相关论文: Learning Lyapunov Functions for Hybrid Systems

The paper proposes a control-theoretic framework for verification of numerical software systems, and puts forward software verification as an important application of control and systems theory. The idea is to transfer Lyapunov functions…

This paper deals with the certification problem for robust quadratic stability, robust state convergence, and robust quadratic performance of linear systems that exhibit bounded rates of variation in their parameters. We consider both…

This work studies the problem of searching for homogeneous polynomial Lyapunov functions for stable switched linear systems. Specifically, we show an equivalence between polynomial Lyapunov functions for systems of this class and quadratic…

Monotone systems preserve a partial ordering of states along system trajectories and are often amenable to separable Lyapunov functions that are either the sum or the maximum of a collection of functions of a scalar argument. In this paper,…

Imitation learning is a paradigm to address complex motion planning problems by learning a policy to imitate an expert's behavior. However, relying solely on the expert's data might lead to unsafe actions when the robot deviates from the…

Barrier Lyapunov functions are suitable for learning control designs, due to their feature of finite duration tracking. This paper presents fractional barrier Lyapunov functions, provided and compared with the conventional ones in the…

In this work, the issue of estimation of reachable sets in continuous bimodal piecewise affine systems is studied. A new method is proposed, in the framework of ellipsoidal bounding, using piecewise quadratic Lyapunov functions. Although…

This paper addresses the stability problem for discrete-time switched systems under autonomous switching. Each mode of the switched system is modeled as a Linear Parameter Varying (LPV) system, the time-varying parameters can vary…

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…

We present a kernel-based methodology for constructing Lyapunov functions for nonlinear dynamical systems using approximate Koopman eigenfunctions. Our approach decomposes principal Koopman eigenfunctions into linear and nonlinear…

Machine learning techniques have demonstrated their effectiveness in achieving autonomy and optimality for nonlinear and high-dimensional dynamical systems. However, traditional black-box machine learning methods often lack formal stability…

In traffic signal control, flow-based (optimizing the overall flow) and pressure-based methods (equalizing and alleviating congestion) are commonly used but often considered separately. This study introduces a unified framework using…

Finding Lyapunov functions to certify the stability of control systems has been an important topic for verifying safety-critical systems. Most existing methods on finding Lyapunov functions require access to the dynamics of the system.…

This work makes several contributions on stability and performance verification of nonlinear dynamical systems controlled by neural networks. First, we show that the stability and performance of a polynomial dynamical system controlled by a…

We present a new approach for constructing polytope Lyapunov functions for continuous-time linear switching systems (LSS). This allows us to decide the stability of LSS and to compute the Lyapunov exponent with a good precision in…

In this paper, we focus on the problem about direct way to design a stable controller for nonlinear system. A framework of learning controller with Lyapunov-based constraint is proposed, which is intended to transform designing and analyis…

Establishing stability certificates for closed-loop systems under reinforcement learning (RL) policies is essential to move beyond empirical performance and offer guarantees of system behavior. Classical Lyapunov methods require a strict…

Recent employments of SMT solvers within the Lyapunov function synthesis provided effective tools for automated construction of Lyapunov functions alongside with sound computer-assisted certificates. The main benefit of the suggested…

We present a methodology for establishing the existence of quadratic Lyapunov inequalities for a wide range of first-order methods used to solve convex optimization problems. In particular, we consider i) classes of optimization problems of…

Safety and stability are common requirements for robotic control systems; however, designing safe, stable controllers remains difficult for nonlinear and uncertain models. We develop a model-based learning approach to synthesize robust…