This paper focuses on disturbance propagation in vehicle strings. It is known that using only relative spacing information to follow a constant distance behind the preceding vehicle leads to string instability. Specifically, small disturbances acting on one vehicle can propagate and have a large effect on another vehicle. We show that this limitation is due to a complementary sensitivity integral constraint. We also examine how the disturbance to error gain for an entire platoon scales with the number of vehicles. This analysis is done for the predecessor following strategy as well as a control structure where each vehicle looks at both neighbors.

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This technical note considers the stability of a feedback connection of a known linear, time-invariant system and a perturbation. The input/output behavior of the perturbation is described by an integral quadratic constraint (IQC). IQC stability theorems can be formulated in the frequency domain or with a time-domain dissipation inequality. The two approaches are connected by a non-unique factorization of the frequency domain IQC multiplier. The factorization must satisfy two properties for the dissipation inequality to be valid. First, the factorization must ensure the time-domain IQC holds for all finite times. Second, the factorization must ensure that a related matrix inequality, when feasible, has a positive semidefinite solution. This technical note shows that a class of frequency domain IQC multipliers has a factorization satisfying these two properties. Thus the dissipation inequality test, with an appropriate factorization, can be used with no additional conservatism. Index Terms-Integral quadratic constraint (IQC), linear time-invariant (LTI).

The problem of discrete time state estimation with lossy measurements is considered. This problem arises, for example, when measurement data is communicated over wireless channels subject to random interference. We describe the loss probabilities with Markov chains and model the joint plant / measurement loss process as a Markovian Jump Linear System. The time-varying Kalman estimator (TVKE) is known to solve a standard optimal estimation problem for Jump Linear Systems. Though the TVKE is optimal, a simpler estimator design, which we term a Jump Linear Estimator (JLE), is introduced to cope with losses. A JLE has predictor/corrector form, but at each time instant selects a corrector gain from a finite set of precalculated gains. The motivation for the JLE is twofold. First, the real-time computational cost of the JLE is less than the TVKE. Second, the JLE provides an upper bound on TVKE performance. In this paper, a special class of JLE, termed Finite Loss History Estimators (FLHE), which uses a canonical gain selection logic is considered. A notion of optimality for the FLHE is defined and an optimal synthesis method is given. In a simulation study for a double integrator system, performances are compared to both TVKE and theoretical predictions.

In this paper we study the effect of communication packet losses in the feedback loop of a control system. Our motivation is derived from vehicle control problems where information is communicated via a wireless local area network. For such problems, we consider a simple packet-loss model for the communicated information and note that results for discrete-time linear systems with Markovian jumping parameters can be applied. The goal is to find a controller (if one exists) such that the closed loop is mean square stable for a given packet loss rate. A linear matrix inequality (LMI) condition is developed for the existence of a stabilizing dynamic output feedback controller. This LMI condition is used to study the effect of communication losses on a vehicle following problem. In summary, these results can be used not only to design controllers but also give a 'worst-case' performance specification (in terms of packet-loss rate) for an acceptable communications system.

The subject of this report is a methodology for the transformation of (experimental) data into predictive models. We use a concrete example, drawn from the field of combustion chemistry, and examine the data in terms of precisely defined modes of scientific collaboration. The numerical methodology that we employ is founded on a combination of response surface technique and robust control theory. The numerical results show that an essential element of scientific collaboration is collaborative processing of data, demonstrating that combining the entire collection of data into a joint analysis extracts substantially more of the information content of the data.

The numerical approach of data collaboration is extended to address the mutual consistency of experimental observations. The analysis rests on the concept of a dataset, which represents an organization of pertinent experimental observations, their uncertainties, and mechanistic knowledge of the subject of interest. The numerical foundation of data collaboration lies in constrained optimization, utilizing solution mapping tools and robust control algorithms. A rigorous measure of dataset consistency is developed, and Lagrange multipliers are used to identify factors that influence consistency. The new analysis is demonstrated on a real-world example, taken from the field of combustion. In performing the consistency test, the new procedure identifies two major outliers of the dataset, which were corrected upon re-examination of the raw experimental data. The results of the analysis suggest a sequential procedure with step-by-step identification of outliers and inspection of the causes. Altogether, the new numerical approach offers an important tool for assessing experimental observations and model building.