Related papers: Model Checking Linear Dynamical Systems under Floa…
We present a black-box method to numerically investigate the linear stability of arbitrary multi-physics problems. While the user just has to enter the system's residual in weak formulation, i.e. by a finite element method, all required…
Floating point arithmetic allows us to use a finite machine, the digital computer, to reach conclusions about models based on continuous mathematics. In this article we work in the other direction, that is, we present examples in which…
This paper presents a time-optimal Model Predictive Control (MPC) scheme for linear discrete-time systems subject to multiplicative uncertainties represented by interval matrices. To render the uncertainty propagation computationally…
This paper proposes a computationally efficient framework, based on interval analysis, for rigorous verification of nonlinear continuous-time dynamical systems with neural network controllers. Given a neural network, we use an existing…
Biological systems are often modeled as a system of ordinary differential equations (ODEs) with time-invariant parameters. However, cell signaling events or pharmacological interventions may alter the cellular state and induce multi-mode…
Round-off errors arising from the difference between real numbers and their floating-point representation cause the control flow of conditional floating-point statements to deviate from the ideal flow of the real-number computation. This…
We present an extension of Willems' Fundamental Lemma to the class of multi-input multi-output discrete-time feedback linearizable nonlinear systems, thus providing a data-based representation of their input-output trajectories. Two sources…
We consider a system consisting of a planar random walk on a square lattice, submitted to stochastic elementary local deformations. Depending on the deformation transition rates, and specifically on a parameter $\eta$ which breaks the…
We consider bounded extremum seeking controls for time-varying linear systems with uncertain coefficient matrices and measurement uncertainty. Using a new change of variables, Lyapunov functions, and a comparison principle, we provide…
Conserved dynamical systems are generally considered to be critical. We study a class of critical routing models, equivalent to random maps, which can be solved rigorously in the thermodynamic limit. The information flow is conserved for…
Bayesian analysis of state-space models includes computing the posterior distribution of the system's parameters as well as filtering, smoothing, and predicting the system's latent states. When the latent states wander around $\mathbb{R}^n$…
Algorithms operating on real numbers are implemented as floating-point computations in practice, but floating-point operations introduce roundoff errors that can degrade the accuracy of the result. We propose $\Lambda_{num}$, a functional…
The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems…
Symmetric matrix-valued dynamical systems are an important class of systems that can describe important processes such as covariance/second-order moment processes, or processes on manifolds and Lie Groups. We address here the case of…
In this paper the local order of convergence used in iterative methods to solve nonlinear systems of equations is revisited, where shorter alternative analytic proofs of the order based on developments of multilineal functions are shown.…
Regular model checking is a well-established technique for the verification of regular transition systems (RTS): transition systems whose initial configurations and transition relation can be effectively encoded as regular languages. In…
We study fundamental reachability problems on pseudo-orbits of linear dynamical systems. Pseudo-orbits can be viewed as a model of computation with limited precision and pseudo-reachability can be thought of as a robust version of classical…
A novel perspective on the design of robust model predictive control (MPC) methods is presented, whereby closed-loop constraint satisfaction is ensured using recursive feasibility of the MPC optimization. Necessary and sufficient conditions…
While the identification of nonlinear dynamical systems is a fundamental building block of model-based reinforcement learning and feedback control, its sample complexity is only understood for systems that either have discrete states and…
This paper studies the closed-loop dynamics of linear systems under approximate model predictive control (MPC). More precisely, we consider MPC implementations based on a finite number of ADMM iterations per time-step. We first show that…