Visibility maintenance via controlled invariance for leader-follower Dubins-like vehicles

The paper studies the visibility maintenance problem (VMP) for a leader-follower pair of Dubins-like vehicles with input constraints, and proposes an original solution based on the notion of controlled invariance. The nonlinear model describing the relative dynamics of the vehicles is interpreted as linear uncertain system, with the leader robot acting as an external disturbance. The VMP is then reformulated as a linear constrained regulation problem with additive disturbances (DLCRP). Positive D-invariance conditions for linear uncertain systems with parametric disturbance matrix are introduced and used to solve the VMP when box bounds on the state, control input and disturbance are considered. The proposed design procedure is shown to be easily adaptable to more general working scenarios. Extensive simulation results are provided to illustrate the theory and show the effectiveness of our approachComment: 17 pages, 24 figures, extended version of the journal paper of the authors submitted to Automatic

Learning Robustness with Bounded Failure: An Iterative MPC Approach

We propose an approach to design a Model Predictive Controller (MPC) for constrained Linear Time Invariant systems performing an iterative task. The system is subject to an additive disturbance, and the goal is to learn to satisfy state and input constraints robustly. Using disturbance measurements after each iteration, we construct Confidence Support sets, which contain the true support of the disturbance distribution with a given probability. As more data is collected, the Confidence Supports converge to the true support of the disturbance. This enables design of an MPC controller that avoids conservative estimate of the disturbance support, while simultaneously bounding the probability of constraint violation. The efficacy of the proposed approach is then demonstrated with a detailed numerical example.Comment: Added GitHub link to all source code

On Communication through a Gaussian Channel with an MMSE Disturbance Constraint

This paper considers a Gaussian channel with one transmitter and two receivers. The goal is to maximize the communication rate at the intended/primary receiver subject to a disturbance constraint at the unintended/secondary receiver. The disturbance is measured in terms of minimum mean square error (MMSE) of the interference that the transmission to the primary receiver inflicts on the secondary receiver. The paper presents a new upper bound for the problem of maximizing the mutual information subject to an MMSE constraint. The new bound holds for vector inputs of any length and recovers a previously known limiting (when the length of vector input tends to infinity) expression from the work of Bustin $\textit{et al.}$ The key technical novelty is a new upper bound on the MMSE. This bound allows one to bound the MMSE for all signal-to-noise ratio (SNR) values $\textit{below}$ a certain SNR at which the MMSE is known (which corresponds to the disturbance constraint). This bound complements the `single-crossing point property' of the MMSE that upper bounds the MMSE for all SNR values $\textit{above}$ a certain value at which the MMSE value is known. The MMSE upper bound provides a refined characterization of the phase-transition phenomenon which manifests, in the limit as the length of the vector input goes to infinity, as a discontinuity of the MMSE for the problem at hand. For vector inputs of size $n=1$, a matching lower bound, to within an additive gap of order $O \left( \log \log \frac{1}{\sf MMSE} \right)$ (where ${\sf MMSE}$ is the disturbance constraint), is shown by means of the mixed inputs technique recently introduced by Dytso $\textit{et al.}$Comment: Submitted to IEEE Transactions on Information Theor