Related papers: Distances between finite-horizon linear behaviors
Given a complex system with a given interface to the rest of the world, what does it mean for a the system to behave close to a simpler specification describing the behavior at the interface? We give several definitions for useful notions…
In this paper, we systematically develop the $m$-contiguity distance between simplicial maps as a discrete approximation framework for homotopical complexity in the category of simplicial complexes. We construct an increasing sequence of…
Markov Decision Processes (MDPs) have been used to formulate many decision-making problems in science and engineering. The objective is to synthesize the best decision (action selection) policies to maximize expected rewards (or minimize…
Inexact methods for model predictive control (MPC), such as real-time iterative schemes or time-distributed optimization, alleviate the computational burden of exact MPC by providing suboptimal solutions. While the asymptotic stability of…
Learning governing dynamics from data is a common goal across the sciences, yet it is only well-posed when the underlying mechanisms are identifiable. In practice, many data-driven methods implicitly assume identifiability; when this…
This paper is concerned with the study of the stability of dynamical systems evolving on time scales. We first {formalize the notion of matrix measures on time scales, prove some of their key properties and make use of this notion to study…
We consider the notion of resilience for cyber-physical systems, that is, the ability of the system to withstand adverse events while maintaining acceptable functionality. We use finite temporal logic to express the requirements on the…
An optimal control law for networked control systems with a discrete-time linear time-invariant (LTI) system as plant and networks between sensor and controller as well as between controller and actuator is proposed. This controller is…
Explicit solutions to optimal control problems are rarely obtainable. Of particular interest are the explicit solutions derived for minimax problems, providing a framework to address adversarial conditions and uncertainty. This work…
This paper deals with the problem of finite-time learning for unknown discrete-time nonlinear systems' dynamics, without the requirement of the persistence of excitation. Two finite-time concurrent learning methods are presented to…
Persistent homology is a popular and useful tool for analysing finite metric spaces, revealing features that can be used to distinguish sets of unlabeled points and as input into machine learning pipelines. The famous stability theorem of…
The minimization of energy-like cost functionals is addressed in the context of optimal control problems. For a general class of dynamical systems, with possibly unstable and nonlinear free dynamics, it is shown that a sequence of solutions…
We develop a general framework for reasoning about distances between transition systems with quantitative information. Taking as starting point an arbitrary distance on system traces, we show how this leads to natural definitions of a…
In this paper, we provide a unified analysis of temporal difference learning algorithms with linear function approximators by exploiting their connections to Markov jump linear systems (MJLS). We tailor the MJLS theory developed in the…
While the design of optimal peak-to-peak controllers/observers for linear systems is known to be a difficult problem, this problem becomes interestingly much easier in the context of interval observers because of the positive nature of the…
Local integrals of motion (LIOMs) play a key role in understanding the long-time properties of closed macroscopic systems. They were found for selected integrable systems via complex analytical calculations. The existence of LIOMs and their…
This paper deals with the finite-time stabilization of a class of nonlinear infinite-dimensional systems. First, we consider a bounded matched perturbation in its linear form. It is shown that by using a set-valued function, both the…
Following a polynomial approach, many robust fixed-order controller design problems can be formulated as optimization problems whose set of feasible solutions is modelled by parametrized polynomial matrix inequalities (PMI). These…
Many functions have been recently defined to assess the similarity among networks as tools for quantitative comparison. They stem from very different frameworks - and they are tuned for dealing with different situations. Here we show an…
Recent advances in generative models have yielded impressive progress on motion in-betweening, allowing for more complex, varied, and realistic motion transitions. However, recent methods still exhibit noticeable limitations in preserving…