Consensus Synthesis of Robust Cooperative Control for Homogeneous Leader-Follower Multi-Agent Systems Subject to Parametric Uncertainty

This paper presents a design of robust consensus for homogeneous leader-follower multiagent systems (MAS). Each agent of MAS is described by a linear time-invariant dynamic model subject to parametric uncertainty. The agents are interconnected through a static interconnection matrix over an undirected graph to cooperate and share information with their neighbours. The consensus design of MAS can be transformed to stability analysis by using decomposition technique. We apply Lyapunov theorem to derive the sufficient condition to ensure the consensus of all independent subsystems. In addition, we design a robust distributed state feedback gain based on linear quadratic regulator (LQR) setting. Controller gain is computed via solving a linear matrix inequality. As a result, we provide a robust design procedure of a cooperative LQR control to achieve consensus objective and maximize the admissible bound of the uncertainty. Finally, we give numerical examples to illustrate the effectiveness of the proposed consensus design. The results show that the response for MAS in presence of uncertainty using robust consensus design follows the response of the leader and is better than that of the existingnominal consensus design

Multilayer Networks

In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications. Such systems include multiple subsystems and layers of connectivity, and it is important to take such "multilayer" features into account to try to improve our understanding of complex systems. Consequently, it is necessary to generalize "traditional" network theory by developing (and validating) a framework and associated tools to study multilayer systems in a comprehensive fashion. The origins of such efforts date back several decades and arose in multiple disciplines, and now the study of multilayer networks has become one of the most important directions in network science. In this paper, we discuss the history of multilayer networks (and related concepts) and review the exploding body of work on such networks. To unify the disparate terminology in the large body of recent work, we discuss a general framework for multilayer networks, construct a dictionary of terminology to relate the numerous existing concepts to each other, and provide a thorough discussion that compares, contrasts, and translates between related notions such as multilayer networks, multiplex networks, interdependent networks, networks of networks, and many others. We also survey and discuss existing data sets that can be represented as multilayer networks. We review attempts to generalize single-layer-network diagnostics to multilayer networks. We also discuss the rapidly expanding research on multilayer-network models and notions like community structure, connected components, tensor decompositions, and various types of dynamical processes on multilayer networks. We conclude with a summary and an outlook.Comment: Working paper; 59 pages, 8 figure

Cooperative control of a network of multi-vehicle unmanned systems

Development of unmanned systems network is currently among one of the most important areas of activity and research with implications in variety of disciplines, such as communications, controls, and multi-vehicle systems. The main motivation for this interest can be traced back to practical applications wherein direct human involvement may not be possible due to environmental hazards or the extraordinary complexity of the tasks. This thesis seeks to develop, design, and analyze techniques and solutions that would ensure and guarantee the fundamental stringent requirements that are envisaged for these dynamical networks. In this thesis, the problem of team cooperation is solved by using synthesis-based approaches. The consensus problem is defined and solved for a team of agents having a general linear dynamical model. Stability of the team is guaranteed by using modified consensus algorithms that are achieved by minimizing a set of individual cost functions. An alternative approach for obtaining an optimal consensus algorithm is obtained by invoking a state decomposition methodology and by transforming the consensus seeking problem into a stabilization problem. In another methodology, the game theory approach is used to formulate the consensus seeking problem in a "more" cooperative framework. For this purpose, a team cost function is defined and a min-max problem is solved to obtain a cooperative optimal solution. It is shown that the results obtained yield lower cost values when compared to those obtained by using the optimal control technique. In game theory and optimal control approaches that are developed based on state decomposition, linear matrix inequalities are used to impose simultaneously the decentralized nature of the problem as well as the consensus constraints on the designed controllers. Moreover, performance and stability properties of the designed cooperative team is analyzed in presence of actuator anomalies corresponding to three types of faults. Steady state behavior of the team members are analyzed under faulty scenarios. Adaptability of the team members to the above unanticipated circumstances is demonstrated and verified. Finally, the assumption of having a fixed and undirected network topology is relaxed to address and solve a more realistic and practical situation. It is shown that the stability and consensus achievement of the network with a switching structure and leader assignment can still be achieved. Moreover, by introducing additional criteria, the desirable performance specifications of the team can still be ensured and guaranteed