A simply structured distributed observer is described for estimating the state of a continuous-time, jointly observable, input-free, linear system whose sensed outputs are distributed across a time-varying network. It is explained how to design a gain $g$ in the observer so that their state estimation errors all converge exponentially fast to zero at a fixed, but arbitrarily chosen rate provided the network's graph is strongly connected for all time. A linear inequality for $g$ is provided when the network's graph is switching according to a switching signal with a dwell time or an average dwell time, respectively. It has also been shown the existence of $g$ when the stochastic matrix of the network's graph is chosen to be doubly stochastic under arbitrarily switching signals. This is accomplished by exploiting several well-known properties of invariant subspaces and properties of perturbed systems.
This paper proposes a novel distributed interval observer design for linear time-invariant (LTI) discrete-time systems subject to bounded disturbances. In the proposed observer algorithm, each agent in a networked group exchanges locally-computed framers or interval-valued state estimates with neighbors, and coordinates its update via an intersection operation. We show that the proposed framers are guaranteed to bound the true state trajectory of the system by construction, i.e., without imposing any additional assumptions or constraints. Moreover, we provide necessary and sufficient condition…
This paper studies the state-of-charge (SoC) balancing and the total charging/discharging power tracking issues for battery energy storage systems (BESSs) with multiple distributed heterogeneous battery units. Different from the traditional cooperative control strategies based on the asymptotical or finite-time distributed observers, two distributed prespecified-time observers are proposed to estimate average battery units state and average desired power, respectively, which can be determined in advance and independent of initial states or control parameters. Finally, two simulation examples a…
This paper considers the design of a distributed state-observer for discrete-time Linear Time-Invariant (LTI) systems in the presence of sensor attacks. We assume there is a network of observer nodes, communicating with each other over an undirected graph, each with partial measurements of the output corrupted by some adversarial attack. We address the case of sparse attacks where the attacker targets a small subset of sensors. An algorithm based on Alternating Direction Method of Multipliers (ADMM) is developed which provides an update law for each observer which ensures convergence of each o…
We consider the distributed $H_\infty$ estimation problem with an additional requirement of resilience to biasing attacks. An attack scenario is considered where an adversary misappropriates some of the observer nodes and injects biasing signals into observer dynamics. The paper proposes a procedure for the derivation of a distributed observer which endows each node with an attack detector which also functions as an attack compensating feedback controller for the main observer. Connecting these controlled observers into a network results in a distributed observer whose nodes produce unbiased r…
Distributed Observers with Dynamic Event-Triggered Communication
School of Automation and Intelligent Sensing, Shanghai Jiao Tong University（上海交通大学自动化与智能传感学院）；Key Laboratory of System Control and Information Processing, Ministry of Education of China（教育部系统控制与信息处理重点实验室）；State Key Laboratory of Submarine Geoscience, Shanghai Jiao Tong University（上海交通大学海洋地质国家重点实验室）
This work presents a notion of strong detectability for linear time varying systems affected by unknown inputs. It is shown that this notion is equivalent to detectability of an auxiliary system without unknown inputs. This allows a straightforward observer design for dependable state estimation in the presence of unknown inputs. The design reduces to a deterministic Kalman filter design problem, where the observer gains can be obtained from the solution of a differential Riccati equation. The efficacy of the proposed approach is demonstrated by means of a numerical example.
The adaptive distributed observer approach has been an effective tool for synthesizing a distributed control law for solving various control problems of leader-follower multiagent systems. However, the existing adaptive distributed observer needs to make use of the full state of the leader system. This assumption not only precludes many practical applications in which only the output of the leader system is available, but also leads to a high dimension observer. In this communique, we propose an adaptive distributed output observer which only makes use of the output of the leader system, and i…
A fixed-order set-valued observer is presented for linear parameter-varying systems with bounded-norm noise and under completely unknown attack signals, which simultaneously finds bounded sets of states and unknown inputs that include the true state and inputs. The proposed observer can be designed using semidefinite programming with LMI constraints and is optimal in the minimum \mathcal{H}_{\infty}-norm sense. We show that the strong detectability of each constituent linear time-invariant system is a necessary condition for the existence of such an observer, as well as the boundedness of set-…
State estimation for a class of linear time-invariant systems with distributed output measurements (distributed sensors) and unknown inputs is addressed in this paper. The objective is to design a network of observers such that the state vector of the entire system can be estimated, while each observer (or node) has access to only local output measurements that may not be sufficient on its own to reconstruct the entire system's state. Existing results in the literature on distributed state estimation assume either that the system does not have inputs, or that all the system's inputs are global…
In this paper, network of agents with identical dynamics is considered. The agents are assumed to be fed by self and neighboring output measurements, while the states are not available for measuring. Viewing distributed estimation as dual to the distributed LQR problem, a distributed observer is proposed by exploiting two complementary distributed LQR methods. The first consists of a bottom-up approach in which optimal interactions between self-stabilizing agents are defined so as to minimize an upper bound of the global LQR criterion. In the second (top-down) approach, the centralized optimal…
The robust distributed state estimation for a class of continuous-time linear time-invariant systems is achieved by a novel kernel-based distributed observer, which, for the first time, ensures fixed-time convergence properties. The communication network between the agents is prescribed by a directed graph in which each node involves a fixed-time convergent estimator. The local observer estimates and broadcasts the observable states among neighbours so that the full state vector can be recovered at each node and the estimation error reaches zero after a predefined fixed time in the absence of …
Conditions for detectability in distributed consensus-based observer networks
School of Engineering and IT, University of NSW at the Australian Defence Force Academy（新南威尔士大学澳大利亚国防军学院工程与信息技术学院）；Australian National University（澳大利亚国立大学）
An observer-based boundary controller for infinite-dimensional port-Hamiltonian systems defined on 1D spatial domains is proposed. The design is based on an early-lumping approach in which a finite-dimensional approximation of the infinite-dimensional system derived by spatial discretization is used to design the observer and the controller. As long as the finite-dimensional approximation approaches the infinite-dimensional model, the performances also do. The main contribution is a constructive method which guarantees that the interconnection between the controller and the infinite-dimensiona…
Distributed Adaptive Neural Interval Observers for Unknown Nonlinear Systems
Faculty of Mechanical Engineering, Ho Chi Minh City University of Technology (HCMUT), Vietnam National University Ho Chi Minh City (VNU-HCM)（胡志明市理工大学机械工程学院，越南国立大学胡志明市分校）；Department of Mathematics and Statistics, University of New Mexico（新墨西哥大学数学与统计系）
In this paper, we present a scheme of fully distributed resilient state estimation for linear dynamical systems under sensor attacks. The proposed state observer consists of a network of local observers, where each of them utilizes local measurements and information transmitted from the neighbors. As a fully distributed scheme, it does not necessarily collect a majority of sensing data for the sake of attack identification, while the compromised sensors are eventually identified by the distributed network and excluded from the observers. For this, the overall network (not the individual local …
Distributed Unknown Input Observer Design: A Geometric Approach
University College London（伦敦大学学院）；Loughborough University（拉夫堡大学）；Imperial College London（帝国理工学院）；Aalborg University（奥尔堡大学）；University of Trieste（的里雅斯特大学）
In this paper we are interested in the problem of adaptive state observation of linear time-varying (LTV) systems where the system and the input matrices depend on unknown time-varying parameters. It is assumed that these parameters satisfy some known LTV dynamics, but with unknown initial conditions. Moreover, the state equation is perturbed by an additive signal generated from an exosystem with uncertain constant parameters. Our main contribution is to propose a globally convergent state observer that requires only a weak excitation assumption on the system.
We study how to design a secure observer-based distributed controller such that a group of vehicles can achieve accurate state estimates and formation control even if the measurements of a subset of vehicle sensors are compromised by a malicious attacker. We propose an architecture consisting of a resilient observer, an attack detector, and an observer-based distributed controller. The distributed detector is able to update three sets of vehicle sensors: the ones surely under attack, surely attack-free, and suspected to be under attack. The adaptive observer saturates the measurement innovatio…
A novel approach to solve the problem of distributed state estimation of linear time-invariant systems is proposed in this paper. It relies on the application of parameter estimation-based observers, where the state observation task is reformulated as a parameter estimation problem. In contrast with existing results our solution achieves convergence in finite-time, without injection of high gain, and imposes very weak assumptions on the communication graph---namely the existence of a Hamiltonian walk. The scheme is shown to be robust vis-á-vis external disturbances and communication delays.
This paper presents a novel Sliding Mode Control (SMC) algorithm to handle mismatched uncertainties in systems via a novel Self-Learning Disturbance Observer (SLDO). A computationally efficient SLDO is developed within a framework of feedback-error learning scheme in which a conventional estimation law and a Neuro-Fuzzy Structure (NFS) work in parallel. In this framework, the NFS estimates the mismatched disturbances and becomes the leading disturbance estimator while the former feeds the learning error to the NFS to learn system behavior. The simulation results demonstrate that the proposed S…
We study the platoon control of vehicles with third-order nonlinear dynamics under the constant spacing policy. We consider a vehicle model with parameter uncertainties and external disturbances and propose a distributed control law based on an event-triggered extended state observer (ESO). First, an event-triggered ESO is designed to estimate the unmodeled dynamics in the vehicle model. Then based on the estimate of the unmodeled dynamics, a distributed control law is designed by using a modified dynamic surface control method. The control law of each follower vehicle only uses the informatio…
