Related papers: Regions of Attraction Approximation Using Individu…
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…
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 develop a comprehensive framework to estimate regions of attraction of equilibria for dynamics associated with general vector fields. This framework combines Koopman operator-based methods with rigorous validation…
The Newton-Raphson basins of attraction, associated with the libration points (attractors), are revealed in the pseudo-Newtonian planar circular restricted three-body problem, where the primaries have equal masses. The parametric variation…
Current flight control validation is heavily based on linear analysis and high fidelity, nonlinear simulations. Continuing developments of nonlinear analysis tools for flight control has greatly enhanced the validation process. Many…
In this paper, we investigate geometric properties of monotone systems by studying their isostables and basins of attraction. Isostables are boundaries of specific forward-invariant sets defined by the so-called Koopman operator, which…
Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…
This paper focuses on the analysis of the Region of Attraction (RoA) for unknown autonomous dynamical systems. A data-driven approach based on the moment-Sum-of-Squares (SoS) hierarchy is proposed, enabling novel RoA outer approximations…
This paper presents a framework for abstracting uncertain or non-polynomial components of dynamical systems using polynomial constraints. This enables the application of polynomial-based analysis tools, such as sum-of-squares programming,…
We consider the problem of learning an inner approximation of the region of attraction (ROA) of an asymptotically stable equilibrium point without an explicit model of the dynamics. Rather than leveraging approximate models with bounded…
We characterize and compute the maximal admissible positively invariant set for asymptotically stable constrained switching linear systems. Motivated by practical problems found, e.g., in obstacle avoidance, power electronics and nonlinear…
This paper illustrates the application of recent research in region-of-attraction analysis for nonlinear hybrid limit cycles. Three example systems are analyzed in detail: the van der Pol oscillator, the "rimless wheel", and the "compass…
Estimating the Region of Attraction (RoA) for nonlinear dynamical systems is a fundamental problem in control theory, with direct implications for stability analysis and safe controller design. Traditional approaches rely on analytically…
The basin of attraction is the set of initial points that will eventually converge to some attracting set. Its knowledge is important in understanding the dynamical behavior of a given dynamical system of interest. In this work, we address…
The review presents a parameter switching algorithm and his applications which allows numerical approximation of any attractor of a class of continuous-time dynamical systems depending linearly on a real parameter. The considered classes of…
Numerous interesting properties in nonlinear systems analysis can be written as polynomial optimization problems with nonconvex sum-of-squares problems. To solve those problems efficiently, we propose a sequential approach of local…
Recent advancements in model-free deep reinforcement learning have enabled efficient agent training. However, challenges arise when determining the region of attraction for these controllers, especially if the region does not fully cover…
The beacon model is a recent paradigm for guiding the trajectory of messages or small robotic agents in complex environments. A beacon is a fixed point with an attraction pull that can move points within a given polygon. Points move…
This paper derives new results for the analysis of nonlinear systems by extending contraction theory in the framework of vector distances. A new tool, vector contraction analysis utilizing a notion of the vector-valued norm which evidently…
The structure of invariant regions and globally attracting regions is fundamental to understanding the dynamical properties of reaction network models. We describe an explicit construction of the minimal invariant regions and minimal…