Related papers: Probabilistic Region-of-Attraction Estimation with…
Approximating regions of attraction in nonlinear systems require extensive computational and analytical efforts. In this paper, nonlinear vector fields are recasted as sum of vectors where each individual vector is used to construct an…
Estimating the region of attraction for partially unknown nonlinear systems is a challenging issue. In this paper, we propose a tractable method to generate an estimated region of attraction with probability bounds, by searching an optimal…
The contributions of this technical note are twofold. Firstly, we formulate an optimization problem to obtain a linear representation of a nonlinear vector field based on a system's trajectory. We also prove that its cost function is…
Accurately modeling and verifying the correct operation of systems interacting in dynamic environments is challenging. By leveraging parametric uncertainty within the model description, one can relax the requirement to describe exactly the…
Analyzing and certifying stability and attractivity of nonlinear systems is a topic of research interest that has been extensively investigated by control theorists and engineers for many years. Despite that, accurately estimating domains…
Control theory can provide useful insights into the properties of controlled, dynamic systems. One important property of nonlinear systems is the region of attraction (ROA), a safe subset of the state space in which a given controller…
In this paper, we consider the problem of computing estimates of the domain-of-attraction for non-polynomial systems. A polynomial approximation technique, based on multivariate polynomial interpolation and error analysis for remaining…
A shortcoming of existing reachability approaches for nonlinear systems is the poor scalability with the number of continuous state variables. To mitigate this problem we present a simulation-based approach where we first sample a number of…
In this paper we propose a convex programming based method for computing robust regions of attraction for state-constrained perturbed discrete-time polynomial systems. The robust region of attraction of interest is a set of states such that…
This work addresses the problem of estimating the region of attraction (RA) of equilibrium points of nonlinear dynamical systems. The estimates we provide are given by positively invariant sets which are not necessarily defined by level…
In this paper, we propose and analyze a trust-region model-based algorithm for solving unconstrained stochastic optimization problems. Our framework utilizes random models of an objective function $f(x)$, obtained from stochastic…
Analysis of nonlinear autonomous systems typically involves estimating domains of attraction, which have been a topic of extensive research interest for decades. Despite that, accurately estimating domains of attraction for nonlinear…
Randomized optimization is an established tool for control design with modulated robustness. While for uncertain convex programs there exist randomized approaches with efficient sampling, this is not the case for non-convex problems.…
This letter describes a method for estimating regions of attraction and bounds on permissible perturbation amplitudes in nonlinear fluids systems. The proposed approach exploits quadratic constraints between the inputs and outputs of the…
Balancing safety and efficiency when planning in crowded scenarios with uncertain dynamics is challenging where it is imperative to accomplish the robot's mission without incurring any safety violations. Typically, chance constraints are…
We present an optimization-based method to plan the motion of an autonomous robot under the uncertainties associated with dynamic obstacles, such as humans. Our method bounds the marginal risk of collisions at each point in time by…
Probabilistic prediction of sequences from images and other high-dimensional data is a key challenge, particularly in risk-sensitive applications. In these settings, it is often desirable to quantify the uncertainty associated with the…
Physical systems experience nonlinear disturbances which have the potential to disrupt desired behavior. For a particular disturbance, whether or not the system recovers from the disturbance to a desired stable equilibrium point depends on…
Quadratic systems with lossless quadratic terms arise in many applications, including models of atmosphere and incompressible fluid flows. Such systems have a trapping region if all trajectories eventually converge to and stay within a…
This paper proposes an algorithm to calculate the maximal probability of unsafety with respect to trajectories of a stochastic process and a hazard set. The unsafe probability estimation problem is cast as a primal-dual pair of…