases. Furthermore, our proposed approach can find an islanding strategy for large-scale test cases such as Polish 2383-bus system, whereas the baseline approach becomes intractable.

math.OC↗

arXiv2023

Pre-processing training data improves accuracy and generalisability of convolutional neural network based landscape semantic segmentation

In this paper, we trialled different methods of data preparation for Convolutional Neural Network (CNN) training and semantic segmentation of land use land cover (LULC) features within aerial photography over the Wet Tropics and Atherton Tablelands, Queensland, Australia. This was conducted through trialling and ranking various training patch selection sampling strategies, patch and batch sizes and data augmentations and scaling. We also compared model accuracy through producing the LULC classification using a single pass of a grid of patches and averaging multiple grid passes and three rotated version of each patch. Our results showed: a stratified random sampling approach for producing training patches improved the accuracy of classes with a smaller area while having minimal effect on larger classes; a smaller number of larger patches compared to a larger number of smaller patches improves model accuracy; applying data augmentations and scaling are imperative in creating a generalised model able to accurately classify LULC features in imagery from a different date and sensor; and producing the output classification by averaging multiple grids of patches and three rotated versions of each patch produced and more accurate and aesthetic result. Combining the findings from the trials, we fully trained five models on the 2018 training image and applied the model to the 2015 test image with the output LULC classifications achieving an average kappa of 0.84 user accuracy of 0.81 and producer accuracy of 0.87. This study has demonstrated the importance of data pre-processing for developing a generalised deep-learning model for LULC classification which can be applied to a different date and sensor. Future research using CNN and earth observation data should implement the findings of this study to increase LULC model accuracy and transferability.

cs.CV↗

arXiv2023

Risk-Aware Distributed Multi-Agent Reinforcement Learning

Autonomous cyber and cyber-physical systems need to perform decision-making, learning, and control in unknown environments. Such decision-making can be sensitive to multiple factors, including modeling errors, changes in costs, and impacts of events in the tails of probability distributions. Although multi-agent reinforcement learning (MARL) provides a framework for learning behaviors through repeated interactions with the environment by minimizing an average cost, it will not be adequate to overcome the above challenges. In this paper, we develop a distributed MARL approach to solve decision-making problems in unknown environments by learning risk-aware actions. We use the conditional value-at-risk (CVaR) to characterize the cost function that is being minimized, and define a Bellman operator to characterize the value function associated to a given state-action pair. We prove that this operator satisfies a contraction property, and that it converges to the optimal value function. We then propose a distributed MARL algorithm called the CVaR QD-Learning algorithm, and establish that value functions of individual agents reaches consensus. We identify several challenges that arise in the implementation of the CVaR QD-Learning algorithm, and present solutions to overcome these. We evaluate the CVaR QD-Learning algorithm through simulations, and demonstrate the effect of a risk parameter on value functions at consensus.

cs.AI↗

arXiv2023

A Compositional Resilience Index for Computationally Efficient Safety Analysis of Interconnected Systems

Interconnected systems such as power systems and chemical processes are often required to satisfy safety properties in the presence of faults and attacks. Verifying safety of these systems, however, is computationally challenging due to nonlinear dynamics, high dimensionality, and combinatorial number of possible faults and attacks that can be incurred by the subsystems interconnected within the network. In this paper, we develop a compositional resilience index to verify safety properties of interconnected systems under faults and attacks. The resilience index is a tuple serving the following two purposes. First, it quantifies how a safety property is impacted when a subsystem is compromised by faults and attacks. Second, the resilience index characterizes the needed behavior of a subsystem during normal operations to ensure safety violations will not occur when future adverse events occur. We develop a set of sufficient conditions on the dynamics of each subsystem to satisfy its safety constraint, and leverage these conditions to formulate an optimization program to compute the resilience index. When multiple subsystems are interconnected and their resilience indices are given, we show that the safety constraints of the interconnected system can be efficiently verified by solving a system of linear inequalities. We demonstrate our developed resilience index using a numerical case study on chemical reactors connected in series.

eess.SY↗

arXiv2023

Cooperative Perception for Safe Control of Autonomous Vehicles under LiDAR Spoofing Attacks

Autonomous vehicles rely on LiDAR sensors to detect obstacles such as pedestrians, other vehicles, and fixed infrastructures. LiDAR spoofing attacks have been demonstrated that either create erroneous obstacles or prevent detection of real obstacles, resulting in unsafe driving behaviors. In this paper, we propose an approach to detect and mitigate LiDAR spoofing attacks by leveraging LiDAR scan data from other neighboring vehicles. This approach exploits the fact that spoofing attacks can typically only be mounted on one vehicle at a time, and introduce additional points into the victim's scan that can be readily detected by comparison from other, non-modified scans. We develop a Fault Detection, Identification, and Isolation procedure that identifies non-existing obstacle, physical removal, and adversarial object attacks, while also estimating the actual locations of obstacles. We propose a control algorithm that guarantees that these estimated object locations are avoided. We validate our framework using a CARLA simulation study, in which we verify that our FDII algorithm correctly detects each attack pattern.

eess.SY↗

arXiv2022

Diffraction imaging of light induced dynamics in xenon-doped helium nanodroplets

We have explored the light induced dynamics in superfluid helium nanodroplets with wide-angle scattering in a pump-probe measurement scheme. The droplets are doped with xenon atoms to facilitate the ignition of a nanoplasma through irradiation with near-infrared laser pulses. After a variable time delay of up to 800 ps, we image the subsequent dynamics using intense extreme ultraviolet pulses from the FERMI free-electron laser. The recorded scattering images exhibit complex intensity fluctuations that are categorized based on their characteristic features. Systematic simulations of wide-angle diffraction patterns are performed, which can qualitatively explain the observed features by employing model shapes with both randomly distributed as well as structured, symmetric distortions. This points to a connection between the dynamics and the positions of the dopants in the droplets. In particular, the structured fluctuations might be governed by an underlying array of quantized vortices in the superfluid droplet as has been observed in previous small-angle diffraction experiments. Our results provide a basis for further investigations of dopant-droplet interactions and associated heating mechanisms.

physics.atm-clus↗

arXiv2022

A Timing-Based Framework for Designing Resilient Cyber-Physical Systems under Safety Constraint

Cyber-physical systems (CPS) are required to satisfy safety constraints in various application domains such as robotics, industrial manufacturing systems, and power systems. Faults and cyber attacks have been shown to cause safety violations, which can damage the system and endanger human lives. Resilient architectures have been proposed to ensure safety of CPS under such faults and attacks via methodologies including redundancy and restarting from safe operating conditions. The existing resilient architectures for CPS utilize different mechanisms to guarantee safety, and currently there is no approach to compare them. Moreover, the analysis and design undertaken for CPS employing one architecture is not readily extendable to another. In this paper, we propose a timing-based framework for CPS employing various resilient architectures and develop a common methodology for safety analysis and computation of control policies and design parameters. Using the insight that the cyber subsystem operates in one out of a finite number of statuses, we first develop a hybrid system model that captures CPS adopting any of these architectures. Based on the hybrid system, we formulate the problem of joint computation of control policies and associated timing parameters for CPS to satisfy a given safety constraint and derive sufficient conditions for the solution. Utilizing the derived conditions, we provide an algorithm to compute control policies and timing parameters relevant to the employed architecture. We also note that our solution can be applied to a wide class of CPS with polynomial dynamics and also allows incorporation of new architectures. We verify our proposed framework by performing a case study on adaptive cruise control of vehicles.

eess.SY↗

arXiv2022

Abstraction-Free Control Synthesis to Satisfy Temporal Logic Constraints under Sensor Faults and Attacks

We study the problem of synthesizing a controller to satisfy a complex task in the presence of sensor faults and attacks. We model the task using Gaussian distribution temporal logic (GDTL), and propose a solution approach that does not rely on computing any finite abstraction to model the system. We decompose the GDTL specification into a sequence of reach-avoid sub-tasks. We develop a class of fault-tolerant finite time convergence control barrier functions (CBFs) to guarantee that a dynamical system reaches a set within finite time almost surely in the presence of malicious attacks. We use the fault-tolerant finite time convergence CBFs to guarantee the satisfaction of `reach' property. We ensure `avoid' part in each sub-task using fault-tolerant zeroing CBFs. These fault-tolerant CBFs formulate a set of linear constraints on the control input for each sub-task. We prove that if the error incurred by system state estimation is bounded by a certain threshold, then our synthesized controller fulfills each reach-avoid sub-task almost surely for any possible sensor fault and attack, and thus the GDTL specification is satisfied with probability one. We demonstrate our proposed approach using a numerical study on the coordination of two wheeled mobile robots.

eess.SY↗

arXiv2022

Barrier Certificate based Safe Control for LiDAR-based Systems under Sensor Faults and Attacks

Autonomous Cyber-Physical Systems (CPS) fuse proprioceptive sensors such as GPS and exteroceptive sensors including Light Detection and Ranging (LiDAR) and cameras for state estimation and environmental observation. It has been shown that both types of sensors can be compromised by malicious attacks, leading to unacceptable safety violations. We study the problem of safety-critical control of a LiDAR-based system under sensor faults and attacks. We propose a framework consisting of fault tolerant estimation and fault tolerant control. The former reconstructs a LiDAR scan with state estimations, and excludes the possible faulty estimations that are not aligned with LiDAR measurements. We also verify the correctness of LiDAR scans by comparing them with the reconstructed ones and removing the possibly compromised sector in the scan. Fault tolerant control computes a control signal with the remaining estimations at each time step. We prove that the synthesized control input guarantees system safety using control barrier certificates. We validate our proposed framework using a UAV delivery system in an urban environment. We show that our proposed approach guarantees safety for the UAV whereas a baseline fails.

eess.SY↗

arXiv2022

LQG Reference Tracking with Safety and Reachability Guarantees under Unknown False Data Injection Attacks

We investigate a linear quadratic Gaussian (LQG) tracking problem with safety and reachability constraints in the presence of an adversary who mounts an FDI attack on an unknown set of sensors. For each possible set of compromised sensors, we maintain a state estimator disregarding the sensors in that set, and calculate the optimal LQG control input at each time based on this estimate. We propose a control policy which constrains the control input to lie within a fixed distance of the optimal control input corresponding to each state estimate. The control input is obtained at each time step by solving a quadratically constrained quadratic program (QCQP). We prove that our policy can achieve a desired probability of safety and reachability using the barrier certificate method. Our control policy is evaluated via a numerical case study.

eess.SY↗

arXiv2022

Electrically pumped quantum-dot lasers grown on 300 mm patterned Si photonic wafers

Monolithic integration of quantum dot (QD) gain materials onto Si photonic platforms via direct epitaxial growth is a promising solution for on-chip light sources. Recent developments have demonstrated superior device reliability in blanket hetero-epitaxy of III-V devices on Si at elevated temperatures. Yet, thick, defect management epi designs prevent vertical light coupling from the gain region to the Si-on-Insulator (SOI) waveguides. Here, we demonstrate the first electrically pumped QD lasers grown on a 300 mm patterned (001) Si wafer with a butt-coupled configuration by molecular beam epitaxy (MBE). Unique growth and fabrication challenges imposed by the template architecture have been resolved, contributing to continuous wave lasing to 60 °C and a maximum double-side output power of 126.6 mW at 20 °C with a double-side wall plug efficiency of 8.6%. The potential for robust on-chip laser operation and efficient low-loss light coupling to Si photonic circuits makes this heteroepitaxial integration platform on Si promising for scalable and low-cost mass production.

physics.optics↗

arXiv2022

A Compositional Approach to Safety-Critical Resilient Control for Systems with Coupled Dynamics

Complex, interconnected Cyber-physical Systems (CPS) are increasingly common in applications including smart grids and transportation. Ensuring safety of interconnected systems whose dynamics are coupled is challenging because the effects of faults and attacks in one sub-system can propagate to other sub-systems and lead to safety violations. In this paper, we study the problem of safety-critical control for CPS with coupled dynamics when some sub-systems are subject to failure or attack. We first propose resilient-safety indices (RSIs) for the faulty or compromised sub-systems that bound the worst-case impacts of faulty or compromised sub-systems on a set of specified safety constraints. By incorporating the RSIs, we provide a sufficient condition for the synthesis of control policies in each failure- and attack- free sub-systems. The synthesized control policies compensate for the impacts of the faulty or compromised sub-systems to guarantee safety. We formulate sum-of-square optimization programs to compute the RSIs and the safety-ensuring control policies. We present a case study that applies our proposed approach on the temperature regulation of three coupled rooms. The case study demonstrates that control policies obtained using our algorithm guarantee system's safety constraints.

eess.SY↗

arXiv2022

An Analytical Framework for Control Synthesis of Cyber-Physical Systems with Safety Guarantee

Cyber-physical systems (CPS) are required to operate safely under fault and malicious attacks. The simplex architecture and the recently proposed cyber resilient architectures, e.g., Byzantine fault tolerant++ (BFT++), provide safety for CPS under faults and malicious cyber attacks, respectively. However, these existing architectures make use of different timing parameters and implementations to provide safety, and are seemingly unrelated. In this paper, we propose an analytical framework to represent the simplex, BFT++ and other practical cyber resilient architectures (CRAs). We construct a hybrid system that models CPS adopting any of these architectures. We derive sufficient conditions via our proposed framework under which a control policy is guaranteed to be safe. We present an algorithm to synthesize the control policy. We validate the proposed framework using a case study on lateral control of a Boeing 747, and demonstrate that our proposed approach ensures safety of the system.

eess.SY↗