Geometric Fault-Tolerant Neural Network Tracking Control of Unknown Systems on Matrix Lie Groups

2025/05/07 by Robin Chhabra, Chhabra, Robin, Farzaneh Abdollahi +1
Computer Science · Engineering · #Adaptive Control of Nonlinear Systems #Artificial Intelligence (cs.AI) #Control and Stability of Dynamical Systems #Distributed Control Multi-Agent Systems #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Robotics (cs.RO) #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2505.04725

openalex publication_date 2025/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a geometric neural network-based tracking controller for systems evolving on matrix Lie groups under unknown dynamics, actuator faults, and bounded disturbances. Leveraging the left-invariance of the tangent bundle of matrix Lie groups, viewed as an embedded submanifold of the vector space \R^{N× N}, we propose a set of learning rules for neural network weights that are intrinsically compatible with the Lie group structure and do not require explicit parameterization. Exploiting the geometric properties of Lie groups, this approach circumvents parameterization singularities and enables a global search for optimal weights. The ultimate boundedness of all error signals -- including the neural network weights, the coordinate-free configuration error function, and the tracking velocity error -- is established using Lyapunov's direct method. To validate the effectiveness of the proposed method, we provide illustrative simulation results for decentralized formation control of multi-agent systems on the Special Euclidean group.

Citations

• Hamiltonian-based Neural ODE Networks on the SE(3) Manifold For Dynamics Learning and Control
• Stability Analysis using Quadratic Constraints for Systems with Neural Network Controllers
• Deep Lagrangian Networks for end-to-end learning of energy-based control for under-actuated systems
• Hamiltonian Neural Networks
• Deep Neural Networks Motivated by Partial Differential Equations
• Multistep Neural Networks for Data-driven Discovery of Nonlinear\n Dynamical Systems
• Optimal Control Problems with Symmetry Breaking Cost Functions
• Integral Control on Lie Groups

Related

• Lie Group Forced Variational Integrator Networks for Learning and Control of Robot Systems
• Exponentially Stable First Order Control on Matrix Lie Groups
• Lie-algebra Adaptive Tracking Control for Rigid Body Dynamics
• Machine learning based state observer for discrete time systems evolving on Lie groups
• Port-Hamiltonian Neural ODE Networks on Lie Groups For Robot Dynamics Learning and Control