Problem Of Linear Systems Research Articles

Distributed online optimization for heterogeneous linear multi-agent systems with coupled constraints

This paper studies a class of distributed online convex optimization problems for heterogeneous linear multi-agent systems. Agents in a network, knowing only their own outputs, need to minimize the time-varying costs through neighboring interaction subject to time-varying coupled inequality constraints. Based on the saddle-point technique, we design a continuous-time distributed controller which is shown to achieve constant regret bound and sublinear fit bound, matching those of the standard centralized online method. We further extend the control law to the event-triggered communication mechanism and show that the constant regret bound and sublinear fit bound are still achieved while reducing the communication frequency. Additionally, we study the situation of communication noise, i.e., the agent’s measurement of the relative states of its neighbors is disturbed by a noise. It is shown that, if the noise is not excessive, the regret and fit bounds are unaffected, which indicates the controller’s noise-tolerance capability to some extent. Finally, a numerical simulation is provided to support the theoretical conclusions.

A robust finite–time model reference adaptive controller for arbitrary order disturbed LTI systems

This manuscript deals with the trajectory-tracking problem for linear time-invariant systems with parameter uncertainties and time-dependent external perturbations. A robust finite-time model reference adaptive controller is proposed. In the absence of external perturbations, the proposed controller ensures finite-time convergence to zero of the tracking and parameter identification errors. In presence of time-dependent external perturbations, the tracking and parameter identification errors converge to a region around the origin in a finite time. The convergence proofs are developed based on Lyapunov and input-to-state stability theory. Finally, simulation results in an academic example and a flexible-joint robot manipulator show the feasibility of the proposed approach.

Distributed Exponential State Estimation for Discrete-Time Linear Systems Over Jointly Connected Switching Networks

The existing results on distributed state estimation problems for discrete-time linear systems were obtained over connected static networks, or every-time connected switching networks by a two-time-scale design. This paper further studies the same problem over jointly connected switching networks which can be disconnected at every time instant by a single-time-scale distributed design. Since the existing distributed designs critically rely on the connectedness assumption on the networks and thus may not apply to jointly connected switching networks, we have to modify the local observers and develop a novel approach which makes use of the uniform complete observability property for a discrete-time time-varying system. Additionally, we establish two exponential stability results for two classes of discrete-time switched systems, which may be of independent interest.

Distributed Multiagent-Based Event-Driven Fault-Tolerant Control of Islanded Microgrids.

This article proposes an observer-based event-driven fault-tolerant (OBEDFT) secondary control strategy for AC microgrids (MGs) to achieve load voltage regulation. First, the input-output feedback linearization method transforms the voltage regulation issue into an output feedback tracking problem for linear multiagent systems (MASs) with nonlinear dynamics. This transformation provides the necessary preprocessing for load voltage regulation. Then, an OBEDFT secondary control protocol that considers full-state immeasurability is proposed. The actuators of distributed generators (DGs) may experience partial loss of effectiveness (PLOE) and bias faults, and these fault parameters may be heterogeneous and time-varying. The protocol introduces adaptive techniques to avoid information related to fault parameters while using event-driven mechanisms to achieve discrete measurements of neighboring DG. Additionally, the protocol uses boundary layers to construct smooth controllers that prevent the chattering effect caused by nonsmooth controllers. Finally, simulation results confirm the effectiveness of this load voltage regulation strategy.

Adaptive Event-Triggered Time-Varying Output Bipartite Formation Containment of Multiagent Systems Under Directed Graphs.

The time-varying output bipartite formation containment (TVOBFC) problem for linear multiagent systems (MASs) under directed graphs is an important problem. However, the methods in existing works rely on the global information of the MASs or do not use event-triggered communication. This article investigates two kinds of TVOBFC problems for heterogeneous linear MASs under signed digraphs by event-triggered communication. For the first case where leaders have the same dynamics, the innovative fully distributed event-triggered protocol for the follower is proposed. In this case, the followers form the preset formation shape. For the second case where leaders have different dynamics, the leaders are divided into two groups. One group can directly obtain the output information of the virtual leader, while the other group cannot. In order to make leaders achieve the formation shape and track the virtual leader, two kinds of innovative observers are designed for two kinds of leaders to estimate the state of the virtual leader, and the control protocol is designed for each leader based on the designed observers. Then, the control law for each follower is designed to solve the formation containment problem. Finally, two examples are introduced to illustrate the main results.

The Binary Distributed Observer Approach to the Cooperative Output Regulation of Linear Multiagent Systems

In this note, the cooperative output regulation problem of general heterogeneous linear multi-agent systems with binary constraints is studied. To speed up the convergence rate, the binary distributed observer is proposed only utilizing sign of the relative state instead of using full relative information. Under some mild conditions, the binary distributed observer can estimate the state of the leader system exponentially in finite time sense. The leader system can generate various reference signals such as step functions, sinusoidal functions or their combinations. Furthermore, both state and output feedback control protocols are synthesized to solve the problem. An illustrative example is presented to support the feasibility of the proposed framework.

Distributed exponential state estimation of linear systems over jointly connected switching networks

Recently, the distributed state estimation problem for continuous-time linear systems over jointly connected switching networks was solved. Due to the use of the generalized Barbalat’s Lemma, it can only show that the estimation errors asymptotically converge to the origin. By a completely different approach, this paper further studies the distributed state estimation problem with two new features. First, the asymptotic convergence is strengthened to the exponential convergence. This strengthened result not only offers a guaranteed convergence rate, but also renders the error system total stability and thus the capability to withstand small disturbances. Second, the coupling gains of our local observers can be different from each other and thus offers greater design flexibility, while the coupling gains in the existing result were required to be identical. These two new features are achieved by establishing exponential stability for two classes of linear time-varying systems, which may have other applications.

A hybrid time/event-triggered interaction framework for multi-agent consensus with relative measurements

This paper is concerned with the output-feedback consensus problem of linear multi-agent systems on undirected graphs. Our focus is on reducing sensing and communication burdens between agents. Based on relative output measurements, a dynamic output-feedback (DOF) protocol is proposed, which, by leveraging the structure of the closed-loop dynamics, integrates a hybrid time/event-triggered sampling mechanism such that only intermittent interaction between agents is needed. Consensus conditions are established by the Lyapunov method and numerical simulations are provided for illustrating the effectiveness of the protocol. Compared with the existing results, the proposed DOF protocol has the following merits: (1) they rely on relative output measurements but do not need absolute measurements about agents; (2) they only require agents to intermittently interact with neighbors and thus can greatly reduce sensing and communication burdens between agents; and (3) the designed event-triggering conditions do not need to perform extra reconstruction operations that are computationally demanding.

Minimal-time problems for linear control systems on homogeneous spaces of low-dimensional solvable nonnilpotent Lie groups

Abstract In this article, we are concerned with minimal-time optimal problems for the class of controllable linear control system on low-dimensional nonnilpotent solvable Lie groups and their homogeneous spaces.

Controllability of fractional dynamical systems having multiple delays in control with ψ‐Caputo fractional derivative

This study investigates the controllability problems for linear and nonlinear fractional control systems with multiple control delays in the context of the ‐Caputo fractional derivative. For the linear case, using the positive definiteness of the Gramian matrix, the necessary and sufficient conditions are obtained. For the nonlinear case, utilizing the iterative technique together with the completeness of the space, sufficient conditions for the existence of a solution are obtained. Just a few examples are included to make theoretical findings easier to grasp, and their respective graphs are plotted.

Linear Combination of Hamiltonian Simulation for Nonunitary Dynamics with Optimal State Preparation Cost.

We propose a simple method for simulating a general class of nonunitary dynamics as a linear combination of Hamiltonian simulation (LCHS) problems. LCHS does not rely on converting the problem into a dilated linear system problem or on the spectral mapping theorem. The latter is the mathematical foundation of many quantum algorithms for solving a wide variety of tasks involving nonunitary processes, such as the quantum singular value transformation. The LCHS method can achieve optimal cost in terms of state preparation. We also demonstrate an application for open quantum dynamics simulation using the complex absorbing potential method with near-optimal dependence on all parameters.

A fully distributed event-Triggered control approach to leader-following consensus of multiagent systems

This paper investigates the leader-following consensus problem for general linear multiagent systems under a fully distributed manner. To avoid using the global information of the communication network, two node-based adaptive parameters are designed and introduced to the fully distributed event-based control law. Such a protocol is more scalable and flexible for large-scaled and complex networked system, such as microgrids or multiple unmanned vehicles. A novel event-triggered rule is presented, and an internal dynamic variable is introduced in it to further cut down the triggering times and save the communication resources. A well-designed Lyapunov function candidate is constructed to not only ensure the convergence of the close-looped systems but also avoid using the eigenvalue of Laplacian matrix in the dynamic variable. Moreover, it is proved that the designed event-triggered conditions can avoid the Zeno behaviour. Finally, a simulation example based on a group of unmanned intelligent vehicle systems is provided to demonstrate the validity of the designed control method.

Observer based stabilization of linear time delay systems using new augmented LKF

This paper addresses the stabilization problem of linear time-varying delay systems with unmeasurable states. A novel augmented Lyapunov–Krasovskii functional (LKF) is proposed that effectively accounts for the impact of time delays, and an observer based stabilization controller is developed employing linear matrix inequality (LMI) based optimization technique. The utilization of extended reciprocally convex matrix inequality (ERCMI) is employed in this work to establish less conservative stabilization conditions within the framework of linear matrix inequalities (LMIs). By formulating a convex optimization problem, the observer gain and controller gains are determined. Simulation results are used to validate the design, and two numerical examples are considered to prove the usefulness of the proposed method over existing methods.

Continuous and discrete gradient-Zhang neuronet (GZN) with analyses for time-variant overdetermined linear equation system solving as well as mobile localization applications

In this paper, a novel continuous gradient-Zhang neuronet (GZN) model and three discrete GZN algorithms are proposed to solve time-variant overdetermined linear equation system (TVOLES) problems, and are developed on the basis of a gradient neuronet and Zhang neuronet. Specifically, the continuous GZN model is proposed and derived in the form of an explicit-dynamic equation, and its stability is analysed and proven using Lyapunov theory. To ensure that the problems can be solved and implemented on digital platforms, three discrete GZN algorithms are established by using three different discretization formulas. The numerical simulative results verify that, compared with the Zhang neuronet model, gradient neuronet model and variant-parameter neuronet model, the proposed continuous GZN model converges faster in some cases. Other computer experiments further substantiate that the proposed continuous model and its corresponding discrete GZN algorithms are effective and efficient. Finally, the proposed discrete GZN algorithms are applied to mobile object localizations, and the simulative results verify their applicability and effectiveness.

Quantized Feedback Control of Discrete-Time MIMO Linear Systems With Input and Output Quantization Over Finite Data Rate Channels

This paper considers a control problem of discrete-time MIMO linear systems involving input quantization (for the output of the controller) and output quantization (for the output of the plant). Based on spherical polar coordinate quantizer, a quantization method with finite data rate is proposed for handling the nested quantization and achieving the convergence to the origin of the system with input and output quantization. Further, an optimalization problem is developed for each quantizer, of which the optimal solution set contains a virtual augmented vector. The quantizers quantize their respective virtual augmented vectors to obtain the estimates of the outputs of the plant and the controller. We present the analytical expression of the optimal solution set for each quantizer. Finally, a method is presented to achieve the parameters of the quantizers and the controller.

Secure Consensus of Multiagent Systems With DoS Attacks via Fully Distributed Dynamic Event-Triggered Control

This article investigates the secure consensus problem of general linear multiagent systems with denial-of-service (DoS) attacks. Owning to the existence of DoS attacks, it is challenging to investigate the event-triggered control of multiagent systems in a fully distributed manner. This article presents a novel dynamic event-triggered mechanism to alleviate the limited communication resources. Moreover, the designed mechanism is fully distributed and scalable owing to the introduction of some adaptive coupling weights. Since the DoS attacks have been considered in the event-triggered rule design, a novel adaptive parameter with an additional exponential term is adopted to deal with DoS attacks. The Lyapunov design also introduces such a term for the subsequent stability analysis. Sufficient conditions guaranteeing the asymptotic consensus of the studied system are developed in light of the controller’s parameters, duration, and frequency of the DoS attacks. Strict proof is provided to demonstrate that a secure consensus can be reached effectively under the proposed control mechanism. Furthermore, it is shown that the Zeno behavior can be excluded from the designed triggering mechanism. Finally, simulations on a multiagent system consisting of interconnected unmanned intelligent vehicles are conducted to verify the results.

Fully Distributed Event-Driven Coordination With Actuator Faults.

This article investigates the event-driven fault-tolerance (ETFT) consensus problem for general linear multiagent systems (MASs) with partial loss of effectiveness (PLOE) and bias faults of actuators in leader-follower networks. Each agent's controller is only updated relatively infrequently at its event moments. A desirable feature of this article is that the proposed event-driven algorithm is fully distributed also independent of global information and additive fault boundaries. Based on this, a consensus error prediction model is used to avoid the limitation that each agent needs to monitor its neighbors' state under event-driven conditions continuously. We further excluded the Zeno behavior by proving that any adjacent event interval for each agent is greater than zero. The simulations verify our results.

Fully Distributed Event-Driven Adaptive Consensus of Unknown Linear Systems.

This article considers the consensus problem of unknown linear multiagent systems (MASs) through adaptive event-driven control in leader-follower and leaderless networks. The proposed event-driven algorithms do not involve any global information related to the network communication structure and rely only on local information exchange to achieve consensus on MASs and are therefore fully distributed. Furthermore, the constraint of continuous communication among the agents is eliminated in terms of control law updates and triggering state monitoring. Another desirable aspect of this article is that the design process of the control algorithms is independent of the parameters of each agent's dynamics and thus does not require precise information about the dynamics of MASs. We further exclude the Zeno behavior of each agent by proving the existence of a strict positive lower bound between any two adjacent events. Finally, the effectiveness of the proposed adaptive event-driven algorithms is verified by a simulation example.

Event-triggered risk-sensitive smoothing for linear Gaussian systems

An event-triggered risk-sensitive smoothing problem for linear Gaussian systems is investigated in this paper. Due to the special cost criterion of the risk-sensitive estimation, the smoothed information state is first constructed under a newly defined reference measure. Its Gaussian density and recursive forms are derived by processing it into the combination of the forward and backward information states, both of which are proven to have Gaussian densities and evolve in linear recursions. A stochastic even-triggering condition is adopted to preserve the Gaussian property during the derivation. Then the proposed problem is reformulated equivalently under the reference measure, expressed by minimizing an integral involving the smoothed information state, and finally solved by utilizing the Gaussian densities of information states. The applicability and effectiveness of the results are illustrated through a numerical example by comparisons with a naive risk-sensitive smoother and the event-triggered MMSE smoother.

Performances of a family of new sequential Bayesian filters for input estimation

During their lifetime, structures are usually subjected to some mechanical shocks that generate high levels of vibration that can damage the structure itself as well as the embedded devices. However, the characteristics of these shocks (location, time history, maximum intensity, etc.) are often unknown due to the inaccessibility of the excitation region for direct force measurements or the inability to instrument the system. Therefore, inverse methods have been developed to quantify these complex excitations. Recently, a Bayesian formulation of the input-state estimation problem for linear systems has been proposed by the authors, which unifies most of the state-of-the-art filters. In this paper, we present two novel Bayesian filters derived from this framework: (a) the Correlated Dual Kalman Filter (CDKF), which is one of the filters that naturally follows from the unified Bayesian formulation, and (b) the Component Bayesian Filter (CBF), which promotes spatial sparsity of the input vector. Essentially, these filters differ in the prior distributions used to convey information about the spatial distribution of the input vector to be identified. The performance of these filters is evaluated through a numerical experiment and a real-world application aimed at reconstructing a sparse and transient excitation acting on a linear structure. A comparison of these original filters with other Bayesian filters proposed in the literature is also proposed. In particular, the numerical experiment allows to study the performance of the proposed filters in different scenarios, such as the number of sensors, the measurement noise level or the sensor configuration, while the real-world application allows to test them in operational conditions. More specifically, it is shown that filters promoting the spatial sparsity of the input vector, such as CBF, lead to a consistent identified excitation profile when acceleration measurements are the only available data.