1. Nonlinear robust H∞ stochastic control design

Nonlinear stochastic H∞ robust control is the most difficult problem in the control theory and design because we need to consider the nonlinearity, stochastic noise and robustness of the systems all together. In the paper “Stochastic H₂/H∞ control with state-dependent noise” IEEE Trans. Automatic control, Vol. 49, No.1 pp.45-51, 2004, the first H₂/H∞ robust controller design is developed for linear stochastic systems. Then these results to nonlinear stochastic systems are extended to nonlinear stochastic case, i.e., “State feedback H∞ control for a class of nonlinear stochastic systems” SIAM J. Control and Optimization, Vol. 44, No. 6, pp.1973-1991, 2006. Finally, the general stochastic stability and detectability problem of stochastic systems is discussed in the paper “Generalized Lyapunov equation approach to state-dependent stochastic detectability criterion”, IEEE Trans. Automatic Control, Vol. 53, No.7, pp.1630-1642, 2008. These journals are top two on theoretical control theory. Also, a new H∞ robust filtering design of nonlinear stochastic systems is also developed in the paper “Robust H∞ filtering for nonlinear stochastic systems” IEEE Trans. Signal Processing, Vol. 53, No.2 pp.589-599, 2005. These robust H∞ control theory and noise filtering in the stochastic systems have also been applied to interpret the molecular noise amplification and filtering of gene regulatory networks. These papers are all highly cited. Obviously, the research of nonlinear stochastic robust control and filter design of Professor Chen is the top ones in the world. Further, Dr. Chen has published many significant papers in fuzzy control theory and applications. These achievements have promoted Dr. Chen to an IEEE fellow in 2001.

2. Robust signal processing and power control of cellular systems

Dr. Chen published a series of robust signal reconstruction filter designs under channel parameter uncertainties and disturbances as well as robust equalizer designs in wireless communication systems. Recently, he has published a series of 5 papers in IEEE Trans. Wireless communication on robust power control design for CDMA cellular communication systems under round-trip delay, channel fading, shadowing and interference to guarantee a desired signal-to-noise ratio (SINR) for a mobile. Totally, Dr. Chen has published more than 35 IEEE regular papers in robust signal processing and communication designs. Obviously, Dr. Chen is also a world-wide researcher in this field.

3. Gene circuit design and systems biology

Because of the richness of microarray and high-throughput experimental data and the development of bioinformatics, the research of biology is shifted from the conventional methods to systems biology methods. If we want to get more insight into the biology systems, we need to integrate biology, mathematics and engineering and should use dynamic model to understand their operation mechanisms and the interactions among different biological networks. Then we can measure different characteristics of biosystems at different levels, such as stability, sensitivity, robustness and noise filtering ability, signal transduction ability etc. Then biology is not a descriptive science but a system science. At present, disease and malfunction can be considered as decay in stability robustness and noise filtering ability. Then the drug design can be considered as how to improve the robust stability and filtering ability of the corresponding biological networks to resist fluctuation and noise, like the robust design in engineering.