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

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

Distributed adaptive fault-tolerant leader-following formation control of nonlinear uncertain second-order multi-agent systems

This paper presents a distributed integrated fault diagnosis and accommodation scheme for leader‐following formation control of a class of nonlinear uncertain second‐order multi‐agent systems. The fault model under consideration includes both process and actuator faults, which may evolve abruptly or incipiently. The time‐varying leader communicates with a small subset of follower agents, and each follower agent communicates to its directly connected neighbors through a bidirectional network with possibly asymmetric weights. A local fault diagnosis and accommodation component are designed for each agent in the distributed system, which consists of a fault detection and isolation module and a reconfigurable controller module comprised of a baseline controller and two adaptive fault‐tolerant controllers, activated after fault detection and after fault isolation, respectively. By using appropriately the designed Lyapunov functions, the closed‐loop stability and asymptotic convergence properties of the leader‐follower formation are rigorously established under different modes of the fault‐tolerant control system

Safe Control for Nonlinear Systems under Faults and Attacks via Control Barrier Functions

Safety is one of the most important properties of control systems. Sensor faults and attacks and actuator failures may cause errors in the sensor measurements and system dynamics, which leads to erroneous control inputs and hence safety violations. In this paper, we improve the robustness against sensor faults and actuator failures by proposing a class of Fault-Tolerant Control Barrier Functions (FT-CBFs) for nonlinear systems. Our approach maintains a set of state estimators according to fault patterns and incorporates CBF-based linear constraints for each state estimator. We then propose a framework for joint safety and stability by integrating FT-CBFs with Control Lyapunov Functions. With a similar philosophy of utilizing redundancy, we proposed High order CBF-based approach to ensure safety when actuator failures occur. We propose a sum-of-squares (SOS) based approach to verify the feasibility of FT-CBFs for both sensor faults and actuator failures. We evaluate our approach via two case studies, namely, a wheeled mobile robot (WMR) system in the presence of a sensor attack and a Boeing 747 lateral control system under actuator failures.Comment: 15 pages, 5 figures, submitted to IEEE Transactions on Automatic Contro

A Robust Nonlinear Observer-based Approach for Distributed Fault Detection of Input-Output Interconnected Systems

This paper develops a nonlinear observer-based approach for distributed fault detection of a class of interconnected input–output nonlinear systems, which is robust to modeling uncertainty and measurement noise. First, a nonlinear observer design is used to generate the residual signals required for fault detection. Then, a distributed fault detection scheme and the corresponding adaptive thresholds are designed based on the observer characteristics and, at the same time, filtering is used in order to attenuate the effect of measurement noise, which facilitates less conservative thresholds and enhanced robustness. Finally, a fault detectability condition characterizing quantitatively the class of detectable faults is derived

Robust model-based fault estimation and fault-tolerant control : towards an integration

To maintain robustly acceptable system performance, fault estimation (FE) is adopted to reconstruct fault signals and a fault-tolerant control (FTC) controller is employed to compensate for the fault effects. The inevitably existing system and estimation uncertainties result in the so-called bi-directional robustness interactions defined in this work between the FE and FTC functions, which gives rise to an important and challenging yet open integrated FE/FTC design problem concerned in this thesis. An example of fault-tolerant wind turbine pitch control is provided as a practical motivation for integrated FE/FTC design.To achieve the integrated FE/FTC design for linear systems, two strategies are proposed. A H∞ optimization based approach is first proposed for linear systems with differentiable matched faults, using augmented state unknown input observer FE and adaptive sliding mode FTC. The integrated design is converted into an observer-based robust control problem solved via a single-step linear matrix inequality formulation.With the purpose of an integrated design with more freedom and also applicable for a range of general fault scenarios, a decoupling approach is further proposed. This approach can estimate and compensate unmatched non-differentiable faults and perturbations by combined adaptive sliding mode augmented state unknown input observer and backstepping FTC controller. The observer structure renders a recovery of the Separation Principle and allows great freedom for the FE/FTC designs.Integrated FE/FTC design strategies are also developed for Takagi-Sugeno fuzzy modelling nonlinear systems, Lipschitz nonlinear systems, and large-scale interconnected systems, based on extensions of the H∞ optimization approach for linear systems.Tutorial examples are used to illustrate the design strategies for each approach. Physical systems, a 3-DOF (degree-of-freedom) helicopter and a 3-machine power system, are used to provide further evaluation of the proposed integrated FE/FTC strategies. Future research on this subject is also outlined

Multiple Faults Estimation in Dynamical Systems: Tractable Design and Performance Bounds

In this article, we propose a tractable nonlinear fault isolation filter along with explicit performance bounds for a class of nonlinear dynamical systems. We consider the presence of additive and multiplicative faults, occurring simultaneously and through an identical dynamical relationship, which represents a relevant case in several application domains. The proposed filter architecture combines tools from model-based approaches in the control literature and regression techniques from machine learning. To this end, we view the regression operator through a system-theoretic perspective to develop operator bounds that are then utilized to derive performance bounds for the proposed estimation filter. In the case of constant, simultaneously and identically acting additive and multiplicative faults, it can be shown that the estimation error converges to zero with an exponential rate. The performance of the proposed estimation filter in the presence of incipient faults is validated through an application on the lateral safety systems of SAE level 4 automated vehicles. The numerical results show that the theoretical bounds of this study are indeed close to the actual estimation error.Comment: 24 pages, 8 figure

Joint State and Fault Estimation of Complex Networks under Measurement Saturations and Stochastic Nonlinearities

10.13039/501100001809-National Natural Science Foundation of China (Grant Number: 61933007, 61873148, 62033008, 61703244 and 61873149); 10.13039/501100000266-Engineering and Physical Sciences Research Council (Grant Number: EP/T005734/1); Shandong Provincial Natural Science Foundation of China (Grant Number: ZR2020MF071); Research Fund for the Taishan Scholar Project of Shandong Province of China; Alexander Von Humboldt Foundation of Germany