Distributed State Estimation for Linear Systems

This paper studies a distributed state estimation problem for both continuous- and discrete-time linear systems. A simply structured distributed estimator is first described for estimating the state of a continuous-time, jointly observable, input free, multi-channel linear system whose sensed outputs are distributed across a fixed multi-agent network. The estimator is then extended to non-stationary networks whose graphs switch according to a switching signal with a fixed dwell time or a variable but with fixed average dwell time, or switch arbitrarily under appropriate assumptions. The estimator is guaranteed to solve the problem, provided a network-widely shared gain is sufficiently large. As an alternative to sharing a common gain across the network, a fully distributed version of the estimator is thus studied in which each agent adaptively adjusts a local gain though the practicality of this approach is subject to a robustness issue common to adaptive control. A discrete-time version of the distributed state estimation problem is also studied, and a corresponding estimator is proposed for time-varying networks. For each scenario, it is explained how to construct the estimator so that its state estimation errors all converge to zero exponentially fast at a fixed but arbitrarily chosen rate, provided the network's graph is strongly connected for all time. This is accomplished by appealing to the ``split-spectrum'' approach and exploiting several well-known properties of invariant subspace. The proposed estimators are inherently resilient to abrupt changes in the number of agents and communication links in the inter-agent communication graph upon which the algorithms depend, provided the network is redundantly strongly connected and redundantly jointly observable.Comment: 17 pages, 8 figures. arXiv admin note: substantial text overlap with arXiv:1903.0548

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)

Problems in Control, Estimation, and Learning in Complex Robotic Systems

In this dissertation, we consider a range of different problems in systems, control, and learning theory and practice. In Part I, we look at problems in control of complex networks. In Chapter 1, we consider the performance analysis of a class of linear noisy dynamical systems. In Chapter 2, we look at the optimal design problems for these networks. In Chapter 3, we consider dynamical networks where interactions between the networks occur randomly in time. And in the last chapter of this part, in Chapter 4, we look at dynamical networks wherein coupling between the subsystems (or agents) changes nonlinearly based on the difference between the state of the subsystems. In Part II, we consider estimation problems wherein we deal with a large body of variables (i.e., at large scale). This part starts with Chapter 5, in which we consider the problem of sampling from a dynamical network in space and time for initial state recovery. In Chapter 6, we consider a similar problem with the difference that the observations instead of point samples become continuous observations that happen in Lebesgue measurable observations. In Chapter 7, we consider an estimation problem in which the location of a robot during the navigation is estimated using the information of a large number of surrounding features and we would like to select the most informative features using an efficient algorithm. In Part III, we look at active perception problems, which are approached using reinforcement learning techniques. This part starts with Chapter 8, in which we tackle the problem of multi-agent reinforcement learning where the agents communicate and classify as a team. In Chapter 9, we consider a single agent version of the same problem, wherein a layered architecture replaces the architectures of the previous chapter. Then, we use reinforcement learning to design the meta-layer (to select goals), action-layer (to select local actions), and perception-layer (to conduct classification)