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.     

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.     

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.     

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.     

具有自适应内模的一类非线性系统输出调节问题

研究一类包含未知非线性项的非线性系统的鲁棒输出调节问题.此类非线性系统由一包含未知参数的线性中性稳定的外系统驱动.首先运用调节器方程组解和标准内模将输出调节问题转化为镇定问题;然后给出控制律镇定闭环系统,同时利用镇定输入项和外系统信息设计出自适应内模方程.控制律使得闭环系统的信号全局最终有界,且误差被调节至预先设定的任意小的精度值.仿真结果验证了所提出设计方法的有效性.     

Tracking control for multi-agent consensus with an active leader and variable topology

In this paper, we consider a multi-agent consensus problem with an active leader and variable interconnection topology. The state of the considered leader not only keeps changing but also may not be measured. To track such a leader, a neighbor-based local controller together with a neighbor-based state-estimation rule is given for each autonomous agent. Then we prove that, with the proposed control scheme, each agent can follow the leader if the (acceleration) input of the active leader is known, and the tracking error is estimated if the input of the leader is unknown.     

Semi-global robust output regulation for a class of singular nonlinear systems via nonlinear internal model

Most of existing results on robust output regulation problem of singular nonlinear systems are limited to local solutions. In this paper, the semi-global robust output regulation problem for a class of singular nonlinear systems is investigated by using a nonlinear internal model. Attaching a nonlinear internal model to the singular nonlinear system yields an augmented singular nonlinear system whose semi-global robust stabilisation solution leads to the solution of the semi-global robust output regulation problem of the original singular nonlinear system. The solvability conditions of the semi-global output regulation problem are established by addressing the solvability of the robust stabilisation problem of augmented singular nonlinear system. Finally, a numerical simulation example is used to illustrate the design of the semi-global regulator for the singular nonlinear systems.     

An invariance principle for nonlinear switched systems

In this paper we address the problem of extending LaSalle Invariance Principle to switched system. We prove an extension of the invariance principle relative to dwell time switched solutions, and a second one relative to constrained switched systems.     

A necessary and sufficient condition for the perspective observability problem

In this paper we derive a necessary and sufficient condition for observing the initial condition of a new class of system known as the perspective system. Such a system has already been applied in the field of computer vision especially in the area of motion estimation problems. Our result generalizes an earlier result by Popov-Belevitch-Hautus on the problem of observing a linear dynamical system.     

A preference processing model for cooperative agents

When multiple valid solutions are available to a problem, preferences can be used to indicate a choice. In a distributed system, such a preference-based solution can be produced autonomous agents cooperating together, but the attempt will lead to contention if the same resource is given preference by several user-agents. To resolve such contentions, this paper proposes a market-based payment scheme for selling and buying preferences by the contenders, in which the best solution is defined as the one where as many preferences as theoretically possible are globally met. After exploring the nature of preference, the paper develops a preference processing model based on the market based scheme, and presents a theoretical performance model to verify the correctness of the processing model. This verification is provided by a simulation study of the processing model. For the simulation study, a manufacturing environment is conjectured, where a set of tasks are resolved into subtasks by coordinator agents, and then these subtasks are allocated to assembler agents through cooperation and negotiation, in which preferred resources are exchanged against payments. The study shows that our agent based strategy not only produces convergence on the total preference value for the whole system, but also reaches that final value irrespective of the initial orderof subtask allocation to the assemblers.     

New filters for internal model control design

In this paper we study the design of a new two-degree-of-freedom filter for the internal model control (IMC) method. The new filter alleviates some disadvantages of the standard IMC filter when the IMC method is applied to unstable plants that do not have non-minimum-phase zeros. We show that by employing the new filter, the resulting system has a flatter frequency response, better stability robustness, and little overshoot in the step response. Furthermore, one of its design parameters can be related directly to the closed-loop bandwidth and the other parameter can be used to control the recovery time after an overshoot has occurred in the step response. These features are important in the application of the IMC method to a new approach of adaptive robust control. Examples are given in the paper to illustrate the new filter design.     

A second-order maximum principle for discrete-time bilinear control systems with applications to discrete-time linear switched systems

A powerful approach for analyzing the stability of continuous-time switched systems is based on using optimal control theory to characterize the “most unstable” switching law. This reduces the problem of determining stability under arbitrary switching to analyzing stability for the specific “most unstable” switching law. For discrete-time switched systems, the variational approach received considerably less attention. This approach is based on using a first-order necessary optimality condition in the form of a maximum principle (MP), and typically this is not enough to completely characterize the “most unstable” switching law. In this paper, we provide a simple and self-contained derivation of a second-order necessary optimality condition for discrete-time bilinear control systems. This provides new information that cannot be derived using the first-order MP. We demonstrate several applications of this second-order MP to the stability analysis of discrete-time linear switched systems.