This paper deals with the problem of stabilizing an unstable system through networked control over the wireless medium. In such a situation a remote sensor communicates the measurements to the system controller through a noisy channel. In particular, in the AWGN scenario, we show that protograph-based LDPC convolutional codes achieve anytime reliability and we also derive a lower bound to the signal-to-noise ratio required to stabilize the system. Moreover, on the Rayleigh-fading channel, we show by simulations that resorting to multiple sensors reduces the SNR required for system stabilization.

This paper initiates a study toward developing and applying randomized algorithms for stability of high-speed communication networks. The focus is on congestion and delay-based flow controllers for sources, which are "utility maximizers" for individual users. First, we introduce a nonlinear algorithm for such source flow controllers, which uses as feedback aggregate congestion and delay information from bottleneck nodes of the network, and depends on a number of parameters, among which are link capacities, user preference for utility, and pricing. We then linearize this nonlinear model around its unique equilibrium point and perform a robustness analysis for a special symmetric case with a single bottleneck node. The "symmetry" here captures the scenario when certain utility and pricing parameters are the same across all active users, for which we derive closed-form necessary and sufficient conditions for stability and robustness under parameter variations. In addition, the ranges of values for the utility and pricing parameters for which stability is guaranteed are computed exactly. These results also admit counterparts for the case when the pricing parameters vary across users, but the utility parameter values are still the same. In the general nonsymmetric case, when closed-form derivation is not possible, we construct specific randomized algorithms which provide a probabilistic estimate of the local stability of the network. In particular, we use Monte Carlo as well as quasi-Monte Carlo techniques for the linearized model. The results obtained provide a complete analysis of congestion control algorithms for internet style networks with a single bottleneck node as well as for networks with general random topologies.

Research on congestion-control algorithms has traditionally focused more on performance than on robustness of the closed-loop system to changes in network conditions. As the performance of the control loop is strictly connected with the quality of service, these systems are natural candidates to be approached by the optimal control theory. Unfortunately, this approach may fail in the presence of transmission delay variations, which are unavoidable in telecommunication systems. In this paper, we first show the fragility of optimal controllers and demonstrate their instability when the control delay is not known exactly. Then we propose a robust control algorithm based on a classical proportional integral derivative scheme which does not suffer from this fragility phenomenon. Its stability versus the control delay variations, as well as versus sources that transmit less than their computed share, is studied with Nyquist analysis. The control algorithm is implemented within a simulator in the framework of the asynchronous transfer mode (ATM) ABR transfer capability. The final part of the paper shows some selected results assessing the performance of the control algorithm in a realistic network environment. ABR was chosen as an example, but the control studied here can be applied in any data network to obtain a robust and reliable congestion-control scheme.

The so-called analytic center approach to parameter estimation has been proposed as an alternative to the well-known least squares approach. This new approach offers a parameter estimate that is consistent with the past data observations, has a simple geometric interpretation, and is computable sequentially. We study the asymptotic performance of the analytic center approach and show that the resulting estimate converges to the true parameter asymptotically, provided some mild conditions are satisfied. These conditions involve some weak persistent excitation and independence between noise and regressor, similar to the least squares case. This result is used to derive a new parameter estimation approach which offers both good transient and asymptotic performance.

In this paper, we point out a theorem of Ando and its application to establishing necessary and sufficient conditions for linearity of spline, interpolatory, and almost strongly optimal algorithms on Lp spaces.

In this paper we prove that a Hilbert structure is necessary as well as sufficient for linearity of the following classes of Banach space approximation algorithms: spline, interpolatory, strongly optimal, and almost strongly optimal. In the context of information-based complexity, this provides a converse to the well-known result that a Hilbert structure is sufficient for such linearity properties.

This paper considers the problem of stopping rules, in the context of sequential Bayesian classification. In particular a new criterion, based on the probability of reversal of the obtained classification, is introduced and compared to more commonly used strategies. The results show good behavior of the proposed technique, with both simulated and real data drawn from biomedical application. In fact it appears that this stopping rule reduces the misallocation error rate with the same mean number of used features, or conversely, with an equal level of misallocation error rate, it reduces the mean number of features necessary to attain it.