Resilience is a system's ability to maintain its function when perturbations and errors occur. Whilst we understand low-dimensional networked systems' behavior well, our understanding of systems consisting of a large number of components is limited. Recent research in predicting the network level resilience pattern has advanced our understanding of the coupling relationship between global network topology and local nonlinear component dynamics. However, when there is uncertainty in the model parameters, our understanding of how this translates to uncertainty in resilience is unclear for a large-scale networked system. Here we develop a polynomial chaos expansion method to estimate the resilience for a wide range of uncertainty distributions. By applying this method to case studies, we not only reveal the general resilience distribution with respect to the topology and dynamics sub-models, but also identify critical aspects to inform better monitoring to reduce uncertainty.
Resilience of coupled systems under deep uncertainty and dynamic complexity: An integrative literature review
Radboud University（拉德堡德大学）；Institute for Management Research（管理研究所）；University of Amsterdam（阿姆斯特丹大学）；Computational Science Institute（计算科学研究所）；Radboud University Medical Centre（拉德堡德大学医学中心）；Leiden University（莱顿大学）；Faculty of Governance and Global Affairs（治理与全球事务学院）；Erasmus University Rotterdam（鹿特丹伊拉斯姆斯大学）；Erasmus School of Social and Behavioural Sciences（伊拉斯姆斯社会与行为科学学院）
Certified Breathing Stability Regions in Nonlinear Dynamical Systems: Composite Lyapunov Certificates, M-Matrix Conditions, and a Resilience-Fragility Correspondence
Supply chains are the backbone of the global economy. Disruptions to them can be costly. Centrally managed supply chains invest in ensuring their resilience. Decentralized supply chains, however, must rely upon the self-interest of their individual components to maintain the resilience of the entire chain. We examine the incentives that independent self-interested agents have in forming a resilient supply chain network in the face of production disruptions and competition. In our model, competing suppliers are subject to yield uncertainty (they deliver less than ordered) and congestion (lead t…
In recent years, it has become crucial to improve the resilience of electricity distribution networks (DNs) against storm-induced failures. Microgrids enabled by Distributed Energy Resources (DERs) can significantly help speed up re-energization of loads, particularly in the complete absence of bulk power supply. We describe an integrated approach which considers a pre-storm DER allocation problem under the uncertainty of failure scenarios as well as a post-storm dispatch problem in microgrids during the multi-period repair of the failed components. This problem is computationally challenging …
Cyber-physical systems (CPS) incorporate the complex and large-scale engineered systems behind critical infrastructure operations, such as water distribution networks, energy delivery systems, healthcare services, manufacturing systems, and transportation networks. Industrial CPS in particular need to simultaneously satisfy requirements of available, secure, safe and reliable system operation against diverse threats, in an adaptive and sustainable way. These adverse events can be of accidental or malicious nature and may include natural disasters, hardware or software faults, cyberattacks, or …
Piecewise Barrier Tubes (PBT) is a new technique for flowpipe overapproximation for nonlinear systems with polynomial dynamics, which leverages a combination of barrier certificates. PBT has advantages over traditional time-step based methods in dealing with those nonlinear dynamical systems in which there is a large difference in speed between trajectories, producing an overapproximation that is time independent. However, the existing approach for PBT is not efficient due to the application of interval methods for enclosure-box computation, and it can only deal with continuous dynamical syste…
This paper studies the design of controllers that guarantee stability and safety of nonlinear control affine systems with parametric uncertainty in both the drift and control vector fields. To this end, we introduce novel classes of robust control barrier functions (RCBF) and robust control Lyapunov functions (RCLF) that facilitate the synthesis of safety-critical controllers in the presence of parametric uncertainty using quadratic programming. Since the initial bounds on the system uncertainty may be highly conservative, we present a data-driven approach to reducing such bounds using input-o…
Robust control is a core approach for controlling systems with performance guarantees that are robust to modeling error, and is widely used in real-world systems. However, current robust control approaches can only handle small system uncertainty, and thus require significant effort in system identification prior to controller design. We present an online approach that robustly controls a nonlinear system under large model uncertainty. Our approach is based on decomposing the problem into two sub-problems, "robust control design" (which assumes small model uncertainty) and "chasing consistent …
California Institute of Technology（加州理工学院）；University of California at Berkeley（加州大学伯克利分校）
Modern nonlinear control theory seeks to endow systems with properties such as stability and safety, and has been deployed successfully across various domains. Despite this success, model uncertainty remains a significant challenge in ensuring that model-based controllers transfer to real world systems. This paper develops a data-driven approach to robust control synthesis in the presence of model uncertainty using Control Certificate Functions (CCFs), resulting in a convex optimization based controller for achieving properties like stability and safety. An important benefit of our framework i…
California Institute of Technology（加州理工学院）；Jet Propulsion Laboratory（喷气推进实验室）
We present gPC-SCP: Generalized Polynomial Chaos-based Sequential Convex Programming to compute a sub-optimal solution for a continuous-time chance-constrained stochastic nonlinear optimal control (SNOC) problem. The approach enables motion planning for robotic systems under uncertainty. The gPC-SCP method involves two steps. The first step is to derive a surrogate problem of \emph{deterministic} nonlinear optimal control (DNOC) with convex constraints by using gPC expansion and the distributionally-robust convex subset of the chance constraints. The second step is to solve the DNOC problem us…
