Final workshop schedule

Here is the proposed final schedule. If any of the information below is incorrect, or there are reasonable conflicts, please let us know.

Please notice that the sessions will take place in different buildings on Friday and Saturday. The two locations are very close to each other.

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Friday, April 21st. Grier Room, 34-401A

1:30	Welcome
1:40	Vincent Blondel, Université Catholique de Louvain / MIT Unsolved problems and applications of long matrix products
2:40	Break
3:00	Derek Paley, Princeton University Collective Motion of Self-Propelled Particles: Stabilizing Symmetric Formations on Closed Curves
3:20	Ming Cao, Yale University Asynchronous agreement in continuous time
3:40	Raphaël Jungers, U. Catholique Louvain / MIT Trackability of an agent in a sensor network
4:00	Break
4:20	Georgios Kotsalis, MIT Model reduction of hidden Markov chains
4:40	Emrah Biyik, Rensselaer Polytechnic Institute Area aggregation and time-scale modeling in sparse nonlinear networks
5:00	Svein Hovland, Norwegian University of Science and Technology / MIT Constrained Optimal Control for Large-Scale Systems via Model Reduction

Saturday, April 22nd. Stata Center, 32-141

8:30	Venkatesh Saligrama, Boston University Search and Discovery in an Uncertain Networked World
9:30	Break
9:40	Seong-Cheol Kang, Boston University On the Benefits of Distributional Information in Robust Linear Optimization
10:00	Erin Aylward, MIT Stability and Robustness Analysis of Nonlinear Systems via Contraction Metrics and SOS Programming
10:20	Jiaping Liu, Princeton University Stochastic stability of optimization-based network resource allocation
10:40	Break
11:00	Haidong Yuan, Harvard University Time optimal control of spin system with unequal coupling
11:20	Keyong Li, Cornell University Layered Optimization in the Trajectory Design of Autonomous Robots
11:40	Nader Motee, U. Pennsylvania Distributed Receding Horizon Control of Spatially Invariant Systems
12:00	Lunch Break
1:30	Shuchin Aeron, Boston University Energy efficient policies for distributed target tracking in multi-hop sensor networks
1:50	Raffaele Potami, Worcester Polytechnic Institute Scheduling policies of intelligent sensor/actuator networks in flexible structures
2:10	Jianfeng Mao, Boston University Optimal Control of Multi-Stage Discrete Event Systems with Real-Time Constraints
2:30	Break
2:50	Henri Aguesse, Boston University Active Interaction Graphs in Consensus and Related Cooperative Control Problems
3:10	Victor Preciado, MIT Low-Order Spectral Moments of Random Graphs with Specified Expected Degrees
3:30	Michael Belyea, U. Massachusetts at Amherst Distributed Robust Control of Nonlinear Sine-Gordon PDE
3:50	Liming Wang, Rutgers University Almost global convergence in singular perturbations of strongly monotone systems
4:10	Break
4:30	Zhiyun Lin, U. of Toronto An overview of reachability analysis of piecewise linear affine systems on simplices
4:50	Marius Kloetzer, Boston University Temporal Logic Control of Linear Systems
5:10	Agung Julius, U. Pennsylvania Approximate abstraction of stochastic systems
5:30	Wrapup

Abstracts

Energy efficient policies for distributed target tracking in multi-hop sensor networks

Shuchin Aeron

Boston University

We consider the problem of distributed target tracking in a sensor network under communication constraints between the sensor nodes, a problem that has recently received significant attention. The problem requires the dynamic selection of which sensor nodes will communicate their information and the selection of a corresponding fusion center which will process the collected information. Ideally, selection of which sensors will communicate and where will fusion take place will be a dynamic process, adapting to new information, to trade off tracking accuracy versus communications usage.
The resulting coupled problem is generally intractable and significant effort has been devoted towards proposing greedy strategies under various performance criteria. In this paper, we propose an adaptive dynamic strategy for sensor selection and fusion location using a certainty equivalence approach that seeks to optimize a tradeoff between tracking error and communications cost We define a certainty equivalent optimization problem for dynamic relocation of the fusion center that uses measures of average multi hop communications cost and average tracking errors, and solve the resulting optimal control problem for classes of tracking problems. The optimal strategy is a hybrid switching strategy, where the fusion center location and reporting sensors are held stationary unless the target estimates move outside of a threshold radius around the sensors. We illustrate the performance of our algorithms on sample tracking experiments with sensor networks.

Active Interaction Graphs in Consensus and Related Cooperative Control Problems

Henri Aguesse

Boston University

Cooperative control problems have a great theoretical interest for exploring the possibilities of synthetic group intelligence, as well as practical use in multi-agent robotic systems. Connectivity in such systems is a major issue and the interaction graph may be understood as the (N + 1)th agent in a N-element system, if this graph is an active variable in the system, instead of remaining a passive constraint. First we gather in a single formulation a class of autonomous systems, referred to as generalized consensus, including consensus and related autonomous cooperative control problems such as chaotic map synchronization and formation reaching. We take this class of problems as a field of experimentation for system with active interaction. Secondly we explore how active interaction can alter or improve the generalized consensus convergence. We propose three active interaction protocols improving the convergence rate, chaotic synchronization ability and acceptance of weak and moving underlying topology. An entropy description is proposed to measure the generalized consensus evolution and then evaluate the performance of these algorithms.

Stability and Robustness Analysis of Nonlinear Systems via Contraction Metrics and SOS Programming

Erin Aylward

MIT

Contraction analysis is a stability theory for nonlinear systems where stability is defined incrementally between two arbitrary trajectories. It provides an alternative framework in which to study uncertain systems or systems with external inputs, and offers advantages when compared with traditional Lyapunov analysis. Existence of a contraction metric for a given system is a necessary and sufficient condition for global exponential convergence of system trajectories.

For systems with polynomial or rational dynamics, we show how the search for contraction metrics can be made fully algorithmic through the use of convex optimization and sum of squares (SOS) programming. The search process is made computationally tractable by relaxing matrix definiteness constraints, whose feasibility indicates existence of a contraction metric, into SOS constraints on polynomial matrices.

We also use SOS methods to find bounds on the maximum amount of uncertainty allowed in certain types of systems in order for the system to retain the property of being contractive with respect to a contraction metric of the unperturbed system. Alternatively, with SOS methods we can also optimize the contraction matrix search to obtain a metric that provides the largest symmetric uncertainty interval for which we can prove the system is contracting. We illustrate our results through examples from the literature, emphasizing the advantages and contrasting the differences between the contraction approach and traditional Lyapunov techniques.

Distributed Robust Control of Nonlinear Sine-Gordon PDE

Michael Belyea

U. Massachusetts at Amherst

Design of controllers for distributed systems that can work effectively in the presence of wide uncertainty is a challenging task. In this talk we will present results on robust $H_2$ control of a prototype highly nonlinear Sine-Gordan partial differential equation that has wide spread applications in mechanics and physics.

Area aggregation and time-scale modeling in sparse nonlinear networks

Emrah Biyik

Rensselaer Polytechnic Institute

We study a nonlinear synchronization problem in which the network structure exhibits areas of internally dense and externally sparse interconnections. The densely connected nodes in these areas synchronize in the fast time-scale, and behave as aggregate nodes that dominate the slow dynamics of the network. We first derive a singular perturbation model which makes this time-scale separation explicit and, next, prove the validity of the reduced-model approximation on the infinite time interval. Our formulation is in part motivated by cooperative control applications where the implications of the communication architecture on the dynamic behavior of the network are not fully understood.

Unsolved problems and applications of long matrix products

Vincent Blondel

Université Catholique de Louvain / MIT

Abstract: In this talk I will survey several aspects of an apparently simple (but so far unsolved) question: under what conditions on the matrices A and B do all infinite products of the type ABBABAAAB... converge to zero? There is no known algorithm for this problem and it is so far unknown if the problem is algorithmically decidable. The maximal asymptotic growth rate that can be obtained by forming long products of matrices was first defined by Rota and Strang in the 60s and is known as the "joint spectral radius" of the matrices. In the last decade this concept has appeared a number of application contexts, including hybrid systems, multi-agent networks, wavelets, capacity of codes, and sensor networks. The joint spectral radius is notoriously difficult to compute even when constraints are imposed on the number of matrices, on their size, or on their entries. I will briefly describe a number of NP-hard, undecidable and other depressing negative results and will then move to more positive aspects. In particular, I will describe an algorithm that computes the joint spectral with arbitrary high accuracy and that is polynomial in the size of the matrices once the desired accuracy is fixed and I will present recent results for the computation of the capacity of codes and for sensor networks. During the talk I will mention a problem that has attracted much attention and that is still unsolved. The problem is this: assume that we want to obtain the largest possible asymptotic rate of growth of long products of matrices; can this optimal rate always be obtained by a periodic product? This is known not to be true for matrices with real entries but the case of rational (or even binary) entries is unsolved. This last question relates to a number of situations where one is asked whether or not optimality can be achieved with a periodic strategy. This is joint work with a number of co-authors, including Y. Nesterov, V. Protassov, J. Tsitsiklis and A. Vladimirov. The work on the trackability of sensor networks is joint work with my student R. Jungers who will present this application in more details at this conference.

Biography: Vincent D. Blondel received a Bachelor Degree in Engineering in Applied Mathematics from the University of Louvain (Louvain-la-Neuve, Belgium) in 1988, a Master Degree in Pure Mathematics from Imperial College (London, UK) and a Doctorate in 1992 from the University of Louvain.
In 1993, he was a visiting scientist at Oxford University. During the academic year 1993-1994, he was the Göran Gustafsson Fellow at the Royal Institute of Technology (Stockholm, Sweden). In 1993-1994 he was a research fellow a the French National Research Center in Control and Computer Science (INRIA, Rocquencourt-Paris). From 1994 to 1999 he was an associate professor at the Institute of Mathematics of the Université de Liège in Belgium. Since October 1999 he is with the University of Louvain where he is currently professor in the Department of Applied Mathematics. He has been a visitor with the Australian National University (1991), the University of California at Berkeley (1998), the Santa Fe Institute (2000), Harvard University (2001) and is visiting the Massachusetts Institute of Technology every year since 1994. He has also been an invited professor at the Ecole Normale Supérieure in Lyon (1998) and at the University of Paris VII (1999 and 2000).
Dr Blondel's major current research interests lie in several area of mathematical control theory and theoretical computer science. He has been a recipient of a Grant from the Trustees of the Mathematics Institute of Oxford University (1992), the Prize Agathon De Potter of the Belgian Royal Academy of Science (1993) and the Prize Paul Dubois of the Montefiore Institute (1993). He is the coordinator of a NATO collaborative grant with the Massachusetts Institute of Technology (USA) and the Russian Academy of Science, and is a partner in a European TMR network on discrete event systems. He is a former associate editor of the European Journal of Control (Springer) and an associate editor of Systems and Control Letters (Elsevier) and of the Journal on Mathematics of Control, Signals, and Systems (Springer). He was awarded the triennal SIAM prize on control and systems theory in 2001.

Asynchronous agreement in continuous time

Ming Cao

Yale University

We formulate and solve a continuous-time version of the widely studied Vicsek consensus problem in which each agent independently updates its heading at times determined by its own clock. It is not assumed that the agents' clocks are synchronized or that the "event" times between which any one agent updates its heading are evenly spaced. Heading updates need not occur instantaneously. Using the concept of "analytic synchronization" together with several key results concerned with properties of "compositions" of directed graphs, it is shown that the conditions under which a consensus is achieved are essentially the same as those applicable in the synchronous discrete-time case provided the notion of an agent's neighbor between its event times is appropriately defined.

Constrained Optimal Control for Large-Scale Systems via Model Reduction

Svein Hovland

Norwegian University of Science and Technology / MIT

Model predictive control (MPC) is a very popular control scheme, partly because of the intuitive way in which constraints can be incorporated in a multivariable control problem formulation. However, the traditional MPC strategy requires solving an optimization problem on line at each sampling time, limiting the use of these kind of controllers to processes with relatively slow dynamics. The recently introduced explicit solution of the MPC problem (eMPC) leads to online MPC functionality without having to solve an optimization problem at each time step, by solving multiparametric quadratic programs off line. The on line effort is reduced to evaluating a piecewise affine function of the system state.

Using eMPC and model reduction, we present methodology for achieving real-time constrained optimal control of system models of very high order, such as systems modeled by partial differential equations. Such systems are often linearized around steady-state operating points, leading to linear systems of potentially very high order. Although often acceptable for simulation purposes, the high order of the discretized (and linearized) models may be prohibitive for controller design. Our methodology tackles complexity reduction in two ways. First, the use of model reduction using a goal-oriented, model-based optimization formulation yields reduced models that are appropriate for use in controller design, tailored to the application at hand. Second, the implementation of eMPC gives a further reduction in computational requirements compared to using traditional MPC based on reduced-order models.

Consequently, a great deal of the computational burden is moved off line, facilitating implementation of constrained optimal control in applications that are described by models of high order, while being characterized by fast sampling or low cost, such as mechatronics, MEMS, rotating machinery, and acoustics, for instance for active control of combustion instability.

Approximate abstraction of stochastic systems

Agung Julius

U. Pennsylvania

The main idea of abstracting dynamical systems is, given a dynamical system, we construct a relatively simpler system that is, in some sense, equivalent to the original. Simpler system usually means a system that can be analyzed with less computing effort. The equivalence between the original system and its abstraction guarantees that the result of the computation performed on the abstraction can be carried over into the original system.

In this talk, I present a relaxed notion of abstraction for a class of stochastic systems, where the abstraction is only required to be approximately equal to the original system. This is done by introducing the concept of stochastic bisimulation function, with which we can measure the distance between the systems and hence the quality of the abstraction. For the class of systems concerned, the construction of such functions leads to a tractable computational problem.

Trackability of an agent in a sensor network

Raphaël Jungers

Université catholique de Louvain / MIT

An agent is moving along the edges of a directed graph whose nodes are colored. After every move of the agent the only information we have is the color of the newly occupied node, and we would like to determine the real trajectory of the agent, or the set of possible trajectories if more than one are possible. More generally, given such a sensor network, and any coloring of the nodes, we would like to know how fast can grow at worst the number of possible trajectories, when the length of the observation increases. If it does not grow too fast, we will say that the network is trackable.

In this talk, I will present the concept of joint spectral radius of sets of matrices and I will show how this concept is useful for characterize the trackability of a given sensor network. In general, questions related to the joint spectral radius are difficult to answer, but I will show that in the specific case of the trackability problem, we can efficiently solve them, and, in particular, we can decide trackability in polynomial time.

This is joint work with Prof. V. Blondel (MIT, Université catholique de Louvain) and V. Protassov (Moscow University).

On the Benefits of Distributional Information in Robust Linear Optimization

Seong-Cheol Kang

Boston University

Linear programming formulations cannot handle the presence of uncertainty in the problem data, and even small variations in the data can render an optimal solution infeasible. A number of robust linear optimization techniques have produced formulations (not necessarily linear) that guarantee the feasibility of the optimal solution for all realizations of the uncertain data. A recent methodology in the literature maintains the linearity of the formulation and is also able to strike a balance between the conservatism and quality of a solution. In this work we demonstrate how to use distributional information on the problem data to improve quality of solutions. We adopt the robust model in the literature and present an approach that leads to much more cost-effective solutions (by 50% or more in some instances) without compromising their conservatism. We apply our methodology to a stochastic inventory control problem with quality of service constraints.

Temporal Logic Control of Linear Systems

Marius Kloetzer

Boston University

We consider the following problem: given a linear system and an arbitrary LTL-X formula over an arbitrary set of linear predicates in its state variables, find a feedback control law with polyhedral bounds and a set of initial states so that all trajectories of the closed loop system satisfy the formula. Our solution to this problem consists of three main steps. First, we partition the state space in accordance with the predicates in the formula and construct a transition system over the partition quotient, which captures our capability of designing controllers. Second, using an approach similar to model checking, we determine runs of the transition system satisfying the formula. Third, we generate the control strategy in the form of a hybrid system. Illustrative examples are included.

Model Reduction for Hidden Markov Chains

Georgios Kotsalis

MIT

Hidden Markov Chains are a widely used model for finite-valued, discrete-time stochastic processes, which have found application in diverse fields ranging from computational biology to operations research. In this talk we present a model reduction method for Hidden Markov Chains. This method shares elements with a balanced truncation algorithm we recently developed for Linear Parameter-Varying Systems. We demonstrate the reduction procedure on a quantized hybrid system driven by white noise.

Layered Optimization in the Trajectory Design of Autonomous Robots

Keyong Li

Cornell University

In the design of autonomous robotic systems and other sophisticated mechatronics systems, separating the design problem into layers is often necessary. Thorough analysis can be carried out and sometimes optimal solutions can be found for each layer. However, the optimality or other desirable features might be lost when the design of each layer is synthesized into the system. Our work has been aimed at this issue. In this talk, we will mostly concentrate on the trajectory design of autonomous mobile robots based on motion primitives. The set of motion primitives presents an optimal control strategy that addresses the robot dynamics; the trajectory design deal with constraints posed by the environment in addition. It is known that the tradeoff between optimality and computation is critical for the combined problem. In our approach the optimality of the motion primitives is extended to the trajectory design with little computation, with the help of dynamic programming and the use of a heuristic cost-to-go function corresponding to avoiding the environmental constraints. We further show through examples that good candidates for the heuristic cost-to-go can be suggested by existing/intuitive design techniques or generated by learning.

An overview of reachability analysis of piecewise linear affine systems on simplices

Zhiyun Lin

University of Toronto

In this talk, we present an overview of recently developed results on reachability analysis of piecewise linear systems on simplices. Specifically, the problem is to find, if possible, a feedback control such that all trajectories of the closed-loop system leave the simplex only through some desired facets. This problem was first introduced by Habets and van Schuppen, which is a subproblem of reachability analysis of hybrid systems. In other words, in order to drive the state of a system from an initial operating region to a desired one while not entering into an unsafe region, the state space is partitioned into a set of adjacent simplices and the reachability problem is then divided into a local control and a supervisory control problem. The local control problem is to reach and cross some selected facets of a simplex ensuring that the state is driven towards the target region. In this talk, several necessary and sufficient conditions on the existence of a feedback control to reach a set of facets of a simplex are provided. An algorithm is also included to check these conditions.

Stochastic stability of optimization-based network resource allocation

Jiaping Liu

Princeton University

Distributed solutions of convex optimization can be used to provide control policies for iterative resource allocation in wired and wireless networks, including TCP congestion control and cross-layer design. However, most of the results are based on deterministic fluid model, ignoring stochastic effects at flow, packet, channel, and topology's levels. Recent results have established stochastic stability at flow and channel levels for limited classes of objective functions, constraint sets, and timescales of interactions. This paper extends the state-of-the-art to provide the most general conclusions thus far on stochastic stability of network resource allocation derived from dual algorithms of a general convex optimization. For any concave utility maximization over a general convex constraint set, stability and stochastic convergence to optimum are established for dual algorithms without timescale separation assumption. In particular, the interior of the feasibility set of the deterministic optimization problem is also the stability region under the Markov flow level stochastic model. The results are then extended to incorporate channel variations, coupled objective functions, and cross-layer design with non-exogenous variables.

Optimal Control of Multi-Stage Discrete Event Systems with Real-Time Constraints

Jianfeng Mao

Boston University

We consider Discrete Event Systems (DES) involving tasks with real-time constraints and seek to control processing times so as to minimize a cost function subject to each task meeting its own constraint. When tasks are processed over a single stage, it has been shown that there are structural properties of the optimal sample path that lead to very efficient solutions of such problems. When tasks are processed over multiple stages and are subject to end-to-end real-time constraints, these properties no longer hold and no obvious extensions are known. We consider a multi-stage problem with not only stage-dependent but also task-dependent cost functions over all tasks at each stage and derive several new optimality properties. These properties lead to the idea of introducing "virtual" deadlines at each stage before the last one, thus partially decoupling the stages so that the known efficient solutions for single-stage problems can be used. We prove that the solution ! obtained by an iterative Virtual Deadline Algorithm (VDA) converges to the global optimal solution of the multi-stage problem and illustrate the efficiency of the VDA through numerical examples.

Collective Motion of Self-Propelled Particles: Stabilizing Symmetric Formations on Closed Curves

Derek Paley

Princeton University

In this talk, I present a Lyapunov design for the stabilization of collective motion in a planar kinematic model of N particles moving at unit speed. I derive a control law that achieves asymptotic stability of symmetric formations, characterized by uniform rotation of M evenly spaced clusters of the particles on closed curves, where M is a divisor of N. In designing the control law, the phases of the particles around the curve are treated as a system of coupled oscillators. I assume that the particle interconnection topology is a fixed, connected, and undirected graph. An example is given for superellipses, which is a class of closed curves that includes circles, ellipses, and rounded rectangles. I will give an extension to the main result which stabilizes symmetric formations of constant (non-unit) speed particles around fixed beacons.

Distributed Receding Horizon Control of Spatially Invariant Systems

Nader Motee

U. Pennsylvania

We present a rigorous framework for the study of distributed spatially invariant systems with input and state constraints. The proposed approach is based on blending tools from operator theory and Fourier analysis of spatially invariant systems with receding horizon control and Multi Parametric Quadratic Programming (MPQP). Our contributions are two-fold: On one hand, we extend the recent results of Bamieh et al. on infinite-horizon optimal control of spatially invariant systems to finite receding horizon control with input and state constraints. On the other hand, our results can be interpreted as extension of the finite dimensional MPQP-based analysis of receding horizon control to distributed, spatially invariant systems. It is assumed that dynamics of each subsystem is uncoupled to the others, but the coupling appears through the finite horizon cost function. Specifically, we prove that for spatially invariant systems with constraints, optimal receding horizon controllers are piece-wise affine (represented as a convolution sum plus an offset). Moreover, the kernel of each convolution sum decays exponentially in the spatial domain mirroring the unconstrained infinite-horizon case.

Scheduling policies of intelligent sensor/actuator networks in flexible structures

Raffaele Potami

Worcester Polytechnic Institute

In this presentation, we revisit the problem of actuator/sensor placement in large civil infrastructures and flexible space structures within the context of spatial robustness. The positioning of these devices becomes more important in systems employing wireless sensor and actuator networks (WSAN) for improved control performance and for faster failure detection. The ability of the sensing and actuating devices to possess the property of spatial robustness results in reduced control energy and therefore the spatial distribution of disturbances is integrated into the location optimization measures.In our studies, the structure under consideration is a flexible plate clamped at all sides. First, we consider the case of sensor placement and the optimization scheme attempts to produce those locations that minimize the effects of the spatial distribution of disturbances on the state estimation error; thus the sensor locations produce state estimators with minimized disturbance-to-error transfer function norms. A two-stage optimization procedure is employed whereby one first considers the open loop system and the spatial distribution of disturbances is found that produces the maximal effects on the entire open loop state. Once this "worst" spatial distribution of disturbances is found, the optimization scheme then finds the locations that produce state estimators with minimum transfer functions. In the second part, we consider the collocated actuator/sensor pairs and the optimization scheme produces those locations that result in compensators with the smallest norms of the disturbance-to-state transfer functions. Going a step further, an intelligent control scheme is presented which, at each time interval, activates a subset of the actuator/sensor pairs in order provide robustness against spatiotemporally moving disturbances and minimize power consumption by keeping some sensor/actuators in sleep mode.

Low-Order Spectral Moments of Random Graphs with Specified Expected Degrees

Victor Preciado

MIT

We introduce a novel technique to analytically estimate the eigenvalue spectrum of the Laplacian of a large random graph. The method is based on analytically determining a few low-order moments of the eigenvalue distribution in the limit of large graphs, and performing a piecewise linear reconstruction of the eigenvalue spectrum that preserves these moments. By making use of algebraic properties of symmetric polynomials and Vieta's formulas, we reach an interesting geometrical interpretation that gives us guidance on shaping the degree sequence to achieve desired characteristics.

Search and Discovery in an Uncertain Networked World

Venkatesh Saligrama

Boston University

Wireless sensor networks---a network of massively distributed tiny devices capable of sensing, processing and exchanging data over a wireless medium---are envisioned to provide real-time information in such diverse applications as environmental remediation, power systems, and manufacturing. Energy fundamentally limits operability and lifetime of sensor networks. Consequently in-network processing, by which one means localized distributed algorithms for processing information, is a critical ingredient for achieving scalability and energy efficiency.

In our talk we will focus on two typical but diametrically opposite scenarios, namely search and discovery, encountered in sensor networks and develop localized distributed algorithms which are energy efficient as well as scalable to large network sizes. In the first scenario, namely, search problems the task is to locate an unknown number of objects with N distributed noisy ``local'' sensors, i.e. sensors that can sense only their local vicinity. In the second scenario, N distributed noisy sensors observe a single global event/target and must collaboratively discover/locate/track the phenomena/target. While discovery problems are characterized by significant spatial correlation between sensors and calls for collaborative processing strategies, search problems are characterized by negligible spatial correlation and entails strategies for efficiently ruling out those sensors that most likely do not contain desired information/target. We utilize random coalescing walks evolving on random graphs to obtain near-optimal energy efficiencies for in-network processing in an asynchronous, noisy, and energy limited communication environment.

Biography: Venkatesh Saligrama is an Associate Professor in the Department of Electrical and Computer Engineering at Boston University. Prior to joining Boston University in 2001, he was a Research Engineer at United Technologies Research Center. He received his Ph.D. from MIT and the B.Tech degree from IIT Madras. He is the recipient of the Presidential Early Career Award for Scientists and Engineers (PECASE), the Office of Naval Research Young Investigator Award, the NSF Career Award and the Outstanding Achievement Award from United Technologies. His team was a finalist in the Crossbow Sensor Network Challenge competition in 2005. He is currently serving as an Associate Editor of IEEE Transactions on Signal Processing since 2005. His research interests are in information and control, and distributed signal processing.

Almost global convergence in singular perturbations of strongly monotone systems

Liming Wang

Rutgers University

Monotone systems constitute a rich class of models for which global and "almost" global convergence properties can be established. They are particularly useful in biochemical models. In this talk, I will explain how we extend the theory of monontone systems using geometric singular perturbation theory.

Time optimal control of spin system with unequal coupling

Haidong Yuan

Harvard University

We study the problem of time optimal manipulation of dynamics of coupled spins in NMR (Nuclear Magnetic Resonance) spectroscopy and quantum information processing. In particular, we analyze the system of three linearly coupled spins with unequal couplings. We give time-optimal control laws for steering the state of the spins between points that are of significance in coherent spectroscopy.