Fault-tolerant Stochastic Distributed Systems

The present doctoral thesis discusses the design of fault-tolerant distributed systems, placing emphasis in addressing the case where the actions of the nodes or their interactions are stochastic. The main objective is to detect and identify faults to improve the resilience of distributed systems to crash-type faults, as well as detecting the presence of malicious nodes in pursuit of exploiting the network. The proposed analysis considers malicious agents and computational solutions to detect faults. Crash-type faults, where the affected component ceases to perform its task, are tackled in this thesis by introducing stochastic decisions in deterministic distributed algorithms. Prime importance is placed on providing guarantees and rates of convergence for the steady-state solution. The scenarios of a social network (state-dependent example) and consensus (time- dependent example) are addressed, proving convergence. The proposed algorithms are capable of dealing with packet drops, delays, medium access competition, and, in particular, nodes failing and/or losing network connectivity. The concept of Set-Valued Observers (SVOs) is used as a tool to detect faults in a worst-case scenario, i.e., when a malicious agent can select the most unfavorable sequence of communi- cations and inject a signal of arbitrary magnitude. For other types of faults, it is introduced the concept of Stochastic Set-Valued Observers (SSVOs) which produce a confidence set where the state is known to belong with at least a pre-specified probability. It is shown how, for an algorithm of consensus, it is possible to exploit the structure of the problem to reduce the computational complexity of the solution. The main result allows discarding interactions in the model that do not contribute to the produced estimates. The main drawback of using classical SVOs for fault detection is their computational burden. By resorting to a left-coprime factorization for Linear Parameter-Varying (LPV) systems, it is shown how to reduce the computational complexity. By appropriately selecting the factorization, it is possible to consider detectable systems (i.e., unobservable systems where the unobservable component is stable). Such a result plays a key role in the domain of Cyber-Physical Systems (CPSs). These techniques are complemented with Event- and Self-triggered sampling strategies that enable fewer sensor updates. Moreover, the same triggering mechanisms can be used to make decisions of when to run the SVO routine or resort to over-approximations that temporarily compromise accuracy to gain in performance but maintaining the convergence characteristics of the set-valued estimates. A less stringent requirement for network resources that is vital to guarantee the applicability of SVO-based fault detection in the domain of Networked Control Systems (NCSs)

A Geographic Unicast Routing Algorithm using no Location Service

In this paper, we present a geographic routing algorithm which can adapt to different levels of mobility by changing its parameters according to the network in which it is running. Routing decisions are based on directions and geographical positions of the nodes and there is no need for an external location system. Discoveries are done using unicast messages resulting in few control messages being sent both to discover and to maintain routing information. After a series of tests, we show the algorithm low overhead, high adaptability and robustness as it only relies on the end-points (source and destination nodes) to guarantee a successful transmission

Self-Triggered Set-Valued Observers

This paper addresses the problem of high computational requirements in the implementation of Set-Valued Observers (SVOs), which places stringent constraints in terms of their use in applications where low computational power is available or the plant is sensitive to delay. It is firstly shown how to determine an overbound for the set-valued estimates, which reduces the overhead by limiting the number of inequalities defining those set-valued state estimates. In the particular setting of distributed gossip problems, the proposed algorithm is shown to have constant complexity. This algorithm is of prime importance to reduce the computational load and enable the use of such estimates for real-time applications. Results are also provided regarding the frequency of the triggers in the worst-case scenario. The performance of the proposed method is evaluated through simulation

Finite-time Average Consensus in a Byzantine Environment Using Set-Valued Observers

This paper addresses the problem of consensus in the presence of Byzantine faults, modeled by an attacker injecting a perturbation in the state of the nodes of a network. It is firstly shown that Set-Valued Observers (SVOs) attain finite-time consensus, even in the case where the state estimates are not shared between nodes, at the expenses of requiring large horizons, thus rendering the computation problem intractable in the general case. A novel algorithm is therefore proposed that achieves finite-time consensus, even if the aforementioned requirement is dropped, by intersecting the set-valued state estimates of neighboring nodes, making it suitable for practical applications and enabling nodes to determine a stopping time. This is in contrast with the standard iterative solutions found in the literature, for which the algorithms typically converge asymptotically and without any guarantees regarding the maximum error of the final consensus value, under faulty environments. The algorithm suggested is evaluated in simulation, illustrating, in particular, the finite-time consensus property

Source Localization and Network Topology Discovery in Infection Networks

Determining the network topology is typically a challenging problem due to the number of nodes and connection between them. Complexity is added whenever this identification problem relies solely on a subset of the outputs of some dynamical system or distributed algorithm running on those nodes. In this paper, we focus on both the source identification and network topology discovery problems in the context of infection networks where a subset of the nodes are elected as observers. The solution consists in writing the binary constraints associated with the problem. Convex relaxations are also proposed and investigated through simulations where a pattern emerges that placing observers in high-degree nodes increases the accuracy of the method

Average Consensus and Gossip Algorithms in Networks with Stochastic Asymmetric Communications

We consider that a set of distributed agents desire to reach consensus on the average of their initial state values, while communicating with neighboring agents through a shared medium. This communication medium allows only one agent to transmit unidirectionally at a given time, which is true, e.g., in wireless networks. We address scenarios where the choice of agents that transmit and receive messages at each transmission time follows a stochastic characterization, and we model the topology of allowable transmissions with asymmetric graphs. In particular, we consider: (i) randomized gossip algorithms in wireless networks, where each agent becomes active at randomly chosen times, transmitting its data to a single neighbor; (ii) broadcast wireless networks, where each agent transmits to all the other agents, and access to the network occurs with the same probability for every node. We propose a solution in terms of a linear distributed algorithm based on a state augmentation technique, and prove that this solution achieves average consensus in a stochastic sense, for the special cases (i) and (ii). Expressions for absolute time convergence rates at which average consensus is achieved are also given

Exact Set-valued Estimation using Constrained Convex Generators for uncertain Linear Systems

Set-valued state estimation when in the presence of uncertainties in the model have been addressed in the literature essentially following three main approaches: i) interval arithmetic of the uncertain dynamics with the estimates; ii) factorizing the uncertainty into matrices with unity rank; and, iii) performing the convex hull for the vertices of the uncertainty space. Approach i) and ii) introduce a lot of conservatism because both disregard the relationship of the parameters with the entries of the dynamics matrix. On the other hand, approach iii) has a large growth on the number of variables required to represent the set or is approximated losing its main advantage in comparison with i) and ii). In this paper, with the application of autonomous vehicles in GPS-denied areas that resort to beacon signals for localization, we develop an exact (meaning no added conservatism) and optimal (smallest growth in the number of variables) closed-form definition for the convex hull of Convex Constrained Generators (CCGs). This results in a more efficient method to represent the minimum volume convex set corresponding to the state estimation. Given that reductions methods are still lacking in the literature for CCGs, we employ an approximation using ray-shooting that is comparable in terms of accuracy with methods for Constrained Zonotopes as the ones implemented in CORA. Simulations illustrate the greater accuracy of CCGs with the proposed convex hull operation in comparison to Constrained Zonotopes.Comment: IFAC paper to be presented at the World Congress in July 202

Finite-time Convergence Policies in State-dependent Social Networks

This paper addresses the problem of finite-time convergence in a social network for a political party or an association, modeled as a distributed iterative system with a graph dynamics chosen to mimic how people interact. It is firstly shown that, in this setting, finite-time convergence is achieved only when nodes form a complete network, and that contacting with agents with distinct opinions reduces to a half the required interconnections. Two novel strategies are presented that enable finite-time convergence, even for the case where each node only contacts the two closest neighbors. These strategies are of prime importance, for instance, in a company environment where agents can be motivated to reach faster conclusions. The performance of the proposed policies is assessed through simulation, illustrating, in particular the finite-time convergence property

OPTool - Documentation v1.2

The OPTool package is an implementation of various state-of-the-art iterative optimization algorithms for differentiable cost functions along with algorithms to solve linear equations. Users can use the toolbox to solve optimization problems, although the code was written to researchers that want to compare their proposals with state-of-the-art implementation. New algorithms can be easily added and the software will be updated to have the most comprehensive list of solvers possible. It also comes with implemented functions to return optimal parameters for these algorithms based on a control-theoretical formulation of the algorithms

Distributed Fault Detection Using Relative Information in Linear Multi-Agent Networks

This paper addresses the problem of fault detection in the context of a collection of agents performing a shared task and exchanging relative information over a communication network. We resort to techniques in the literature to construct a meaningful observable system and overcome the issue that the system of systems is not observable. A solution involving Set-Valued Observers (SVOs) is proposed to estimate the state in a distributed fashion and a proof of convergence of the estimates is given under mild assumptions. The performance of the proposed algorithm is assessed through simulations