Showing papers by "Ali Saberi published in 2008"

Designing spatially heterogeneous strategies for control of virus spread

Abstract: The spread of a virus - whether in a human population, computer network or cell-to-cell - is closely tied to the spatial (graph) topology of the interactions among the possible infectives. The authors study the problem of allocating limited control resources (e.g. quarantine or recovery resources) in these networks in a way that exploits the topological structure, so as to maximise the speed at which the virus is eliminated. For both multi-group and contact-network models for spread, these problems can be abstracted to a particular decentralised control problem for which the goal is to minimise the dominant eigenvalue of a system matrix. Explicit solutions to these problems are provided, using eigenvalue sensitivity ideas together with constrained optimisation methods employing Lagrange multipliers. The proposed design method shows that the optimal strategy is to allocate resources so as to equalise the propagation impact of each network component, as best as possible within the constraints on the resource. Finally, we show that this decentralised control approach can provide significant advantage over a homogeneous control strategy, in the context of a model for SARS transmission in Hong Kong.

Improving the quality of nanocrystalline MgAl2O4 spinel coating on graphite by a prior oxidation treatment on the graphite surface

Abstract: This paper aims to report the effect of surface oxidation treatment on graphite flakes and its effect on the improvement of MgAl2O4 spinel coating developed by sol–gel citrate process. The graphite surface was oxidized by hydrogen peroxide and the coating was subsequently applied. The coating structure, water-wettability and oxidation resistance of coated samples were taken as criteria to evaluate the coating integrity. It was clarified that the oxidation treatment developed hydrophilic functional groups on graphite surface. This helped the formation of an even and smooth MgAl2O4 spinel coating texture on graphite flakes. The water-wettability and oxidation resistance were also found to be improved significantly compared to non-treated samples. The results were supported by thermogravimetric analysis, contact angle and zeta-potential measurements.

A new focus in the science of networks: towards methods for design

Abstract: In recent years, a realization that networks are ubiquitous in the natural and engineered worlds has led to a burgeoning interest in finding commonalities in their structures and dynamics. Here, we introduce a new design focus in this science of networks by proposing generic methods for synthesizing network controllers that exploit the topological structure. That is, we motivate a canonical controller synthesis problem for networks that has applications in such diverse areas as virus-spreading control and air traffic flow management. We address this design problem by using new techniques from decentralized control theory. Specifically, we mesh optimization machinery together with eigenvalue sensitivity and graph theory notions to identify general structural features of optimally actuated networks. From these features, we are in turn able to explicitly construct high-performance controllers, i.e. the ones that best exploit the network’s topological structure. Our general approach for controller design is important because it both provides a broad insight into the structure of well-designed networks and contributes engineering solutions in numerous application areas (e.g. reduction in management delays and human-controller workload in air traffic systems).

On the structure of graph edge designs that optimize the algebraic connectivity

Abstract: We take a structural approach to the problem of designing the edge weights in an undirected graph subject to an upper bound on their total, so as to maximize the algebraic connectivity. Specifically, we first characterize the eigenvector(s) associated with the algebraic connectivity at the optimum, using optimization machinery together with eigenvalue sensitivity notions. Using these characterizations, we fully address optimal design in tree graphs that is quadratic in the number of vertices, and also obtain a suite of results concerning the topological and eigen-structure of optimal designs for bipartite and general graphs.

A multiple-derivative and multiple-delay paradigm for decentralized controller design: Introduction using the canonical double-integrator network

Abstract: We are engaged in a major effort to design decentralized controllers for modern networks, that is fundamentally based on 1) applying feedback of multiple derivatives of local observations and 2) implementing these derivative feedbacks using multiple-delay controllers. Here, we fully motivate and introduce the design paradigm in the context of a canonical sensing-network model, namely a network of saturating double integrators with general sensing topology that is subject to measurement delays. In this context, we illustrate that our design paradigm yields practical high-performance (in particular, group pole-placement) decentralized controllers that exploit the network topology while distributing the complexity and actuation requirements among the agents.

Majorizations for the dominant eigenvector of a nonnegative matrix

Abstract: Motivated by network controller design applications, we develop several majorization results for the dominant eigenvector of an irreducible nonnegative matrix.

A Flexible Stochastic Automaton-Based Algorithm for Network Self-Partitioning

Abstract: This article proposes a flexible and distributed stochastic automaton-based network partitioning algorithm that is capable of finding the optimal k-way partition with respect to a broad range of cost functions, and given various constraints, in directed and weighted graphs. Specifically, we motivate the distributed partitioning (self-partitioning) problem, introduce the stochastic automaton-based partitioning algorithm, and show that the algorithm finds the optimal partition with probability 1 for a large class of partitioning tasks. Also, a discussion of why the algorithm can be expected to find good partitions quickly is included, and its performance is further illustrated through examples. Finally, applications to mobile/sensor classification in ad hoc networks, fault-isolation in electric power systems, and control of autonomous vehicle teams are pursued in detail.

On multiple-delay static output feedback stabilization of LTI plants

Abstract: We develop a control methodology for linear time-invariant plants that uses multiple delayed observations in feedback. Using the special coordinate basis (SCB), we show that multiple-delay controllers can always be designed to stabilize minimum-phase plants, and identify a class of non-minimum-phase plants that can be stabilized using these controllers.

An alternative approach to designing stabilizing compensators for saturating linear time-invariant plants

Abstract: We present a new methodology for designing low-gain linear time-invariant (LTI) controllers for semi-global stabilization of an LTI plant with actuator saturation, that is based on representation of a proper LTI feedback using a precompensator plus static-output-feedback architecture. We also mesh the new design methodology with time-scale notions to develop lower-order controllers for some plants.

On time-scale designs for networks

Abstract: We motivate the problem of designing a subset of the edge weights in a graph, to shape the spectrum of an associated linear time-invariant dynamics. We address a canonical design problem of this form by applying time-scale assignment methods, and give graph-theoretic characterizations of the designed dynamics.

On external semi-global stochastic stabilization of a double integrator with input saturation

Abstract: This paper considers external semi-global stochastic stabilization for linear plants with saturating actuators, driven by a stochastic external disturbance, and having random Gaussian-distributed initial conditions. Recently, it has been shown that for critically stable systems there exists a linear static state feedback law that achieves global asymptotic stability in the absence of disturbances, while guaranteeing a bounded variance of the state vector in the presence of disturbances and Gaussian distributed initial conditions. We report how this result extends to a double integrator with input saturation.