Andrés A. Peters

Francisco Aguilera, Víctor Jaque, Andrés A. Peters et al.

This paper studies expected $\mathcal{L}_2$ string stability of event-triggered vehicle platoons in which a human driver leads a chain of cooperatively controlled autonomous followers under stochastic communication delays. The leader's driving behavior propagates through the string via vehicle-to-vehicle (V2V) communication, so human-induced disturbances must not amplify along the platoon. Unlike deterministic approaches based on worst-case delay bounds, we derive string-stability conditions depending on the full delay distribution through integral inequalities. The closed-loop platoon is modeled as a stochastic hybrid system capturing vehicle dynamics, communication events, and event-triggering. This framework certifies string stability even when delays exceed deterministic admissible bounds with nonzero probability. Results are evaluated under several delay distributions using the MATLAB HyEQ simulator.

Andrés A. Peters, Francisco J. Vargas

In this work we present a framework for studying the eigenvalues of a family of matrices with a particular displacement structure. The family admits a specific decomposition as the product of an upper and a lower triangular matrices having an increasing number of real parameters in predefined positions. Similar matrices appear naturally when solving some kinds of optimal control problems. In our case, as stated by Nehari's theorem, the eigenvalues and eigenvectors fully characterize the solution. Commonly, such problems are solved by numerical means, making it difficult to obtain insight in the role that the parameters play on the solution. Our results provide a framework that enables to compute individually, under some simple assumptions, the eigenvalues of the matrices as roots of a monotone transcendental function with many desirable properties. In order to do so, we first obtain a three-term recursive characterization of the corresponding characteristic polynomials. This enables the aforementioned representation. Our framework also allows for the computation of bounds, numerical methods and even analytical characterizations with closed form solutions, whenever the problem parameters satisfy simple conditions.