Publications

Variational unscented Kalman filter on matrix Lie groups
Automatica, 172: 111995, 2025 (Regular Paper).
[Paper PDF]
Tianzhi Li and Jinzhi Wang

Brief Abstract: 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
Automatica, 164: 111626, 2024 (Regular Paper).
[Paper PDF]
Tianzhi Li, Rui Fu, and Jinzhi Wang

Brief Abstract: 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.

Multisymplectic unscented Kalman filter for geometrically exact beams
In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information (GSI 2023). Lecture Notes in Computer Science, vol 14072. Springer, Cham.
[Paper PDF]
Tianzhi Li and Jinzhi Wang

Brief Abstract: We propose a geometric estimation algorithm for geometrically exact beams based on geometric mechanics and classical field theory. The structure-preserving property of the proposed filter is demonstrated by numerical results.

Principle for Stochastic Nonholonomic Systems Part I: Continuous-Time Formulation
Accepted by Geometric Science of Information (GSI 2025)
Tianzhi Li, Francois Gay-Balmaz, Donghua Shi, and Jinzhi Wang

Brief Abstract: 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.

Principle for Stochastic Nonholonomic Systems Part II: Stochastic Nonholonomic Integrator
Accepted by Geometric Science of Information (GSI 2025)
Tianzhi Li, Francois Gay-Balmaz, Donghua Shi, and Jinzhi Wang

Brief Abstract: We propose stochastic discrete variational principles for stochastic nonholonomic systems and construct the associated stochastic nonholonomic integrator based on Hamel's formalism. The links between the proposed approach and existing geometric numrical integration methods (such as Verlet method, sysmplectic-momentum integrator, and Hamel integrator) are analyzed.

A structure-preserving learning scheme on SO(3)
43rd IEEE Chinese Control Conference (CCC), Kunming, China, pp. 5149-5152, 2024.
[Paper PDF]
Tianzhi Li and Jinzhi Wang

Brief Abstract: 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
42nd IEEE Chinese Control Conference (CCC), Tianjin, China, pp. 5163-5167, 2023.
[Paper PDF]
Tianzhi Li and Jinzhi Wang

Brief Abstract: We introduce a Gaussian process regression algorithm for the prediction of planar pendulum dynamics. Numerical results show that the proposed method preserves some key numerical quantities of the system, including the numerical energy and the physical length of the pendulum.

A statistical dynamical algorithm for Gaussian multi-agent systems under Hamel's formalism
34th IEEE Chinese Control and Decision Conference (CCDC), Hefei, China, pp. 1344-1349, 2022.
[Paper PDF]
Tianzhi Li and Jinzhi Wang

Brief Abstract: 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.