Related papers: Estimation of non-symmetric and unbounded region o…
This paper presents a novel approach for computing enlarged Region of Attractions (ROA) for nonlinear dynamical systems through the integration of multiple coordinate transformations and piecewise quadratic Lyapunov functions within the…
Appropriate estimation of Region of Attraction for a nonlinear dynamical system plays a key role in system analysis and control design. Sum-of-Squares optimization is a powerful tool enabling Region of Attraction estimation for polynomial…
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…
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…
The increasing uptake of inverter based resources (IBRs) has resulted in many new challenges for power system operators around the world. The high level of complexity of IBR generators makes accurate classical model-based stability analysis…
A method is presented to estimate the region of attraction (ROA) of stochastic systems with finite second moment and uncertainty-dependent equilibria. The approach employs Polynomial Chaos (PC) expansions to represent the stochastic system…
This paper introduces a novel framework to construct the region of attraction (ROA) of a power system centered around a stable equilibrium by using stable state trajectories of system dynamics. Most existing works on estimating ROA rely on…
Estimating the region of attraction (ROA) of general nonlinear autonomous systems remains a challenging problem and requires a case-by-case analysis. Leveraging the universal approximation property of neural networks, in this paper, we…
This paper presents a novel method for estimating larger Region of Attractions (ROAs) for continuous-time nonlinear systems modeled via the Takagi-Sugeno (TS) framework. While classical approaches rely on a single TS representation derived…
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…
Stability analysis tools are essential to understanding and controlling any engineering system. Recently sum-of-squares (SOS) based methods have been used to compute Lyapunov based estimates for the region-of-attraction (ROA) of polynomial…
Traditional Lyapunov based transient stability assessment approaches focus on identifying the stability region (SR) of the equilibrium point under study. When trying to estimate this region using Lyapunov functions, the shape of the final…
Leveraging a stochastic extension of Zubov's equation, we develop a physics-informed neural network (PINN) approach for learning a neural Lyapunov function that captures the largest probabilistic region of attraction (ROA) for stochastic…
In this paper, we propose an iterative method for using SOS programming to estimate the region of attraction of a polynomial vector field, the conjectured convergence of which necessitates the existence of polynomial Lyapunov functions…
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…
This paper presents a method for calculating the Region of Attraction (ROA) of nonlinear dynamical systems, both with and without control. The ROA is determined by solving a hierarchy of semidefinite programs (SDPs) defined on a splitting…
We address the long-standing problem of computing the region of attraction (ROA) of a target set (e.g., a neighborhood of an equilibrium point) of a controlled nonlinear system with polynomial dynamics and semialgebraic state and input…
Nonlinear networks are often multistable, exhibiting coexisting stable states with competing regions of attraction (ROAs). As a result, ROAs can have complex "tentacle-like" morphologies that are challenging to characterize analytically or…
We consider the problem of nonlinear system identification when prior knowledge is available on the region of attraction (ROA) of an equilibrium point. We propose an identification method in the form of an optimization problem, minimizing…
This work estimates safe invariant subsets of the Region of Attraction (ROA) for a seven-state vehicle-with-driver system, capturing both asymptotic stability and the influence of state-safety bounds along the system trajectory. Safe sets…