arXiv subjects

Tyler Westenbroek

Publications and source records attributed to Tyler Westenbroek.

21 records · Page 2Linked to original sources

arXiv2017

On the Relaxation of Hybrid Dynamical Systems

Hybrid dynamical systems have proven to be a powerful modeling abstraction, yet fundamental questions regarding the dynamical properties of these systems remain. In this paper, we develop a novel class of relaxations which we use to recover a number of classic systems theoretic properties for hybrid systems, such as existence and uniqueness of trajectories, even past the point of Zeno. Our relaxations also naturally give rise to a class of provably convergent numerical approximations, capable of simulating through Zeno. Using our methods, we are also able to perform sensitivity analysis about nominal trajectories undergoing a discrete transition -- a technique with many practical applications, such as assessing the stability of periodic orbits.

math.DS↗

arXiv2017

Statistical Estimation with Strategic Data Sources in Competitive Settings

In this paper, we introduce a preliminary model for interactions in the data market. Recent research has shown ways in which a data aggregator can design mechanisms for users to ensure the quality of data, even in situations where the users are effort-averse (i.e. prefer to submit lower-quality estimates) and the data aggregator cannot observe the effort exerted by the users (i.e. the contract suffers from the principal-agent problem). However, we have shown that these mechanisms often break down in more realistic models, where multiple data aggregators are in competition. Under minor assumptions on the properties of the statistical estimators in use by data aggregators, we show that there is either no Nash equilibrium, or there is an infinite number of Nash equilibrium. In the latter case, there is a fundamental ambiguity in who bears the burden of incentivizing different data sources. We are also able to calculate the price of anarchy, which measures how much social welfare is lost between the Nash equilibrium and the social optimum, i.e. between non-cooperative strategic play and cooperation.

cs.GT↗

arXiv2016

Optimal Control of Hybrid Systems Using a Feedback Relaxed Control Formulation

We present a numerically tractable formulation for computing the optimal control of the class of hybrid dynamical systems whose trajectories are continuous. Our formulation, an extension of existing relaxed-control techniques for switched dynamical systems, incorporates the domain information of each discrete mode as part of the constraints in the optimization problem. Moreover, our numerical results are consistent with phenomena that are particular to hybrid systems, such as the creation of sliding trajectories between discrete modes.

math.OC↗