## Jinhua Li

### Research

My research interest is in hybrid system identification, numerical method for hybrid system optimal control, and traffic flow management.

Hybrid systems are dynamical systems with interaction continuous dynamics (modeled, for example, by differential equations) and discrete event dynamics (modeled, for example, by automata). A statistical method of inference and learning of a hybrid system given a sequence of observation data is to treat all unknown quantities as random variables, assign priors to these quantities, and then infers posterior probabilities given observed data. Methods for linear hybrid system identification include dynamical programming, neural network, variational learning, and MCMC. Traditional methods such as Kalman smoothing and Baum-Welch algorithm have been successfully applied to identify the parameters of continuous systems and discrete systems respectively. However, to overcome the potential intractable problem due to the inter-correlations between the continuous dynamics and discrete dynamics in the hybrid system, recent researches have been focusing on to apply methods from other areas, such as dynamical programming, Bayesian statistics, and geometry algorithm etc., for the hybrid system identification. My interest is just to explore those methods to develop a new and effective identification algorithm, which I have been successfully applied the Variational approximation methods to identify a class of stochastic linear hybrid systems.

I have been also working on developing differential transformation based numerical algorithms for the optimal control problems of nonlinear and hybrid systems.Differential transformation is an effective computational method for solving linear (or nonlinear) ordinary (or partial) differential equations with their corresponding boundary conditions. The main idea is: by using differential transformation, a set of differential equations with their corresponding boundary conditions is converted into a system of algebraic equations in a transformed domain; and by solving the system of algebraic equations, the numerical solution of the differential equations in the time domain can be obtained in the form of a finite-term series of a chosen basis system. We have developed effective numerical algorithms for solving nonlinear and hybrid system optimal controol problem.

Currently, I am investigating mathmatical modeling and congestion control of air traffic based on the kinematic flow.

**Publications:**

[1] I. Hwang, J. Li, and D. Du, A Numerical Algorithm for Optimal Control of A Class of Hybrid Systems: Differential Transformation Based Approach, International Journal of Control, 2007, accepted.

[2] J. Li, D. Du, and I. Hwang, A Differential Transformation Based Computational Method for Switched Linear Quadratic Optimal Control, CDC, 2007, accepted

[3] D. Du, J. Li, and I. Hwang, A Computational Method for Optimal Control of Hybrid Systems Using Differential Transformation, CDC, 2007, accepted

### Background

- Ph.D., Dynamics and Control, School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN
- M.S., Mechanical Engineering, University of Kentucky, Lexington, KY
- B.S., Automation, University of Science and Technology of China, Hefei, Anhui, China

### Contact

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