Related papers: Scalable Formal Verification of Incremental Stabil…
Deep networks are commonly used to model dynamical systems, predicting how the state of a system will evolve over time (either autonomously or in response to control inputs). Despite the predictive power of these systems, it has been…
This work proposes a new a framework for determining robust periodic invariant sets and their associated control laws for constrained uncertain linear systems. Necessary and sufficient conditions for stabilizability by periodic controllers…
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…
While ensuring stability for linear systems is well understood, it remains a major challenge for nonlinear systems. A general approach in such cases is to compute a combination of a Lyapunov function and an associated control policy.…
Learning controllers merely based on a performance metric has been proven effective in many physical and non-physical tasks in both control theory and reinforcement learning. However, in practice, the controller must guarantee some notion…
We propose a method for data-driven practical stabilization of nonlinear systems with provable guarantees, based on the concept of Nonparametric Chain Policies (NCPs). The approach employs a normalized nearest-neighbor rule to assign, at…
This paper is concerned with stability analysis of nonlinear time-varying systems by using Lyapunov function based approach. The classical Lyapunov stability theorems are generalized in the sense that the time-derivative of the Lyapunov…
Fixed-time stable dynamical systems are capable of achieving exact convergence to an equilibrium point within a fixed time that is independent of the initial conditions of the system. This property makes them highly appealing for designing…
This paper considers a wide class of smooth continuous dynamic nonlinear systems (control objects) with a measurable vector of state. The problem is to find a special function (Lyapunov function), which in the framework of the second…
There are recent shifts in demand for design controllers from simplified to complex model-based. Although simplification approaches are successful in many areas of engineering control systems, high-fidelity simulation-based control design,…
We propose an automatic and formally sound method for synthesising Lyapunov functions for the asymptotic stability of autonomous non-linear systems. Traditional methods are either analytical and require manual effort or are numerical but…
Lyapunov functions provide a tool to analyze the stability of nonlinear systems without extensively solving the dynamics. Recent advances in sum-of-squares methods have enabled the algorithmic computation of Lyapunov functions for…
Distributed consensus-based controllers for optimal secondary frequency regulation of microgrids and power systems have received substantial attention in recent years. This paper provides a Lyapunov-based proof that, under a time-scale…
This paper develops a direct data-driven framework for infinite networks with unknown nonlinear polynomial subsystems, enabling the synthesis of controllers that ensure the entire network is uniformly globally asymptotically stable (UGAS).…
As an emerging artificial intelligence technology, graph neural networks (GNNs) have exhibited promising performance across a wide range of graph-related applications. However, information exchanges among neighbor nodes in GNN pose new…
In this paper, by using a characterization of functions having fractional derivative, we propose a rigorous fractional Lyapunov function candidate method to analyze stability of fractional-order nonlinear systems. First, we prove an…
Hyperexponential stability is investigated for dynamical systems with the use of both, explicit and implicit, Lyapunov function methods. A nonlinear hyperexponential control is designed for stabilizing linear systems. The tuning procedure…
Stability certificates play a critical role in ensuring the safety and reliability of robotic systems. However, deriving these certificates for complex, unknown systems has traditionally required explicit knowledge of system dynamics, often…
Graph Neural Networks (GNNs) have become the standard for graph representation learning but remain vulnerable to structural perturbations. We propose a novel framework that integrates persistent homology features with stability…
Identifying critical nodes and links in graphs is a crucial task. These nodes/links typically represent critical elements/communication links that play a key role in a system's performance. However, a majority of the methods available in…