General Linear Systems Research Articles

Dynamic consensus and adaptive bias compensation for multi-agent linear systems over directed networks

Biased measurements in an inter-networked systems can have severe repercussions in closed-loop stability of the individual systems and decelerate dynamical consensus among the interacting agents. Bias in the measurement, even constant, cannot be dealt with ad hoc techniques of robust control, in the presence of additive perturbations, because the control gain amplifies the disturbance. One way to account for the effect of measurement bias is then to rely on adaptive control. This has been done in the literature in the context of individual systems, but to the best of our knowledge not for multi-agent systems, while ensuring consensus control. In this paper we provide a model-reference-adaptive-control scheme to ensure dynamic consensus of generic (stabilizable) linear systems interconnected over directed graphs and under the influence of constant bias measurements. Our controller ensures global asymptotic stability of the synchronization manifold and convergence of the bias estimates.

Event-Triggered Formation Tracking Control With Application to Multiple Mobile Robots

In this article, we address the distributed event-triggered leader–follower formation tracking control problem of general linear multiagent systems with a dynamic leader in sampled-data settings. A novel locally computable state-estimate-based event generator is established for each follower agent to regulate the interagent communication at each sampling instant. Then, we propose a distributed formation tracking protocol based on the triggered sampled information such that the formation tracking control problem can be formulated as a stability-analysis problem of the closed-loop formation error dynamics. The event generator and formation tracking controller gains can then be co-designed using the feasible linear matrix inequality conditions that are derived from Lyapunov-based stability-analysis methods that guarantee the ultimate boundedness of the closed-loop formation error dynamics. Finally, numerical simulations along with experiment implementations were conducted for a group of linearized unicycle-type mobile robots to demonstrate the effectiveness and advantages of the proposed method.

Adaptively Distributed Nash Equilibrium Seeking of Noncooperative Games for Uncertain Heterogeneous Linear Multi-Agent Systems

This paper presents the design of adaptively distributed Nash Equilibrium (NE) seeking algorithms in noncooperative games for heterogeneous general linear multi-agent systems (MASs) under unknown unmodeled dynamics and bounded disturbances. Different from existing works that only consider single or multiple integrators, we aim to steer agents' outputs of MASs with nonidentical dynamics to the NE in a distributed way and not needing known information on the Lipschitz and monotone constants of pseudo-gradients as well as the algebraic connectivity of the graph. To overcome difficulties brought by heterogeneous dynamics and NE seeking requirements, we first present an adaptively distributed NE seeking algorithm that can tune on-line the edges of graphs to solve the studied problem. By leveraging monotone and matrix properties, the global asymptotic convergence to the NE is obtained. Moreover, this design is extended to develop another adaptively distributed NE seeking algorithm to tackle the impact of unknown dynamics and disturbances. Two exam -ples with numerical simulation results are provided to illustrate the effectiveness of the developed NE seeking algorithms.

Distributed Event-Triggered Output Consensus for General Linear Heterogeneous Multi-Agent Systems With System Uncertainties

Distributed Event-Triggered Output Consensus for General Linear Heterogeneous Multi-Agent Systems With System Uncertainties

Fully Distributed Robust Adaptive Formation Control for Linear Multi-agent System with Uncertainties and Communication Delays⋆

This paper investigates fully distributed robust adaptive formation control problems of a class of general linear higher-order systems subject to heterogeneous uncertainties over a deterministic network under time-varying communication delays. A novel robust adaptive strategy is developed to cope with the uncertainties dependent on control inputs as well as system states. Thereafter, an original fully distributed formation controller is designed, which incorporates two parts, namely, the nominal controller relying on delayed neighbouring information to attain the desired formation and the robust adaptive compensating signal to restrain the influences of uncertainties. The controller design and implementation require neither the global information about interaction graph nor the upper bounds of uncertainties. Based on the Lyapunov-Krasovskii arguments, sufficient conditions for the closed-loop system in the presence of network latency to achieve the desired formation is derived. Numerical simulation results are presented to demonstrate the effectiveness of the proposed formation protocol.

Entropic Model Predictive Optimal Transport for Underactuated Linear Systems

This letter investigates dynamical optimal transport of underactuated linear systems over an infinite time horizon. In our previous work, we proposed to integrate model predictive control and the celebrated Sinkhorn algorithm to perform efficient dynamical transport of agents. However, the proposed method requires the invertibility of input matrices, which severely limits its applicability. To resolve this issue, we extend the method to (possibly underactuated) controllable linear systems. In addition, we ensure the convergence properties of the method for general controllable linear systems. The effectiveness of the proposed method is demonstrated by a numerical example.

Partition-based distributed moving horizon state estimation with system disturbances and sensor noise penalties

In this article, partition-based distributed state estimation of general linear systems is considered. A distributed moving horizon state estimation algorithm is developed via partitioning the entire system model and the global objective function of centralized moving horizon estimation into subsystem models and local objective functions, respectively. Based on moving horizon estimation, we design unconstrained subsystem estimators of the distributed scheme. These estimators are required to be executed iteratively within each sampling period. The objective function of each estimator penalizes both the estimates of system disturbances and the estimate of output measurement noise. Convergence and stability of the estimation error dynamics are analyzed under the unconstrained setting. A benchmark chemical example is used to illustrate the proposed approach.

Event-triggered consensus control for singular multi-agent systems based on observers

This paper is devoted to the problem of event-triggered consensus for a class of general linear singular multi-agent systems with undirected topology. Considering that the system states are not measurable, state observers are designed first, and then a new observer-based event-triggered sampling mechanism is proposed, which naturally avoids Zeno behavior. Furthermore, a distributed event-triggered consensus protocol is designed. By employing the Lyapunov-Krasovskii functional method and model transformation approach, sufficient conditions are obtained such that the consensus of the singular multi-agent systems can be achieved, while the explicit dynamic expression of the consensus function is also given. Finally, a numerical example is included to illustrate the effectiveness of the proposed results.

The stability of a stochastic discrete SIVS epidemic model with general nonlinear incidence

In this paper, based on Euler–Marryama method and theory of stochastic processes, a stochastic discrete SIVS epidemic model with general nonlinear incidence and vaccination is proposed by adding random perturbation and then discretizing the corresponding stochastic differential equation model. Firstly, the basic properties of continuous and discrete deterministic SIVS epidemic models are obtained. Then a criterion on the asymptotic mean-square stability of zero solution for a general linear stochastic difference system is established. As the applications of this criterion, the sufficient conditions on the stability in probability of the disease-free and endemic equilibria for the stochastic discrete SIVS epidemic model are obtained. The numerical simulations are given to illustrate the theoretical results.

Multivariate moment-matching for model order reduction of quadratic-bilinear systems using error bounds

We propose an adaptive moment-matching framework for model order reduction of quadratic-bilinear systems. In this framework, an important issue is the selection of those shift frequencies where moment-matching is to be achieved. So far, the choice often has been random or linked to the linear part of the nonlinear system. In this paper, we extend the use of an existing a posteriori error bound for general linear time invariant systems to quadratic-bilinear systems and develop a greedy-type framework to select a good choice of interpolation points for the construction of the projection matrices. The results are compared with standard quadratic-bilinear projection methods and we observe that the approximations obtained by the proposed method yield high accuracy.

Output Consensus of General Linear Networked Multiagent Systems With Unknown Disturbances via Cloud Computing

For a general linear multiagent system (MAS) with multigroup suffering from disturbances, a cloud-based output consensus control scheme, including a cloud predictive control protocol and a disturbance observer, is proposed to achieve output consensus via cloud computing. In a cloud framework, agents in each group only send their own information to a corresponding cloud node, and cloud nodes transmit next control command for agents. Accordingly, the communication burden of an individual agent is reduced in each group. Moreover, the communication burden of each agent remains constant despite the scale of the network, and energy consumption is also reduced effectively from the perspective of one agent. In a cloud, delayed states of agents are reconstructed via delayed outputs received from a sensor, and a predictor is designed based on observed delay states. A cloud predictive control protocol is developed by dynamic variables and the predicted output to compensate for network delays from a cloud to an actuator, and a disturbance observer is presented based on predicted and local outputs. In theory, sufficient conditions for stability are presented and analyzed, and it is proved that the proposed cloud-based control scheme renders the MAS stable and to achieve output consensus. Finally, two simulations are presented to verify the proposed control scheme.

Fault-Tolerant Periodic Event-Triggered Consensus Under Communication Delay and Multiple Attacks

This article proposes a resilient strategy for leaderless and leader–following consensus in general linear multiagent systems under simultaneous presence of false data injection and denial-of-service (DoS) attacks. To save energy, local control updates and communication between the neighboring agents are based on a distributed periodic event-triggered scheme. Sufficient conditions to guarantee the exponential mean square bounded consensus are derived as linear matrix inequality (LMI) conditions obtained from some delay-dependent Lyapunov–Krasovskii functionals. The proposed design framework computes the required consensus control gain based on a desired level of resilience to DoS. The guaranteed level of resilience in our proposed LMI-based method is less conservative (more realistic) compared to the existing analytical solutions. Two physical constraints, namely nonuniform time-varying communication delay and actuator faults, are also included in the problem formulation to enhance the practicability of the proposed solution. Simulations results demonstrate the effectiveness of the proposed framework in the presence of the considered cyberthreats and physical constraints.

Observer-Based Output Feedback Event-Triggered Adaptive Control for Linear Multiagent Systems Under Switching Topologies.

The consensus problem of general linear multiagent systems (MASs) is studied under switching topologies by using observer-based event-triggered control method in this article. On the basis of the output information of agents, two kinds of novel event-triggered adaptive control schemes are designed to achieve the leaderless and leader-follower consensus problems, which do not need to utilize the global information of the communication networks. Finally, two simulation examples are introduced to show that the consensus error converges to zero and Zeno behavior is eliminated in MASs. Compared with the existing output feedback control research, one of the significant advantages of our methods is that the controller protocols and triggering mechanisms do not rely on any global information, are independent of the network scale, and are fully distributed ways.

Distributed Time-Varying Group Formation Tracking for Multiagent Systems With Switching Interaction Topologies via Adaptive Control Protocols

In this article, time-varying group formation (TVGF) tracking problems for general linear multiagent systems (GLMASs) with switching interaction topologies are investigated. Different from previous studies, a novel TVGF tracking approach is proposed, where all agents are divided into three types: the virtual leader, the group leader, and the follower. The virtual leader is designed to assign the trajectory of GLMASs. Subgroups can be interacted with each other by cooperation among group leaders such that the relative configuration between different groups can be adjusted simultaneously. The followers in each group can achieve time-varying subformations. Moreover, under the influence of external disturbances and switching topologies, based on the distributed observer, two different distributed adaptive control protocols are constructed without using any global information such as the eigenvalue of the Laplacian matrix related to the communication topologies, the upper boundness of the leader’s input, and so on. The algorithms to determine parameters of control protocols are also presented. Furthermore, the closed-loop stability of GLMASs is proven by the Lyapunov theory. Finally, numerical simulations are given to verify the effectiveness of theoretical results.

Differential initial-value privacy and observability of linear dynamical systems

This paper studies the relationship between the differential privacy of initial values and the observability for general linear dynamical systems with Gaussian process and sensor noises, where certain initial values are privacy-sensitive and the rest is assumed to be public. First of all, necessary and sufficient conditions are established for preserving the differential privacy and unobservability of the global sensitive initial values, respectively to show their independent properties. Specifically, we show that the observability matrix reduced by the set of sensitive initial states not only characterizes the structural property of noises for achieving the differential privacy, but also affects the achievable privacy levels, while the unobservability relies on the rank of such reduced observability matrix. Next, the inherent network nature of the considered linear system is explored, where each individual state corresponds to a node and the state and output matrices induce interaction and sensing graphs, leading to a network system. Under this network perspective, the previously established results are extended for initial values of local nodes to study their differential privacy and connections with their observability. Moreover, it is shown that the qualitative property of the differential initial-value privacy is either preserved generically or lost generically, which is the same as the unobservability in the local sense, while subject to a subtle difference from the unobservability in the global sense that is either preserved fully or lost generically. Finally, a privacy-preserving consensus algorithm is revisited to illustrate the effectiveness of the established results.

Improved convergence of the Arrow–Hurwicz iteration for the Navier–Stokes equation via grad–div stabilization and Anderson acceleration

We consider two modifications of the Arrow–Hurwicz (AH) iteration for solving the incompressible steady Navier–Stokes equations for the purpose of accelerating the algorithm: grad–div stabilization, and Anderson acceleration. AH is a classical iteration for general saddle point linear systems and it was later extended to Navier–Stokes iterations in the 1970’s which has recently come under study again. We apply recently developed ideas for grad–div stabilization and divergence-free finite element methods along with Anderson acceleration of fixed point iterations to AH in order to improve its convergence. Analytical and numerical results show that each of these methods improves AH convergence, but the combination of them yields an efficient and effective method that is competitive with more commonly used solvers.

Optimal Output Regulation for General Linear Systems via Adaptive Dynamic Programming.

In this article, we consider an adaptive optimal output regulation problem for general linear systems. The purpose of the optimal output regulation problem is to guarantee the stability of the closed-loop system and disturbance rejection, as well by minimizing some predefined performance indices. It can be realized by using an optimal controller, in which both optimal feedback control gain and optimal feedforward control gain are included. First, an adaptive dynamic programming (ADP) technique is used to solve the optimal feedback control gain. Next, the unknown system matrices of the plant are explicitly computed. In addition, based on the property of the minimal polynomial, the coefficient of the exogenous disturbance in the expression of the regulated output can also be calculated. Finally, according to the regulator equation, an extra cost function is given, which aims to obtain the optimal feedforward control gain. The linear vector space optimization methods are used to solve the optimal problem. As a result, the linear optimal output regulation problem can be solved by the approximately optimal feedback and feedforward control gains.

Time-Varying Group Formation-Containment Tracking Control for General Linear Multiagent Systems With Unknown Inputs.

Time-varying group formation-containment tracking problems for general linear multiagent systems with unknown control input are investigated. Agents are classified into tracking leaders, formation leaders, and followers and assigned in groups. Tracking leaders with unknown control inputs provide unpredictable trajectories as macroscopic moving references. Formation leaders accomplish desired subformations while following the trails of tracking leaders. At the same time, followers converge into different convex hulls spanned by formation leaders. First, formation-containment tracking protocols are designed with neighboring relative information and effects of unknown input of tracking leaders. Then, the design of group division is analyzed by adjusting the properties in Laplacian matrices, which represent interaction relationships. An algorithm to determine the parameters in control protocols is proposed, and the formation tracking feasible constraint is presented. Next, it is proved that the general linear multiagent system can achieve time-varying group formation-containment control effectively with errors uniformly asymptotically converging to zero under designed protocols. Finally, a numerical simulation is given to verify the effectiveness of obtained theoretical results.

Leader-Following and Leaderless Consensus of Linear Multiagent Systems Under Directed Graphs by Double Dynamic Event-Triggered Mechanism

This article proposes a unified framework to investigate the leader-following and leaderless consensus problem of general linear multiagent systems under the directed communication topology only containing a spanning tree. To further reduce the use of resources for the control objective, an energy-saving control algorithm is introduced composed of double dynamic event-triggered mechanisms that work independently: one intends to control the communication of agents with their neighbors and the other to decide the update of controllers. It is shown that the control algorithm performs well compared to most existing control algorithms in terms of the communication cost between agents and the update cost of controllers. In addition, a new procedure to choose parameters is obtained by the developed Lyapunov stabilty method, with the potential of achieving less conservative parameters than related results. Finally, the effectiveness of the proposed control scheme is verified by numerical simulations.

Event-Triggered Distributed Moving Horizon State Estimation of Linear Systems

In this article, an event-triggered distributed state estimation mechanism is proposed for general linear systems that comprise several subsystems. Two distributed moving horizon estimation (MHE) algorithms that can handle constraints on disturbances and noise are proposed. An event scheduler is exploited to govern the evaluation of the estimators and networked information exchange between the plant and the estimators, such that good estimates can be provided while both the usage of processors and networked communication frequency can be reduced. The estimation error provided by the event-triggered estimation mechanism is proven to be convergent and bounded. A numerical example and a chemical process example are used to verify the effectiveness and applicability of the proposed method.