On the existence of virtual exosystems for synchronized linear networks

When dealing with heterogeneous networks, where the agents are governed by non-identical models, interesting questions arise regarding the ability of the network to synchronize to a common non-trivial output trajectory, as well as the nature of such a trajectory. On this topic, Wieland, Allgöwer, and Sepulchre have recently derived results showing that for a class of heterogeneous networks of dynamically controlled linear agents, non-trivial output synchronization implies the existence of an observable virtual exosystem for which the regulator equations are solvable for each agent. Moreover, this virtual exosystem defines the output trajectories on the agreement manifold and is contained within each agent as an internal model. In this paper, we shed further light on this topic by showing that, under a more general set of assumptions, non-trivial output synchronization can occur in the absence of such a virtual exosystem. We propose a modified result for this case that specifies the existence of a possibly unobservable virtual exosystem for which the regulator equations are solvable, and for which the observable part defines the output trajectories on the agreement manifold. We also show that a variation of the virtual exosystem is contained within each agent as an internal model.     

The synchronization of linear systems under quantized measurements

This paper studies the synchronization of high order linear systems in the presence of quantized relative state information. Using the Lyapunov method and non-smooth analysis, it is shown that when a uniform quantizer is used, the original multi-agent system can reach finite-time practical synchronization under the given communication protocol. It is also pointed out that when a logarithmic quantizer is considered, the given systems can reach synchronization under some conditions. The obtained results generalized the existing results of single integrator systems and double integrator systems. Numerical examples are given to illustrate the given results.     

Synchronization in networks of identical linear systems

The paper investigates the synchronization of a network of identical linear state-space models under a possibly time-varying and directed interconnection structure. The main result is the construction of a dynamic output feedback coupling that achieves synchronization if the decoupled systems have no exponentially unstable mode and if the communication graph is uniformly connected. The result can be interpreted as a generalization of classical consensus algorithms. Stronger conditions are shown to be sufficient–but to some extent, also necessary–to ensure synchronization with the diffusive static output coupling often considered in the literature.     

Global robust distributed output consensus of multi-agent nonlinear systems: An internal model approach

This paper studies the problem of global robust distributed output consensus of heterogeneous leader–follower multi-agent nonlinear systems by general directed output interactions. For a class of minimum-phase single-input single-output nonlinear agents having unity relative degree, it is shown that the problem is solvable by an internal model approach under certain mild conditions. A Lyapunov function based output-feedback control law is developed by converting the global output consensus into a global distributed stabilization problem for an augmented network.     

基于模型参考和内模原理的线性系统鲁棒控制设计

不确定性因素会使系统性能恶化,它包括系统不确定性参数和各种外部干扰等.本文针对这种不确定性线性系统,利用模型参考和内模原理,建立鲁棒控制系统结构,分析了其能控性条件,通过选择参考模型和内模实现系统能控,在此条件下,将鲁棒控制设计转换为控制系统的LQR问题进行研究,并运用最优控制理论,计算其反馈控制律.仿真结果表明该设计方法将"模型参考"与"内模原理"有机结合起来,提高了系统的鲁棒稳定性,有效抑制干扰,并实现系统性能的改善.     

Robust stabilizer design for linear time-varying internal model based output regulation and its application to an electrohydraulic system

This paper focuses on the design of a low order robust stabilizer for the tracking/disturbance rejection problem based on the internal model principle in the time-varying setting and its application to the hydraulic pressure tracking with varying frequency. The problem of this kind known as output regulation generally consists of two major parts: internal model unit construction and stabilizer design. While the construction of the time-varying internal model unit is non-trivial by itself and a very recent research outcome enables its synthesis for a class of linear time-varying systems, the effective stabilization of the augmented system (internal model unit and plant) for practical applications remains a challenge. This is due to the need to stabilize the high order time-varying augmented system using a low order stabilizer in a robust fashion and with desirable transient performance. While directly applying the stabilization approaches for a general LTV system will result in a high order stabilizer, a new method is proposed in this paper that overcomes this bottleneck by taking advantage of the unique structure of the internal model based control system. Instead of using a dynamic stabilizer with high order, this approach uses a sequence of time-varying gains that are directly injected into the internal model unit. A critical issue addressed is how to avoid the non-convex optimization associated with the time-varying gain synthesis and then convert the stabilizer design into a series of Linear Matrix Inequalities (LMIs). The proposed control approach is then demonstrated on an electrohydraulic system.     

Consensus of high-order linear systems using dynamic output feedback compensator: Low gain approach

In this paper, we study the consensus (and synchronization) problem for multi-agent linear dynamic systems. All the agents have identical MIMO linear dynamics which can be of any order, and only the output information of each agents is delivered throughout the communication network. It is shown that consensus is reached if there exists a stable compensator which simultaneously stabilizes N−1 systems in a special form, where N is the number of agents. We show that there exists such a compensator under a very general condition. Finally, the consensus value is characterized as a function of initial conditions with stable compensators in place.     

Distributed self-tuning consensus and synchronization

The problem of self-tuning of coupling parameters in multi-agent systems is considered. Agent dynamics are described by a discrete-time double integrator with unknown input gain. Each agent locally tunes the strength of interaction with neighboring agents by using a normalized gradient algorithm (NGA). The tuning algorithm minimizes the square of the error between an individual agent’s state (velocity) and the one step delayed average of its own state and the states of its neighbors. Assuming that the network graph is strongly connected, it is proved that the sequence of coupling parameters is convergent and all velocities converge toward the same constant value.     

Robust asymptotic model matching and its application to output synchronization of heterogeneous multi-agent systems

Output synchronization of heterogeneous multi-agent systems has been one of the most interesting cooperative control problems. This paper first gives a brief survey of the research on the problem from which we see that the problem can be solved in a two-step manner with the aid of a properly designed local reference for each agent: (i) a controller is designed for each agent to achieve the trajectory regulation of the agent output to its associated reference; (ii) network collaboration is added to achieve consensus among references. In the presence of system uncertainties, the robust trajectory regulation problem in (i) can be solved by an internal model design. In this paper, we formulate a novel robust asymptotic model matching problem which is less conservative than trajectory regulation and can be solved by a static controller not relying on an internal model. Moreover, network collaboration is designed in (ii) within the so-called output communication setting such that consensus among references occurs concurrently with robust asymptotic model matching. As a result, output synchronization of heterogeneous multi-agent systems is achieved with a novel approach.     

A noninteracting control strategy for the robust output synchronization of linear heterogeneous networks

This paper deals with the problem of robust output synchronization for heterogeneous multi-agent systems. First, a new synchronization approach is presented to synchronize the outputs of heterogeneous agents. Based on noninteracting control techniques, a method is derived for homogenizing the input-output behavior of every agent. Hence, applying the same reference input signal to every agent leads to synchronization. Furthermore, a strategy for increasing the robustness of the synchronization process against exogenous disturbances is presented, which leads to a structurally constrained optimization problem. However, by a convenient reformulation of the problem, well established tools from robust control theory can be used. Moreover, it is shown that this procedure allows to separate the robustness issue from the synchronization task. The effectiveness of the approach is illustrated by a robust output synchronization example for a heterogeneous aircraft fleet.     

Cooperative semi-global robust output regulation for a class of nonlinear uncertain multi-agent systems

In this paper, we study the cooperative semi-global robust output regulation problem for a class of minimum phase nonlinear uncertain multi-agent systems. This problem is a generalization of the leader-following tracking problem in the sense that it further addresses such issues as disturbance rejection, robustness with respect to parameter uncertainties. To solve this problem, we first introduce a type of distributed internal model that converts the cooperative semi-global robust output regulation problem into a cooperative semi-global robust stabilization problem of the so-called augmented system. We then solve the semi-global stabilization problem via distributed dynamic output control law by utilizing and combining a block semi-global backstepping technique, a simultaneous high gain feedback control technique, and a distributed high gain observer technique.     

Cooperative global optimal preview tracking control of linear multi-agent systems: an internal model approach

This paper investigates the cooperative global optimal preview tracking problem of linear multi-agent systems under the assumption that the output of a leader is a previewable periodic signal and the topology graph contains a directed spanning tree. First, a type of distributed internal model is introduced, and the cooperative preview tracking problem is converted to a global optimal regulation problem of an augmented system. Second, an optimal controller, which can guarantee the asymptotic stability of the augmented system, is obtained by means of the standard linear quadratic optimal preview control theory. Third, on the basis of proving the existence conditions of the controller, sufficient conditions are given for the original problem to be solvable, meanwhile a cooperative global optimal controller with error integral and preview compensation is derived. Finally, the validity of theoretical results is demonstrated by a numerical simulation.     

Decomposition principle in model predictive control for linear systems with bounded disturbances

Considering a constrained linear system with bounded disturbances, this paper proposes a novel approach which aims at enlarging the domain of attraction by combining a set-based MPC approach with a decomposition principle. The idea of the paper is to extend the “pre-stabilizing” MPC, where the MPC control sequence is parameterized as perturbations to a given pre-stabilizing feedback gain, to the case where the pre-stabilizing feedback law is given as the linear combination of a set of feedback gains. This procedure leads to a relatively large terminal set and consequently a large domain of attraction even when using short prediction horizons. As time evolves, by minimizing the nominal performance index, the resulting controller reaches the desired optimal controller with a good asymptotic performance. Compared to the standard “pre-stabilizing” MPC, it combines the advantages of having a flexible choice of feedback gains, a large domain of attraction and a good asymptotic behavior.     

Adaptive narrow band disturbance rejection applied to an active suspension—an internal model principle approach

This paper presents a methodology for feedback adaptive control of active vibration systems in the presence of time varying unknown narrow band disturbances. A direct adaptive control scheme based on the internal model principle and the use of the Youla-Kucera parametrization is proposed. This approach is comparatively evaluated with respect to an indirect adaptive control scheme based on the estimation of the disturbance model. The comparative evaluation is done in real time on an active suspension system.     

Convex necessary and sufficient stabilisability conditions in switched linear systems with rank-one modes

ABSTRACT

A novel convex necessary and sufficient condition for state-feedback exponential stabilisability in discrete-time switched linear systems, whose modes are described by rank-one matrices, is reported and proved in the present communication. A switched linear system, of this class, is shown to be state-feedback exponentially stabilisable if and only if a set of linear matrix inequalities (LMIs) associated to the system is feasible. And the solvability of this set of LMIs associated to the system is shown to be equivalent to that of a set of (standard) linear inequalities associated to the system. It is also proved that each solution to this set of LMIs (associated to the system) yields, through explicit formulas, to an exponentially stabilising state-feedback mapping, and also to a Lyapunov function for the exponential stability of the trivial solution of the corresponding closed-loop system (obtained by means of that feedback mapping). And such a Lyapunov function is always represented by a number of quadratic functionals that equals the number of modes composing the switched system.     

An integrated trust and reputation model for open multi-agent systems

Trust and reputation are central to effective interactions in open multi-agent systems (MAS) in which agents, that are owned by a variety of stakeholders, continuously enter and leave the system. This openness means existing trust and reputation models cannot readily be used since their performance suffers when there are various (unforseen) changes in the environment. To this end, this paper presents FIRE, a trust and reputation model that integrates a number of information sources to produce a comprehensive assessment of an agent’s likely performance in open systems. Specifically, FIRE incorporates interaction trust, role-based trust, witness reputation, and certified reputation to provide trust metrics in most circumstances. FIRE is empirically evaluated and is shown to help agents gain better utility (by effectively selecting appropriate interaction partners) than our benchmarks in a variety of agent populations. It is also shown that FIRE is able to effectively respond to changes that occur in an agent’s environment.     

Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems

This paper studies some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems. First, basic theoretical analysis is carried out for the case where for each agent the second-order dynamics are governed by the position and velocity terms and the asymptotic velocity is constant. A necessary and sufficient condition is given to ensure second-order consensus and it is found that both the real and imaginary parts of the eigenvalues of the Laplacian matrix of the corresponding network play key roles in reaching consensus. Based on this result, a second-order consensus algorithm is derived for the multi-agent system facing communication delays. A necessary and sufficient condition is provided, which shows that consensus can be achieved in a multi-agent system whose network topology contains a directed spanning tree if and only if the time delay is less than a critical value. Finally, simulation examples are given to verify the theoretical analysis.     

On ultimate boundedness around non-assignable equilibria of linear time-invariant systems

In this note we investigate the following questions: given a (finite-dimensional) linear time-invariant (LTI) multivariable system and a constant desired value for its output, say y_?. Assume there is no assignable equilibrium point corresponding to y_?. How “close” to y_? can we ultimately keep the output using LTI static state-feedback stabilizing controllers? Can this neighborhood of y_? be reduced with dynamic, nonlinear, time-varying controllers? Our main contributions are the proof that the optimal ultimate boundedness neighborhood is achieved with LTI static state-feedback, the explicit computation of the neighborhood's size and the proof, under some reasonable rank assumptions, that the system has non-assignable values for the output if and only if it has a transmission zero at zero. Interestingly, there is no connection between this problem and the more familiar concepts of controllability and observability.