This paper presents control and coordination algorithms for groups of vehicles. The focus is on autonomous vehicle networks performing distributed sensing tasks where each vehicle plays the role of a mobile tunable sensor. The paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies. The resulting closed-loop behavior is adaptive, distributed, asynchronous, and verifiably correct.

Coverage control for mobile sensing networks

In this paper, the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization. Stable feedback schemes obtainable from a given plant are parameterized. Salient properties of sensitivity reducing schemes are derived, and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity. The theory is developed for input-output systems in a general setting of Banach algebras, and then specialized to a class of multivariable, time-invariant systems characterized by n × n matrices of H? frequency response functions, either with or without zeros in the right half-plane. The approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity, and on the concept of an approximate inverse. Approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction. An indicator of approximate invertibility, called a measure of singularity, is introduced. The measure of singularity of a linear time-invariant plant is shown to be determined by the location of its right half-plane zeros. In the absence of plant uncertainty, the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure. In particular, if there are no right half-plane zeros, sensitivity can be made arbitrarily small. The feedback schemes used in the optimization of sensitiviiy resemble the lead-lag networks of classical control design. Some of their properties, and methods of constructing them in special cases are presented.

Feedback and Optimal Sensitivity: Model Reference Transformations, Multiplicative Seminorms, and Approximate Inverses

Robust consensus of uncertain linear multi-agent systems via dynamic output feedback

This technical note investigates a model reduction scheme for large-scale multiagent systems. The studied system is composed of identical linear subsystems interconnected by undirected weighted networks. To reduce the network complexity, a notion of nodal dissimilarity is established on the $\mathcal {H}_2$ -norms of transfer function deviations, and a new graph clustering algorithm is proposed to aggregate the pairs of nodes with smaller dissimilarities. The simplified system is verified to preserve an interconnection structure and the synchronization property. Moreover, a computable bound of the approximation error between the full-order and reduced-order models is provided, and the feasibility of the proposed approach is demonstrated by network examples.

https://pure.rug.nl/ws/files/134267923/Model_Reduction_of_Multiagent_Systems_Using_Dissimilarity_Based_Clustering.pdf

Model Reduction of Multiagent Systems Using Dissimilarity-Based Clustering

Network systems consist of subsystems and their interconnections, and provide a powerful framework for analysis, modeling and control of complex systems. However, subsystems may have high-dimensional dynamics, and the amount and nature of interconnections may also be of high complexity. Therefore, it is relevant to study reduction methods for network systems. An overview on reduction methods for both the topological (interconnection) structure of the network and the dynamics of the nodes, while preserving structural properties of the network, and taking a control systems perspective, is provided. First topological complexity reduction methods based on graph clustering and aggregation are reviewed, producing a reduced-order network model. Second, reduction of the nodal dynamics is considered by using extensions of classical methods, while preserving the stability and synchronization properties. Finally, a structure-preserving generalized balancing method for simplifying simultaneously the topological structure and the order of the nodal dynamics is treated.

/pdf/model-reduction-methods-for-complex-network-systems-3aik8rwq8w.pdf

Model Reduction Methods for Complex Network Systems

In the recent paper (Monshizadeh et al. in IEEE Trans Control Netw Syst 1(2):145–154, 2014. https://doi.org/10.1109/TCNS.2014.2311883
 ), model reduction of leader–follower multi-agent networks by clustering was studied. For such multi-agent networks, a reduced order network is obtained by partitioning the set of nodes in the graph into disjoint sets, called clusters, and associating with each cluster a single, new, node in a reduced network graph. In Monshizadeh et al. 
(2014), this method was studied for the special case that the agents have single integrator dynamics. For a special class of graph partitions, called almost equitable partitions, an explicit formula was derived for the $$\mathcal {H}_2$$
 model reduction error. In the present paper, we will extend and generalize the results from Monshizadeh et al. 
(2014) in a number of directions. Firstly, we will establish an a priori upper bound for the $$\mathcal {H}_2$$
 model reduction error in case that the agent dynamics is an arbitrary multivariable input–state–output system. Secondly, for the single integrator case, we will derive an explicit formula for the $$\mathcal {H}_\infty $$
 model reduction error. Thirdly, we will prove an a priori upper bound for the $$\mathcal {H}_\infty $$
 model reduction error in case that the agent dynamics is a symmetric multivariable input–state–output system. Finally, we will consider the problem of obtaining a priori upper bounds if we cluster using arbitrary, possibly non almost equitable, partitions.

/pdf/model-reduction-of-linear-multi-agent-systems-by-clustering-2zohrjqc9c.pdf

Model reduction of linear multi-agent systems by clustering with H-2 and H_infinity error bounds

Robust synchronization of coprime factor perturbed networks

In this paper, we consider the problem of model reduction of consensus networks. We propose a new method of model reduction based on removing edges that close cycles in the network graph. The agent dynamics of the consensus network is given by a symmetric multivariable input-state-output system. In the network, the agents exchange relative output information with their neighbors. We assume that the network graph is connected, unweighted, and undirected. The network used to approximate the original system is defined on the same number of nodes as the original graph, but its edge set is a strict subset of the original edge set. Explicit expressions and upper bounds for the approximation errors are formulated in terms of the signed path vectors of the removed edges and the eigenvalues of the Laplacian matrices of the original and reduced network graphs.

/pdf/model-reduction-of-networked-multiagent-systems-by-cycle-55ooeedlug.pdf

Model Reduction of Networked Multiagent Systems by Cycle Removal

In this paper we consider the problem of approximating a consensus network by a less complex network, by removing cycles from the original network graph. The consensus network consists of agents that exchange relative state information with their neighbors in the network. We assume the agents have single-integrator dynamics and the network graph is undirected. The network used to approximate the original system has the same nodes as the original graph, but its edge set is a strict subset of the original edge set. We obtain a priori upper bounds on the absolute approximation error, depending on the length of the removed cycles, the algebraic connectivity of a chosen spanning tree of the network graph, and the largest eigenvalue of the Laplacian matrix of that spanning tree.

Model reduction of consensus networks by graph simplification

This paper deals with robust synchronization of directed and undirected multi-agent networks with uncertain agent dynamics. Given a network with identical nominal dynamics, we allow uncertainty in the form of coprime factor perturbations of the transfer matrix of the agent dynamics. These perturbations are assumed to be stable and have H∞norm that is bounded by an a priori given desired tolerance. We derive state space equations for dynamic observer based protocols that achieve robust synchronization in the presence of such uncertainty. We show that this robust synchronization of the network by the dynamic protocol is equivalent to robust stabilization of a single linear system by all controllers from a given set of feedback controllers. The synchronizing protocols are expressed in terms of real symmetric solutions to algebraic Riccati equations related to the nominal agent dynamics, and contain a weighting factor depending on the eigenvalues of the graph Laplacian. We obtain an achievable interval, i.e. an interval such that for each value of the tolerance contained in this interval there exists a robustly synchronizing protocol. For undirected networks, the supremum of this interval is proportional to the square root of the quotient of the smallest and the largest eigenvalue of the graph Laplacian.

Hidde-Jan Jongsma

Papers

Model reduction of linear multi-agent systems by clustering with H-2 and H_infinity error bounds

Robust synchronization of coprime factor perturbed networks

Model Reduction of Networked Multiagent Systems by Cycle Removal

Model reduction of consensus networks by graph simplification

Robust synchronization of directed networks with coprime factor perturbed agent dynamics