Distributed Weight Selection in Consensus Protocols by Schatten Norm Minimization

In average consensus protocols, nodes in a network perform an iterative weighted average of their estimates and those of their neighbors. The protocol converges to the average of initial estimates of all nodes found in the network. The speed of convergence of average consensus protocols depends on the weights selected on links (to neighbors). We address in this paper how to select the weights in a given network in order to have a fast speed of convergence for these protocols. We approximate the problem of optimal weight selection by the minimization of the Schatten p-norm of a matrix with some constraints related to the connectivity of the underlying network. We then provide a totally distributed gradient method to solve the Schatten norm optimization problem. By tuning the parameter p in our proposed minimization, we can simply trade-off the quality of the solution (i.e. the speed of convergence) for communication/computation requirements (in terms of number of messages exchanged and volume of data processed). Simulation results show that our approach provides very good performance already for values of p that only needs limited information exchange. The weight optimization iterative procedure can also run in parallel with the consensus protocol and form a joint consensus-optimization procedure.Comment: N° RR-8078 (2012

Communication-constrained feedback stability and Multi-agent System consensusability in Networked Control Systems

With the advances in wireless communication, the topic of Networked Control Systems (NCSs) has become an interesting research subject. Moreover, the advantages they offer convinced companies to implement and use data networks for remote industrial control and process automation. Data networks prove to be very efficient for controlling distributed systems, which would otherwise require complex wiring connections on large or inaccessible areas. In addition, they are easier to maintain and more cost efficient. Unfortunately, stability and performance control is always going to be affected by network and communication issues, such as band-limited channels, quantization errors, sampling, delays, packet dropouts or system architecture. The first part of this research aims to study the effects of both input and output quantization on an NCS. Both input and output quantization errors are going to be modeled as sector bounded multiplicative uncertainties, the main goal being the minimization of the quantization density, while maintaining feedback stability. Modeling quantization errors as uncertainties allows for robust optimal control strategies to be applied in order to study the accepted uncertainty levels, which are directly related to the quantization levels. A new feedback law is proposed that will improve closed-loop system stability by increasing the upper bound of allowed uncertainty, and thus allowing the use of a coarser quantizer. Another aspect of NCS deals with coordination of the independent agents within a Multi-agent System (MAS). This research addresses the consensus problem for a set of discrete-time agents communicating through a network with directed information flow. It examines the combined effect of agent dynamics and network topology on agents\u27 consensusability. Given a particular consensus protocol, a sufficient condition is given for agents to be consensusable. This condition requires the eigenvalues of the digraph modeling the network topology to be outer bounded by a fan-shaped area determined by the Mahler measure of the agents\u27 dynamics matrix

An Overview of Recent Progress in the Study of Distributed Multi-agent Coordination

This article reviews some main results and progress in distributed multi-agent coordination, focusing on papers published in major control systems and robotics journals since 2006. Distributed coordination of multiple vehicles, including unmanned aerial vehicles, unmanned ground vehicles and unmanned underwater vehicles, has been a very active research subject studied extensively by the systems and control community. The recent results in this area are categorized into several directions, such as consensus, formation control, optimization, task assignment, and estimation. After the review, a short discussion section is included to summarize the existing research and to propose several promising research directions along with some open problems that are deemed important for further investigations

COORDINATION OF LEADER-FOLLOWER MULTI-AGENT SYSTEM WITH TIME-VARYING OBJECTIVE FUNCTION

This thesis aims to introduce a new framework for the distributed control of multi-agent systems with adjustable swarm control objectives. Our goal is twofold: 1) to provide an overview to how time-varying objectives in the control of autonomous systems may be applied to the distributed control of multi-agent systems with variable autonomy level, and 2) to introduce a framework to incorporate the proposed concept to fundamental swarm behaviors such as aggregation and leader tracking. Leader-follower multi-agent systems are considered in this study, and a general form of time-dependent artificial potential function is proposed to describe the varying objectives of the system in the case of complete information exchange. Using Lyapunov methods, the stability and boundedness of the agents\u27 trajectories under single order and higher order dynamics are analyzed. Illustrative numerical simulations are presented to demonstrate the validity of our results. Then, we extend these results for multi-agent systems with limited information exchange and switching communication topology. The first steps of the realization of an experimental framework have been made with the ultimate goal of verifying the simulation results in practice

Distributed Kalman Filters over Wireless Sensor Networks: Data Fusion, Consensus, and Time-Varying Topologies

Kalman filtering is a widely used recursive algorithm for optimal state estimation of linear stochastic dynamic systems. The recent advances of wireless sensor networks (WSNs) provide the technology to monitor and control physical processes with a high degree of temporal and spatial granularity. Several important problems concerning Kalman filtering over WSNs are addressed in this dissertation. First we study data fusion Kalman filtering for discrete-time linear time-invariant (LTI) systems over WSNs, assuming the existence of a data fusion center that receives observations from distributed sensor nodes and estimates the state of the target system in the presence of data packet drops. We focus on the single sensor node case and show that the critical data arrival rate of the Bernoulli channel can be computed by solving a simple linear matrix inequality problem. Then a more general scenario is considered where multiple sensor nodes are employed. We derive the stationary Kalman filter that minimizes the average error variance under a TCP-like protocol. The stability margin is adopted to tackle the stability issue. Second we study distributed Kalman filtering for LTI systems over WSNs, where each sensor node is required to locally estimate the state in a collaborative manner with its neighbors in the presence of data packet drops. The stationary distributed Kalman filter (DKF) that minimizes the local average error variance is derived. Building on the stationary DKF, we propose Kalman consensus filter for the consensus of different local estimates. The upper bound for the consensus coefficient is computed to ensure the mean square stability of the error dynamics. Finally we focus on time-varying topology. The solution to state consensus control for discrete-time homogeneous multi-agent systems over deterministic time-varying feedback topology is provided, generalizing the existing results. Then we study distributed state estimation over WSNs with time-varying communication topology. Under the uniform observability, each sensor node can closely track the dynamic state by using only its own observation, plus information exchanged with its neighbors, and carrying out local computation

Convex Identifcation of Stable Dynamical Systems

This thesis concerns the scalable application of convex optimization to data-driven modeling of dynamical systems, termed system identi cation in the control community. Two problems commonly arising in system identi cation are model instability (e.g. unreliability of long-term, open-loop predictions), and nonconvexity of quality-of- t criteria, such as simulation error (a.k.a. output error). To address these problems, this thesis presents convex parametrizations of stable dynamical systems, convex quality-of- t criteria, and e cient algorithms to optimize the latter over the former. In particular, this thesis makes extensive use of Lagrangian relaxation, a technique for generating convex approximations to nonconvex optimization problems. Recently, Lagrangian relaxation has been used to approximate simulation error and guarantee nonlinear model stability via semide nite programming (SDP), however, the resulting SDPs have large dimension, limiting their practical utility. The rst contribution of this thesis is a custom interior point algorithm that exploits structure in the problem to signi cantly reduce computational complexity. The new algorithm enables empirical comparisons to established methods including Nonlinear ARX, in which superior generalization to new data is demonstrated. Equipped with this algorithmic machinery, the second contribution of this thesis is the incorporation of model stability constraints into the maximum likelihood framework. Speci - cally, Lagrangian relaxation is combined with the expectation maximization (EM) algorithm to derive tight bounds on the likelihood function, that can be optimized over a convex parametrization of all stable linear dynamical systems. Two di erent formulations are presented, one of which gives higher delity bounds when disturbances (a.k.a. process noise) dominate measurement noise, and vice versa. Finally, identi cation of positive systems is considered. Such systems enjoy substantially simpler stability and performance analysis compared to the general linear time-invariant iv Abstract (LTI) case, and appear frequently in applications where physical constraints imply nonnegativity of the quantities of interest. Lagrangian relaxation is used to derive new convex parametrizations of stable positive systems and quality-of- t criteria, and substantial improvements in accuracy of the identi ed models, compared to existing approaches based on weighted equation error, are demonstrated. Furthermore, the convex parametrizations of stable systems based on linear Lyapunov functions are shown to be amenable to distributed optimization, which is useful for identi cation of large-scale networked dynamical systems

Optimal Time-Invariant Distributed Formation Tracking for Second-Order Multi-Agent Systems

This paper addresses the optimal time-invariant formation tracking problem with the aim of providing a distributed solution for multi-agent systems with second-order integrator dynamics. In the literature, most of the results related to multi-agent formation tracking do not consider energy issues while investigating distributed feedback control laws. In order to account for this crucial design aspect, we contribute by formalizing and proposing a solution to an optimization problem that encapsulates trajectory tracking, distance-based formation control, and input energy minimization, through a specific and key choice of potential functions in the optimization cost. To this end, we show how to compute the inverse dynamics in a centralized fashion by means of the Projector-Operator-based Newton's method for Trajectory Optimization (PRONTO) and, more importantly, we exploit such an offline solution as a general reference to devise a novel online distributed control law. Finally, numerical examples involving a cubic formation following a straight path in the 3D space are provided to validate the proposed control strategies.Comment: 28 pages, 2 figures, submitted to the European Journal of Control on June 23rd, 2023 (version 1

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