Dr. Andrea Carron
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Postdoc Fellow, |
Research Topics
Safe Learning for Distributed Systems with Bounded Uncertainties
Learning in interacting dynamical systems can lead to instabilities and violations of critical safety constraints, which is limiting its application to constrained system networks. This work introduces two safety frameworks that can be applied together with any learning method for ensuring constraint satisfaction in a network of uncertain systems, which are coupled in the dynamics and in the state constraints. The proposed techniques make use of a safe set to modify control inputs that may compromise system safety, while accepting safe inputs from the learning procedure. Two different safe sets for distributed systems are proposed by extending recent results for structured invariant sets. The sets differ in their dynamical allocation to local sets and provide different trade-offs between required communication and achieved set size. The proposed algorithms are proven to keep the system in the safe set at all times and their effectiveness and behavior is illustrated in a numerical example.
On a Correspondence between Probabilistic and Robust Invariant Sets for Linear Systems
Dynamical systems with stochastic uncertainties are ubiquitous in the field of control, with linear systems under additive Gaussian disturbances a most prominent example. The concept of probabilistic invariance was introduced to extend the widely applied concept of invariance to this class of problems. Computational methods for their synthesis, however, are limited. In this work we present a relationship between probabilistic and robust invariant sets for linear systems, which enables the use of well-studied robust design methods. Conditions are shown, under which a robust invariant set, designed with a confidence region of the disturbance, results in a probabilistic invariant set. We furthermore show that this condition holds for common box and ellipsoidal confidence regions, generalizing and improving existing results for probabilistic invariant set computation. We finally exemplify the synthesis for an ellipsoidal probabilistic invariant set. Two numerical examples demonstrate the approach and the advantages to be gained from exploiting robust computations for probabilistic invariant sets.
Scalable Model Predictive Control of Autonomous Mobility on Demand Systems
Technological advances in self driving vehicles will soon enable the implementation of large-scale mobility-on-demand systems with autonomous agents. The efficient management of the vehicle fleet remains a key challenge, in particular for enabling a demand-aligned distribution of available vehicles, commonly referred to as rebalancing. In this work we present a discrete-time model of an autonomous mobility-on-demand system, in which unit capacity self driving vehicles serve transportation requests consisting of a (time, origin, destination) tuple on a directed graph. Time delays in the discrete time model are approximated as first-order lag elements yielding a sparse model suitable for model-predictive control. The well-posedness of the model is demonstrated and a characterization of its equilibrium points is given. Furthermore, we show the stabilizability of the model and propose a scalable model-predictive control scheme with complexity that scales linearly with the size of the city. We verify the performance of the scheme in a multi-agent transport simulation and demonstrate that service levels outperform those of existing rebalancing schemes at identical fleet sizes