Consensus Control of a Class of Uncertain Nonlinear Multiagent Systems via Gradient-Based Algorithms

Output-Feedback Self-Synchronization of Directed Lur'e Networks via Global Connectivity

In this article, we generalize the results on self-synchronization of Lur'e networks diffusively interconnected through dynamic relative output-feedback from the undirected graph case in Zhang et al. 2016 to the general directed graph case. A linear dynamic self-synchronization protocol of the same structure is adopted as the one proposed in Zhang et al. 2016. That is, the Lur'e-type nonlinearity is not involved in our self-synchronization protocol. It is in fact unknown and only assumed to be incrementally sector bounded within a given sector. In the absence of a leader Lur'e system defining the synchronization trajectory, we construct a novel self-synchronization manifold in order to derive the self-synchronization error dynamics. Meanwhile, the connectivity of the general directed graph having a directed spanning tree is quantified by the global connectivity, instead of the so-called general algebraic connectivity used in the directed graph case under static relative state feedback. The global connectivity plays a crucial role in handling self-synchronization problems of directed nonlinear networks via dynamic relative output feedback, including directed networks with the Lipschitz nonlinear node dynamics, which is also discussed in this article. The protocol parameter matrix design is performed by solving the obtained LMI conditions in sequence. In addition, some discussions are complemented on the important technical details in our self-synchronization protocol design along with extensions. Finally, our theoretical results are illustrated through numerical simulations over a directed nonlinear dynamical network.

Optimal Steady-State Regulator Design for a Class of Nonlinear Systems With Arbitrary Relative Degree

In this article, we consider the regulator design problem for a class of uncertain multi-input-multioutput (MIMO) nonlinear systems with arbitrary relative degree. The objective is to regulate the output of the nonlinear system to an optimal steady state that solves a constrained optimization problem, without computing the optimal solution in advance. By embedding saddle-point dynamics, both state and output-feedback-based regulators are proposed and the resulting closed-loop systems are modeled in standard singularly perturbed forms. By invoking the singular perturbation analysis, exponential stability is established under some regularity condition. Compared with the existing methods, the proposed regulators can deal with a class of nonlinear systems with uncertainties and arbitrary relative degree. Furthermore, the current results can include some recent works on the distributed optimization problem as special cases. Finally, the effectiveness of the proposed methods is validated through numerical simulations.

Distributed Model Reference Adaptive Optimization of Disturbed Multiagent Systems With Intermittent Communications

This article pays close attention to a distributed optimization problem for multiagent systems subject to exogenous disturbances. A novel distributed model reference adaptive control (D-MRAC) scheme is proposed that no explicit disturbance observer or internal model unit is involved, which not only enhances robustness but also improves transient performance. In contrast to the continuous communication that is often assumed in the existing distributed optimization works, the new method allows for more realistic scenarios in which the agents communicate with each other at discrete-time instants. It is shown by Lyapunov analysis that the concerned distributed optimization problem can be solved by the proposed D-MRAC scheme as long as the communication interval is smaller than a given threshold, which can be calculated by following the steps given in this article. Numerical simulations have shown the effectiveness of the presented method.

On Iterative Proportional Updating: Limitations and Improvements for General Population Synthesis

Population synthesis is the foundation of the agent-based social simulation. Current approaches mostly consider basic population and households, rather than other social organizations. This article starts with a theoretical analysis of the iterative proportional updating (IPU) algorithm, a representative method in this field, and then gives an extension to consider more social organization types. The IPU method, for the first time, proves to be unable to converge to an optimal population distribution that simultaneously satisfies the constraints from individual and household levels. It is further improved to a bilevel optimization, which can solve such a problem and include more than one type of social organization. Numerical simulations, as well as population synthesis using actual Chinese nationwide census data, support our theoretical conclusions and indicate that our proposed bilevel optimization can both synthesize more social organization types and get more accurate results.

Interval Multiobjective Optimization With Memetic Algorithms

One of the most important and widely faced optimization problems in real applications is the interval multiobjective optimization problems (IMOPs). The state-of-the-art evolutionary algorithms (EAs) for IMOPs (IMOEAs) need a great deal of objective function evaluations to find a final Pareto front with good convergence and even distribution. Further, the final Pareto front is of great uncertainty. In this paper, we incorporate several local searches into an existing IMOEA, and propose a memetic algorithm (MA) to tackle IMOPs. At the start, the existing IMOEA is utilized to explore the entire decision space; then, the increment of the hypervolume is employed to develop an activation strategy for every local search procedure; finally, the local search procedure is conducted by constituting its initial population, whose center is an individual with a small uncertainty and a big contribution to the hypervolume, taking the contribution of an individual to the hypervolume as its fitness function, and performing the conventional genetic operators. The proposed MA is empirically evaluated on ten benchmark IMOPs as well as an uncertain solar desalination optimization problem and compared with three state-of-the-art algorithms with no local search procedure. The experimental results demonstrate the applicability and effectiveness of the proposed MA.

Distributed Control for Leader-Following Consensus Problem of Second-Order Multi-Agent Systems and Its Application to Motion Synchronization

This paper solves the leader-following consensus problem for a class of second-order multi-agent systems with input quantized by a newly proposed adaptive dynamic quantizer. The novel dynamic quantizer is an adaptive quantizer that combines the logarithmic quantizer and the uniform quantizer by introducing dynamic gain parameters to achieve quantizer adaptive adjustment. It has advantages of logarithmic, uniform, and adaptive dynamic quantizers in ensuring reducible communication expenses and acceptable quantizer errors for better system performance. On this basis, we transform the guide way climbing frame (GWCF) under ideal conditions into a second-order multi-agent system and solve the motion synchronization problem of GWCF. Finally, we illustrate our approach by numerical examples.