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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 |

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.

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.

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.

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.

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.

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).

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.