Amir G. Aghdam

A Class of Bounded Distributed Control Strategies for Connectivity Preservation in Multi-Agent Systems

This technical note proposes a general class of distributed potential-based control laws with the connectivity preserving property for single-integrator agents. The potential functions are designed in such a way that when an edge in the information flow graph is about to lose connectivity, the gradient of the potential function lies in the direction of that edge, aiming to shrink it. The results are developed for a static information flow graph first, and then are extended to the case of dynamic edge addition. Connectivity preservation for problems involving static leaders is covered as well. The potential functions are chosen to be smooth, resulting in bounded control inputs. Other constraints may also be imposed on the potential functions to satisfy various design criteria such as consensus, containment, and formation convergence. The effectiveness of the proposed control strategy is illustrated by simulation for examples of consensus and containment.

A Model Predictive Decentralized Control Scheme With Reduced Communication Requirement for Spacecraft Formation

This brief investigates the control problem for a number of cooperative spacecraft with communication constraints. It is assumed that a set of cooperative local controllers corresponding to the individual spacecraft is given which satisfies the desired objectives of the formation. It is to be noted that due to the information exchange between the local controllers, the overall control structure can be considered centralized in general. However, communication in flight formation is expensive. Thus, it is desired to have some form of decentralization in control structure, which has a lower communication requirement. This decentralized controller consists of local estimators inherently, so that each local controller estimates the state of the whole formation. Necessary and sufficient conditions for the stability of the formation under the proposed decentralized controller are obtained. It is shown that the decentralized control system, if stable, behaves almost the same as its centralized counterpart. Moreover, robustness of the decentralized controller is studied and compared to that of the corresponding centralized controller. It is finally shown that the proposed decentralized controller comprises most of the features of its centralized counterpart. The efficacy of the proposed method is demonstrated through simulations.

Distributed Deployment Algorithms for Improved Coverage in a Network of Wireless Mobile Sensors

In this paper, efficient sensor deployment strategies are developed to increase coverage in wireless mobile sensor networks. The sensors find coverage holes within their Voronoi polygons and then move in an appropriate direction to minimize them. Novel edge-based and vertex-based strategies are introduced, and their performances are compared with existing techniques. The proposed movement strategies are based on the distances of each sensor and the points inside its Voronoi polygon from the edges or vertices of the polygon. Simulations confirm the effectiveness of the proposed deployment algorithms and their superiority to the techniques reported in the literature.

Distributed Deployment Strategies for Improved Coverage in a Network of Mobile Sensors With Prioritized Sensing Field

Efficient deployment strategies are proposed for a mobile sensor network, where the coverage priority of different points in the field is specified by a given function. The multiplicatively weighted Voronoi (MW-Voronoi) diagram is utilized to find the coverage holes of the network for the case where the sensing ranges of different sensors are not the same. Under the proposed strategies, each sensor detects coverage holes within its MW-Voronoi region, and then moves in a proper direction to reduce their size. Since the coverage priority of the field is not uniform, the target location of each sensor is determined based on the weights of the vertices or the points inside the corresponding MW-Voronoi region. Simulations validate the theoretical results.

Brief paper: Simultaneous LQ control of a set of LTI systems using constrained generalized sampled-data hold functions

In this paper, sampled-data control of a set of continuous-time LTI systems is considered. It is assumed that a predefined guaranteed continuous-time quadratic cost function, which is, in fact, the sum of the performance indices for all systems, is given. The main objective here is to design a decentralized periodic output feedback controller with a prespecified form, e.g., polynomial, piecewise constant, exponential, etc., which minimizes the above mentioned guaranteed cost function. This problem is first formulated as a set of matrix inequalities, and then by using a well-known technique, it is reformulated as a LMI problem. The set of linear matrix inequalities obtained provides necessary and sufficient conditions for the existence of a decentralized optimal simultaneous stabilizing controller with the prespecified form (rather than a general form). Moreover, an algorithm is presented to solve the resultant LMI problem. Finally, the efficiency of the proposed method is demonstrated in two numerical examples.

Brief paper: Leader localization in multi-agent systems subject to failure: A graph-theoretic approach

In this paper, structural controllability of a leader-follower multi-agent system with multiple leaders is studied. A graphical condition for structural controllability based on the information flow graph of the system is provided. The notions of p-link and q-agent controllability in a multi-leader setting are then introduced, which provide quantitative measures for the controllability of a system subject to failure in the agents and communication links. The problem of leader localization is introduced, which is concerned with finding the minimum number of agents whose selection as leaders results in a p-link or q-agent controllable network. Polynomial-time algorithms are subsequently presented to solve the problem for both cases of undirected and directed information flow graphs.

Structural controllability of multi-agent networks: Robustness against simultaneous failures

In this paper, structural controllability of a leader-follower multi-agent system with multiple leaders is studied from a graph-theoretic point of view. The problem of preservation of structural controllability under simultaneous failures in both the communication links and the agents is investigated. The effects of the loss of agents and communication links on the controllability of an information flow graph are previously studied. In this work, the corresponding results are exploited to introduce some useful indices and importance measures that help characterize and quantify the role of individual links and agents in the controllability of the overall network. Existing results are then extended by considering the effects of losses in both links and agents at the same time. To this end, the concepts of joint (r,s)-controllability and joint t-controllability are introduced as quantitative measures of reliability for a multi-agent system, and their important properties are investigated. Lastly, the class of jointly critical digraphs is introduced, and it is stated that if a digraph is jointly critical, then joint t-controllability is a necessary and sufficient condition for remaining controllable following the failure of any set of links and agents, with cardinality less than t. Various examples are exploited throughout the paper to elaborate on the analytical findings.

Self-Deployment Algorithms for Coverage Problem in a Network of Mobile Sensors with Unidentical Sensing Ranges

In this paper, efficient sensor deployment algorithms are proposed to improve the coverage area in the target field. The proposed algorithms calculate the position of the sensors iteratively, based on the existing coverage holes in the target field. The multiplicatively weighted Voronoi (MW-Voronoi) diagram is used to discover the coverage holes corresponding to different sensors with different sensing ranges. Under the proposed procedures, the sensors move in such a way that the coverage holes in the target field are reduced. Simulation results are provided to demonstrate the effectiveness of the deployment schemes proposed in this paper.

Brief paper: Control of continuous-time LTI systems by means of structurally constrained controllers

This paper deals with the characterization of the fixed modes of multi-channel systems with respect to linear time-invariant (LTI) structurally constrained controllers. Fixed modes can be found numerically for any LTI system with respect to any given control structure, using a random number generator. The existing analytical methods, however, are not capable of characterizing the fixed modes in the most general case of non-strictly proper systems with non-block diagonal (i.e., overlapping) control structure, efficiently. The notion of a decentralized overlapping fixed mode (DOFM) is introduced in this paper to address the above problem in the most general case. To this end, the knowledge of the overlapping control structure is translated into a bipartite graph, whose vertices correspond to the input and output vectors of various control channels. An efficient technique is applied to the obtained graph to identify the DOFMs of the system. It is to be noted that a system is stabilizable via an appropriate LTI decentralized overlapping controller if and only if it does not have any unstable DOFM. Moreover, it is shown how those modes which are not DOFMs can be placed freely in the complex plane using a proper LTI decentralized overlapping controller. The efficacy of this work is demonstrated through an example.

Technical communique: Sufficient conditions for the convergence of a class of nonlinear distributed consensus algorithms

This paper is concerned with the convergence of a class of continuous-time nonlinear consensus algorithms for single integrator agents. In the consensus algorithms studied here, the control input of each agent is assumed to be a state-dependent combination of the relative positions of its neighbors in the information flow graph. Using a novel approach based on the smallest order of the nonzero derivative, it is shown that under some mild conditions the convex hull of the agents has a contracting property. A set-valued LaSalle-like approach is subsequently employed to show the convergence of the agents to a common point. The results are shown to be more general than the ones reported in the literature in some cases. An illustrative example demonstrates how the proposed convergence conditions can be verified.