28 citations · 61 across the 15 of their papers we have counts for
15 papers
A Globally Asymptotically Stable Planar Homogeneous Polynomial Vector Field With No Polynomial Lyapunov Function
Jun Liu, Maxwell Fitzsimmons
We disprove the conjecture that every globally asymptotically stable homogeneous polynomial vector field admits a homogeneous polynomial Lyapunov function. The counterexample is a…
Safe and Robust Domains of Attraction for Discrete-Time Systems: A Set-Based Characterization and Certifiable Neural Network Estimation
Mohamed Serry, Maxwell Fitzsimmons, Jun Liu
Analyzing nonlinear systems with attracting robust invariant sets (RISs) requires estimating their domains of attraction (DOAs). Despite extensive research, accurately characterizi…
Rigorous Error Certification for Neural PDE Solvers: From Empirical Residuals to Solution Guarantees
Amartya Mukherjee, Maxwell Fitzsimmons, David C. Del Rey Fernández +1
Uncertainty quantification for partial differential equations is traditionally grounded in discretization theory, where solution error is controlled via mesh/grid refinement. Physi…
Computing Control Lyapunov-Barrier Functions: Softmax Relaxation and Smooth Patching with Formal Guarantees
Jun Liu, Maxwell Fitzsimmons
We present a computational framework for synthesizing a single smooth Lyapunov function that certifies both asymptotic stability and safety. We show that the existence of a strictl…
A Converse Control Lyapunov Theorem for Joint Safety and Stability
Thanin Quartz, Maxwell Fitzsimmons, Jun Liu
We show that the existence of a strictly compatible pair of control Lyapunov and control barrier functions is equivalent to the existence of a single smooth Lyapunov function that…
Symbolic Reduction for Formal Synthesis of Global Lyapunov Functions
Jun Liu, Maxwell Fitzsimmons
We investigate the formal synthesis of global polynomial Lyapunov functions for polynomial vector fields. We establish that a sign-definite polynomial must satisfy specific algebra…
Formally Verified Physics-Informed Neural Control Lyapunov Functions
Jun Liu, Maxwell Fitzsimmons, Ruikun Zhou +1
Control Lyapunov functions are a central tool in the design and analysis of stabilizing controllers for nonlinear systems. Constructing such functions, however, remains a significa…
LyZNet: A Lightweight Python Tool for Learning and Verifying Neural Lyapunov Functions and Regions of Attraction
Jun Liu, Yiming Meng, Maxwell Fitzsimmons +1
In this paper, we describe a lightweight Python framework that provides integrated learning and verification of neural Lyapunov functions for stability analysis. The proposed tool,…
Compositionally Verifiable Vector Neural Lyapunov Functions for Stability Analysis of Interconnected Nonlinear Systems
Jun Liu, Yiming Meng, Maxwell Fitzsimmons +1
While there has been increasing interest in using neural networks to compute Lyapunov functions, verifying that these functions satisfy the Lyapunov conditions and certifying stabi…
Physics-Informed Neural Network Policy Iteration: Algorithms, Convergence, and Verification
Yiming Meng, Ruikun Zhou, Amartya Mukherjee +3
Solving nonlinear optimal control problems is a challenging task, particularly for high-dimensional problems. We propose algorithms for model-based policy iterations to solve nonli…
Physics-Informed Neural Network Lyapunov Functions: PDE Characterization, Learning, and Verification
Jun Liu, Yiming Meng, Maxwell Fitzsimmons +1
We provide a systematic investigation of using physics-informed neural networks to compute Lyapunov functions. We encode Lyapunov conditions as a partial differential equation (PDE…
Quantum Maps Between CPTP and HPTP
Ningping Cao, Maxwell Fitzsimmons, Zachary Mann +2
For an open quantum system to evolve under CPTP maps, assumptions are made on the initial correlations between the system and the environment. Hermitian-preserving trace-preserving…
Towards Learning and Verifying Maximal Neural Lyapunov Functions
Jun Liu, Yiming Meng, Maxwell Fitzsimmons +1
The search for Lyapunov functions is a crucial task in the analysis of nonlinear systems. In this paper, we present a physics-informed neural network (PINN) approach to learning a…
Smooth Converse Lyapunov-Barrier Theorems for Asymptotic Stability with Safety Constraints and Reach-Avoid-Stay Specifications
Yiming Meng, Yinan Li, Maxwell Fitzsimmons +1
Stability and safety are two important aspects in safety-critical control of dynamical systems. It has been a well established fact in control theory that stability properties can…
A Necessary Condition on Chain Reachable Robustness of Dynamical Systems
Maxwell Fitzsimmons, Jun Liu
It is ``folklore'' that the solution to a set reachability problem for a dynamical system is only noncomputable because of non-robustness reasons. A robustness condition that can b…