Publications

Stochastic geometrically exact beam: Continuous-time geometric principles and variational discretizations
Minghang Du, François Gay-Balmaz, Tianzhi Li, and Donghua Shi

In preparation, 2026.
[Website]

We introduce stochastic variational principles for stochastic geometrically exact beams in both continuous- and discrete-time settings. The resulting stochastic variational integrators are shown to be stochastic extensions of the well-known staggered leapfrog scheme for the wave equation, and also stochastic extensions of Yee's scheme for spatially one-dimensional computational electromagnetism.

Variational Unscented Kalman Filter on Matrix Lie Groups
Tianzhi Li and Jinzhi Wang

Automatica, 172: 111995, 2025 (Regular Paper).
[Paper Link]

We propose a family of computationally efficient unscented Kalman filters (UKF-Vs) for mechanical systems on matrix Lie groups.

Reduced Dynamics and Geometric Optimal Control of Nonequilibrium Thermodynamics: Gaussian Case
Tianzhi Li, Rui Fu, and Jinzhi Wang

Automatica, 164: 111626, 2024 (Regular Paper).
[Paper Link]

We study the geometric structures of n-DOF Gaussian distributions, and we propose a geometric optimal control algorithm for minimum-energy optimal control problem of Gaussian distributions.

Physics-Informed Gaussian Process Learning on Lie Groups
Tianzhi Li and Jinzhi Wang

Journal of Guidance, Control, and Dynamics, 48 (11), pp. 2654-2662, 2025.
[Paper Link]

We introduce a physics-informed Gaussian process learning method for mechanical systems on Lie groups and on a special class of homogeneous manifolds based on discrete mechanics theory.

Structure-Preserving Unscented Kalman Filter for Planar Mobile Robots
Tianzhi Li, Jinzhi Wang, and Zhisheng Duan

IEEE Control Systems Letters, vol. 9, pp. 2157-2162, 2025.
[Paper Link]

We introduce a structure-preserving filtering method (SP-UKF) for constrained planar mobile robots. The proposed SP-UKF is energy-conserving, constraint-preserving, and manifold-structure-preserving.

Variational Principle for Stochastic Nonholonomic Systems Part II: Stochastic Nonholonomic Integrator
Tianzhi Li, François Gay-Balmaz, Donghua Shi, and Jinzhi Wang

In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information (GSI 2025), Saint-Malo, France. Lecture Notes in Computer Science, vol 16034, pp. 225-233. Springer, Cham, 2026.
[Paper Link]

We propose stochastic discrete variational principles for stochastic nonholonomic systems and construct a stochastic nonholonomic integrator.

Variational Principle for Stochastic Nonholonomic Systems Part I: Continuous-Time Formulation
Tianzhi Li, François Gay-Balmaz, Donghua Shi, and Jinzhi Wang

In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information (GSI 2025), Saint-Malo, France. Lecture Notes in Computer Science, vol 16034, pp. 204-213. Springer, Cham, 2026.
[Paper Link]

We introduce stochastic variational principles for stochastic unconstrained and stochastic nonholonomically constrained systems based on Hamel's formalism. An interesting example of the stochastic rolling disk is given to demonstrate the effectivness of the proposed approach.

Multisymplectic Unscented Kalman Filter for Geometrically Exact Beams
Tianzhi Li and Jinzhi Wang

In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information (GSI 2023), Saint-Malo, France. Lecture Notes in Computer Science, vol 14072. Springer, Cham, 2023.
[Paper Link]

We propose a geometric estimation algorithm for geometrically exact beams based on geometric mechanics and classical field theory.

A Structure-Preserving Learning Scheme on SO(3)
Tianzhi Li and Jinzhi Wang

43rd IEEE Chinese Control Conference (CCC), Kunming, China, pp. 5149-5152, 2024.
[Paper Link]

We propose a physics-guided Gaussian learning method for SO(3) attitude dynamics prediction. Numerical results are given to demonstrate the structure-preserving properties of the proposed method, such as energy conservation, constraint preservation, and geometry preservation.

A Physics-Informed Gaussian Process Regression Algorithm for The Dynamics of The Planar Pendulum
Tianzhi Li and Jinzhi Wang

42nd IEEE Chinese Control Conference (CCC), Tianjin, China, pp. 5163-5167, 2023.
[Paper Link]

We introduce a Gaussian process regression algorithm for the prediction of planar pendulum dynamics.

A Statistical Dynamical Algorithm for Gaussian Multi-Agent Systems Under Hamel's Formalism
Tianzhi Li and Jinzhi Wang

34th IEEE Chinese Control and Decision Conference (CCDC), Hefei, China, pp. 1344-1349, 2022.
[Paper Link]

We study the geometric structure of n-DOF Gaussian distributions (normal distributions) using Lie group and homogeneous manifold theories. In particular, the metric matrix and the Lagrangian of the system is determined and the discrete dynamics is derived using a discrete variational principle. The resulting geometric integrator for n-DOF Gaussian distributions exhibits properties of energy conservation compared with Runge-Kutta method.