An Information Theory of Finite Abstractions:
fundamental scalability limits and what to do next
How large does a finite abstraction need to be to represent a dynamical system accurately? After decades of research, abstractions are known to suffer from scalability bottlenecks and the curse of dimensionality, yet there has been no formal result on their size-accuracy tradeoff. This talk connects abstractions to rate-distortion theory, the information theory of lossy compression, to uncover fundamental limits on their scalability and develop a quantitative theory on their size-accuracy tradeoff.
IEEE Conference on Decision and Control (CDC) · 2021
Abstracting the Sampling Behaviour of Stochastic Linear
Periodic Event-Triggered Control Systems
Event-triggered control (ETC) reduces unnecessary sampling, but its
sampling patterns become difficult to characterize in the
presence of stochastic disturbances. I present an approach
using interval Markov chains to bound the expected values of
sampling-performance metrics expressed as discounted cumulative
rewards, providing a formal way to assess stochastic ETC's sampling behaviour.
IEEE Conference on Decision and Control (CDC) · 2020
Traffic Abstractions of Nonlinear Homogeneous
Event-Triggered Control Systems
Scheduling communication in networks of event-triggered
controllers requires models of when each controller may
transmit. I present finite-state abstractions that capture
the sampling behaviour of nonlinear homogeneous systems,
extending an approach previously developed for linear systems.
The talk also discusses how the construction could be
extended to more general nonlinear dynamics.