Related papers: Invariant, Viability and Discriminating Kernel Und…
A kernel-based framework for spatio-temporal data analysis is introduced that applies in situations when the underlying system dynamics are governed by a dynamic equation. The key ingredient is a representer theorem that involves…
This doctoral thesis develops new methods for set-based state estimation and active fault diagnosis (AFD) of (i) nonlinear discrete-time systems, (ii) discrete-time nonlinear systems whose trajectories satisfy nonlinear equality constraints…
This paper proposes new methods for set-based state estimation and active fault diagnosis (AFD) of linear descriptor systems (LDS). Unlike intervals, ellipsoids, and zonotopes, constrained zonotopes (CZs) can directly incorporate linear…
Hybrid systems - more precisely, their mathematical models - can exhibit behaviors, like Zeno behaviors, that are absent in purely discrete or purely continuous systems. First, we observe that, in this context, the usual definition of…
Recent deep learning models increasingly rely on depth without structural guarantees on the validity of intermediate representations, rendering early stopping and adaptive computation ill-posed. We address this limitation by formulating a…
Reachable set computation is an important technique for the verification of safety properties of dynamical systems. In this paper, we investigate reachable set computation for discrete nonlinear systems based on parallelotope bundles. The…
In this paper we consider autonomous driving of miniature race cars. The viability kernel is used to efficiently generate finite look-ahead trajectories that maximize progress while remaining recursively feasible with respect to static…
We revisit the problem of computing (robust) controlled invariant sets for discrete-time linear systems. Departing from previous approaches, we consider implicit, rather than explicit, representations for controlled invariant sets.…
Uncrewed aerial systems have tightly coupled energy and motion dynamics which must be accounted for by onboard planning algorithms. This work proposes a strategy for coupled motion and energy planning using model predictive control (MPC). A…
Many robotic systems are underactuated, meaning not all degrees of freedom can be directly controlled due to lack of actuators, input constraints, or state-dependent actuation. This property, compounded by modeling uncertainties and…
We consider the problem of computing reachable sets directly from noisy data without a given system model. Several reachability algorithms are presented for different types of systems generating the data. First, an algorithm for computing…
The paper presents a collection of results on continuous dependence for solutions to nonlocal problems under perturbations of data and system parameters. The integral operators appearing in the systems capture interactions via heterogeneous…
Quantum simulation - the use of one quantum system to simulate a less controllable one - may provide an understanding of the many quantum systems which cannot be modeled using classical computers. Impressive progress on control and…
For the analysis of molecular processes, the estimation of time-scales, i.e., transition rates, is very important. Estimating the transition rates between molecular conformations is -- from a mathematical point of view -- an invariant…
Classifiers and rating scores are prone to implicitly codifying biases, which may be present in the training data, against protected classes (i.e., age, gender, or race). So it is important to understand how to design classifiers and scores…
3D action recognition was shown to benefit from a covariance representation of the input data (joint 3D positions). A kernel machine feed with such feature is an effective paradigm for 3D action recognition, yielding state-of-the-art…
Transformers are designed for discrete tokens, yet many real-world signals are continuous processes observed through noisy sampling. Discrete tokenizations (raw values, patches, finite differences) can be brittle in low signal-to-noise…
We study positive definite kernels pulled back along a finite family of self-maps under a subinvariance inequality for the associated branching operator. Iteration produces an increasing kernel tower with defect kernels. Under diagonal…
Mixed-monotone systems are separable via a decomposition function into increasing and decreasing components, and this decomposition function allows for embedding the system dynamics in a higher-order monotone embedding system. Embedding the…
Recent contributions in the field of quantum state tomography have shown that, despite the exponential growth of Hilbert space with the number of subsystems, tomography of one-dimensional quantum systems may still be performed efficiently…