Related papers: Data-driven Reachability using Christoffel Functio…
We consider approximation or recovery of functions based on a finite number of function evaluations. This is a well-studied problem in optimal recovery, machine learning, and numerical analysis in general, but many fundamental insights were…
We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…
The problem of function approximation by neural dynamical systems has typically been approached in a top-down manner: Any continuous function can be approximated to an arbitrary accuracy by a sufficiently complex model with a given…
Predictions in the form of sets of probability distributions, so-called credal sets, provide a suitable means to represent a learner's epistemic uncertainty. In this paper, we propose a theoretically grounded approach to credal prediction…
A new analytical approximation function is proposed to accurately fit the solution of a fractional differential equation of order one-half, whose nonhomogeneous term is defined by a modified Bessel function of the first kind. The exact…
To verify the correct operation of systems, engineers need to determine the set of configurations of a dynamical model that are able to safely reach a specified configuration under a control law. Unfortunately, constructing models for…
Several problems in modeling and control of stochastically-driven dynamical systems can be cast as regularized semi-definite programs. We examine two such representative problems and show that they can be formulated in a similar manner. The…
Hybrid dynamical systems with nonlinear dynamics are one of the most general modeling tools for representing robotic systems, especially contact-rich systems. However, providing guarantees regarding the safety or performance of nonlinear…
There has been an increasing interest in using neural networks in closed-loop control systems to improve performance and reduce computational costs for on-line implementation. However, providing safety and stability guarantees for these…
This paper investigates reachability analysis for max-plus linear systems (MPLS), an important class of dynamical systems that model synchronization and delay phenomena in timed discrete-event systems. We specifically focus on backward…
In this work, we present a novel Koopman spectrum-based reachability verification method for nonlinear systems. Contrary to conventional methods that focus on characterizing all potential states of a dynamical system over a presupposed time…
This paper is concerned with identifying linear system dynamics without the knowledge of individual system trajectories, but from the knowledge of the system's reachable sets observed at different times. Motivated by a scenario where the…
In this paper, we present an analytical approach for the synthesis of ellipsoidal probabilistic reachable sets of saturated systems subject to unbounded additive noise. Using convex optimization methods, we compute a contraction factor of…
In this paper the infinite horizon optimal regulation problem is solved online for a deterministic control-affine nonlinear dynamical system using the state following (StaF) kernel method to approximate the value function. Unlike…
We investigate the problem of data-driven, on-the-fly control of systems with unknown nonlinear dynamics where data from only a single finite-horizon trajectory and possibly side information on the dynamics are available. Such side…
Christoffel polynomials are classical tools from approximation theory. They can be used to estimate the (compact) support of a measure $\mu$ on $\mathbb{R}^d$ based on its low-degree moments. Recently, they have been applied to problems in…
We employ reachability analysis in designing dynamic quantization schemes for the remote state estimation of linear systems over a finite date rate communication channel. The quantization region is dynamically updated at each transmission…
Conformance is defined as a measure of distance between the behaviors of two dynamical systems. The notion of conformance can accelerate system design when models of varying fidelities are available on which analysis and control design can…
We characterize the reachability probabilities in stochastic directed graphs by means of reinforcement learning methods. In particular, we show that the dynamics of the transition probabilities in a stochastic digraph can be modeled via a…
In continuous-time optimal control, evaluating the Hamiltonian requires solving a constrained optimization problem using the system's dynamics model. Hamilton-Jacobi reachability analysis for safety verification has demonstrated practical…