Learning Performance-Oriented Control Barrier Functions Under Complex Safety Constraints and Limited Actuation

Control Barrier Functions (CBFs) provide an elegant framework for designing safety filters for nonlinear control systems by constraining their trajectories to an invariant subset of a prespecified safe set. However, the task of finding a CBF that concurrently maximizes the volume of the resulting control invariant set while accommodating complex safety constraints, particularly in high relative degree systems with actuation constraints, continues to pose a substantial challenge. In this work, we propose a novel self-supervised learning framework that holistically addresses these hurdles. Given a Boolean composition of multiple state constraints that define the safe set, our approach starts with building a single continuously differentiable function whose 0-superlevel set provides an inner approximation of the safe set. We then use this function together with a smooth neural network to parameterize the CBF candidate. Finally, we design a training loss function based on a Hamilton-Jacobi partial differential equation to train the CBF while enlarging the volume of the induced control invariant set. We demonstrate the effectiveness of our approach via numerical experiments.Comment: This work was submitted to L4DC 202

Verification-Aided Learning of Neural Network Barrier Functions with Termination Guarantees

Barrier functions are a general framework for establishing a safety guarantee for a system. However, there is no general method for finding these functions. To address this shortcoming, recent approaches use self-supervised learning techniques to learn these functions using training data that are periodically generated by a verification procedure, leading to a verification-aided learning framework. Despite its immense potential in automating barrier function synthesis, the verification-aided learning framework does not have termination guarantees and may suffer from a low success rate of finding a valid barrier function in practice. In this paper, we propose a holistic approach to address these drawbacks. With a convex formulation of the barrier function synthesis, we propose to first learn an empirically well-behaved NN basis function and then apply a fine-tuning algorithm that exploits the convexity and counterexamples from the verification failure to find a valid barrier function with finite-step termination guarantees: if there exist valid barrier functions, the fine-tuning algorithm is guaranteed to find one in a finite number of iterations. We demonstrate that our fine-tuning method can significantly boost the performance of the verification-aided learning framework on examples of different scales and using various neural network verifiers.Comment: This is an online extended version of the same paper accepted to American Control Conference 202

DeepSplit: Scalable Verification of Deep Neural Networks via Operator Splitting

Analyzing the worst-case performance of deep neural networks against input perturbations amounts to solving a large-scale non-convex optimization problem, for which several past works have proposed convex relaxations as a promising alternative. However, even for reasonably-sized neural networks, these relaxations are not tractable, and so must be replaced by even weaker relaxations in practice. In this work, we propose a novel operator splitting method that can directly solve a convex relaxation of the problem to high accuracy, by splitting it into smaller sub-problems that often have analytical solutions. The method is modular and scales to problem instances that were previously impossible to solve exactly due to their size. Furthermore, the solver operations are amenable to fast parallelization with GPU acceleration. We demonstrate our method in obtaining tighter bounds on the worst-case performance of large convolutional networks in image classification and reinforcement learning settings

Safety Filter Design for Neural Network Systems via Convex Optimization

With the increase in data availability, it has been widely demonstrated that neural networks (NN) can capture complex system dynamics precisely in a data-driven manner. However, the architectural complexity and nonlinearity of the NNs make it challenging to synthesize a provably safe controller. In this work, we propose a novel safety filter that relies on convex optimization to ensure safety for a NN system, subject to additive disturbances that are capable of capturing modeling errors. Our approach leverages tools from NN verification to over-approximate NN dynamics with a set of linear bounds, followed by an application of robust linear MPC to search for controllers that can guarantee robust constraint satisfaction. We demonstrate the efficacy of the proposed framework numerically on a nonlinear pendulum system.Comment: This paper has been accepted to the 2023 62nd IEEE Conference on Decision and Control (CDC

Re-channelization of turbidity currents in South China Sea abyssal plain due to seamounts and ridges

Turbidity currents can be characterized as net-erosive, net-depositional or net-bypassing. Whether a flow is erosive, depositional or bypasses depends on the flow velocity, concentration and size but these can also be impacted by external controls such as the degree of confinement, slope gradient and substrate type and erodibility. Our understanding of the relative importance of these controls comes from laboratory experiments and numerical modelling, as well as from field data due to the proliferation of high-resolution 3D seismic and bathymetric data, as well as the outcrop and rock record. In this study, based on extensive multibeam and seismic reflection surveys in combination with International Ocean Discovery Program cores from the South China Sea, we document a new mechanism of turbidity current transformation from depositional to erosive resulting in channel incision. We show how confinement by seamounts and bedrock highs of previously unconfined turbidity currents has resulted in the development of seafloor channels. These channels are inferred to be the result of confinement of flows, which have traversed the abyssal plain, leading to flow acceleration allowing them to erode the seafloor substrate. This interpretation is further supported by the coarsening of flow deposits within the area of the seamounts, indicating that confinement has increased flow competency, allowing turbidity currents to carry larger volumes of coarse sediment which has been deposited in this region. This basin-scale depositional pattern suggests that pre-established basin topography can have an important control on sedimentation which can impact characteristics such as potential hydrocarbon storage

Improving detection and notification of tuberculosis cases in students in Shaanxi province, China: an intervention study

<p>Abstract</p> <p>Background</p> <p>Cooperation between different public and private health institutes involved in tuberculosis (TB) control has proven to enhance TB control in different settings. In China, such a mechanism has not been set up yet between Centers for Disease Control (CDCs) and university hospitals despite an increased TB incidence among students. This study aims to improve arrival of TB suspects identified by universities at the CDCs in order to manage them under standardized, directly observed treatment-short course (DOTS) conditions according to the National Tuberculosis Programme (NTP) guidelines.</p> <p>Methods</p> <p>Five matched pairs of universities were randomly assigned to the control and intervention group. After a baseline survey, a cooperation mechanism between local CDCs and university hospitals was set up in the intervention group. The effects on referral of TB suspects to the local CDC, tracing by the local CDC, and arrival at the local CDCs were assessed. Differences were tested by means of the chi-square test.</p> <p>Results</p> <p>During the baseline survey, the referral, tracing and arrival rates were between 37% and 46%. After implementation of the cooperation mechanism, these rates had not changed in the control group but increased significantly in the intervention group: the referral, tracing and arrival rates were 97%, 95%, and 93%, respectively.</p> <p>Conclusions</p> <p>It is feasible and effective to set up cooperation between CDCs and university hospitals to increase the number of TB suspects examined by CDCs and increase the number of TB patients treated under DOTS conditions. These public-public mix (PPM) activities should be expanded to cover all other university hospitals in China.</p

The protective effect of glycyrrhetinic acid on carbon tetrachloride-induced chronic liver fibrosis in mice via upregulation of Nrf2.

This study was designed to investigate the potentially protective effects of glycyrrhetinic acid (GA) and the role of transcription factor nuclear factor-erythroid 2(NF-E2)-related factor 2 (Nrf2) signaling in the regulation of Carbon Tetrachloride (CCl(4))-induced chronic liver fibrosis in mice. The potentially protective effects of GA on CCl(4)-induced chronic liver fibrosis in mice were depicted histologically and biochemically. Firstly, histopathological changes including regenerative nodules, inflammatory cell infiltration and fibrosis were induced by CCl(4).Then, CCl(4) administration caused a marked increase in the levels of serum aminotransferases (GOT, GPT), serum monoamine oxidase (MAO) and lipid peroxidation (MDA) as well as MAO in the mice liver homogenates. Also, decreased nuclear Nrf2 expression, mRNA levels of its target genes such as superoxide dismutase 3 (SOD3), catalase (CAT), glutathione peroxidase 2 (GPX2), and activity of cellular antioxidant enzymes were found after CCl(4) exposure. All of these phenotypes were markedly reversed by the treatment of the mice with GA. In addition, GA exhibited the antioxidant effects in vitro by on FeCl(2)-ascorbate induced lipid peroxidation in mouse liver homogenates, and on DPPH scavenging activity. Taken together, these results suggested that GA can protect the liver from oxidative stress in mice, presumably through activating the nuclear translocation of Nrf2, enhancing the expression of its target genes and increasing the activity of the antioxidant enzymes. Therefore, GA may be an effective hepatoprotective agent and viable candidate for treating liver fibrosis and other oxidative stress-related diseases