相关论文: Region of attraction analysis of nonlinear stochas…

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 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…

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…

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 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…

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…

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 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…

A method is presented to analyze the stability of feedback systems with neural network controllers. Two stability theorems are given to prove asymptotic stability and to compute an ellipsoidal inner-approximation to the region of attraction…

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…

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…

A general numerical method using sum of squares programming is proposed to address the problem of estimating the region of attraction (ROA) of an asymptotically stable equilibrium point of a nonlinear polynomial system. The method is based…

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…

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…

The estimation for the region of attraction (ROA) of an asymptotically stable equilibrium point is crucial in the analysis of nonlinear systems. There has been a recent surge of interest in estimating the solution to Zubov's equation, whose…

This study presents a machine learning-aided approach to accurately estimate the region of attraction (ROA) of a multi-rotor unmanned aerial vehicle (UAV) controlled using a linear quadratic regulator (LQR) controller. Conventional ROA…

Nonlinear underactuated systems such as two-wheeled inverted pendulums (TWIPs) exhibit a limited region of attraction (RoA), which defines the set of initial conditions from which the closed-loop system converges to the equilibrium. The RoA…

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…

Linear-quadratic regulators (LQR) are a well known and widely used tool in control theory for both linear and nonlinear dynamics. For nonlinear problems, an LQR-based controller is usually only locally viable, thus, raising the problem of…

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…