Demetri P. Spanos

Approximate distributed Kalman filtering in sensor networks with quantifiable performance

We analyze the performance of an approximate distributed Kalman filter proposed in recent work on distributed coordination. This approach to distributed estimation is novel in that it admits a systematic analysis of its performance as various network quantities such as connection density, topology, and bandwidth are varied. Our main contribution is a frequency-domain characterization of the distributed estimators steady-state performance; this is quantified in terms of a special matrix associated with the connection topology called the graph Laplacian, and also the rate of message exchange between immediate neighbors in the communication network.

Robust connectivity of networked vehicles

We present a simple geometric analysis of wireless connectivity in vehicle networks. We introduce a localized notion of connectedness, and construct a function that measures the robustness of this local connectedness to variations in position. Under a mild feasibility hypothesis, this function provides a sufficient condition for global connectedness of the network. Further, it is distributed, in the sense that both the function and its gradients can be calculated using only neighbor-to-neighbor communications. It can thus form the basis for distributed motion-control algorithms which respect connectivity constraints. We conclude with two simple examples of target applications.

Asynchronous distributed averaging on communication networks

Distributed algorithms for averaging have attracted interest in the control and sensing literature. However, previous works have not addressed some practical concerns that will arise in actual implementations on packet-switched communication networks such as the Internet. In this paper, we present several implementable algorithms that are robust to asynchronism and dynamic topology changes. The algorithms are completely distributed and do not require any global coordination. In addition, they can be proven to converge under very general asynchronous timing assumptions. Our results are verified by both simulation and experiments on Planetlab, a real-world TCP/IP network. We also present some extensions that are likely to be useful in applications.

Motion planning with wireless network constraints

This work discusses feasibility aspects of motion planning for groups of agents connected by a range-constrained wireless network. Specifically, we address the difficulties encountered when trajectories are required to preserve the connectedness of the network. The analysis utilizes a quantity called the connectivity robustness of the network, which can be calculated in a distributed fashion, and thus is applicable to distributed motion planning problems arising in control of vehicle networks. Further, these results show that network constraints posed as connectivity robustness constraints have minimal impact on reachability, provided that an appropriate topology control algorithm is implemented. This contrasts with more naive approaches to connectivity maintenance, which can significantly reduce the reachable set.

On LQG control across a stochastic packet-dropping link

In this paper, we consider the problem of optimal linear quadratic Gaussian control of a system in which communication between the sensor and the controller occurs across a packet-dropping link. We first prove a separation principle that allows us to solve this problem using a standard LQR state-feedback design, along with an optimal algorithm for propagating and using the information across the unreliable link. Then we present one such optimal algorithm, which consists of a Kalman filter at the sensor side of the link, and a switched linear filter at the controller side. Our design does not assume any statistical model of the packet drop events, and is thus optimal for any arbitrary packet drop pattern. Further, the solution is appealing from a practical point of view because it can be implemented as a small modification of an existing LQG control design.

Distributed Averaging on Asynchronous Communication Networks

Distributed algorithms for averaging have attracted interest in the control and sensing literature. However, previous works have not addressed some practical concerns that will arise in actual implementations on packet-switched communication networks such as the Internet. In this paper, we present several implementable algorithms that are robust to asynchronism and dynamic topology changes. The algorithms do not require global coordination and can be proven to converge under very general asynchronous timing assumptions. Our results are verified by both simulation and experiments on a real-world TCP/IP network.

Optimization flow control with estimation error

We analyze the effects of price estimation error in a dual-gradient optimization flow control scheme, and characterize the performance of the algorithm in this case. By treating estimation error as inexactness of the gradient, we utilize sufficient conditions for convergence subject to bounded error to characterize the long-term dynamics of the link utilization in terms of a region, which the trajectory enters in finite time. We explicitly find bounds for this region under a particular quantization error model, and provide simulation results to verify the predicted behavior of the system. Finally, we analyze the effects of the stepsize on the convergence of the algorithm, and provide analytical and numerical results, which suggest a particular choice for this parameter.