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In recent 20 years, the Dynamics and Control Theory is an important research direction in the area of mechanics, control and mathematics. It includes various research topics such as dynamics analysis, multi-body dynamics, nonlinear dynamics,  control of mechanical systems, analysis and synthesis of flight systems, analysis and control of multi-agent systems, their applications in biology and medical engineering, and so forth. The current research areas of the Dynamics and Control group include cooperative control of multi-agent systems, distributed control of interconnected systems, dynamics and control of flight systems, control of complex mechanical systems, robust and nonlinear control.
 
Impacts: The members of the Dynamics and Control group have conducted more than 20 research projects including three key projects and one outstanding youth research project from the National Natural Science Fund of China. The first class award of natural science from the Ministry of Education of China was issued in 2011. One professor was selected as Chang Jiang scholar in 2013, and one professor obtained the national excellent doctoral dissertation award was in 2012. One paper was awarded by the 2013 IET Control Theory and Application Premium Award. Each year, more than 30 papers have been published in international renowned journals, including IEEE Transactions, Automatica, Systems and Control Letters, etc. A three-day "International Workshop on Networks and Nonlinear Science" was held at Peking University on May 25-27, 2010.
 
Members:Zhisheng Duan,ZhiYong Geng,Lin Huang,Zhongkui Li,Jinzhi Wang,Yong Wang,Jianying Yang,Ying Yang
 
Listed below are selected research achievements in the area of Dynamics and Control.
 
a)      Cooperative Control of Multi-agent Systems
Cooperative control of multi-agent systems is an emerging and important research topic in the international systems and control community. Striking progress on this research topic has been made, such as: proposing a systematic consensus region approach for studying the consensus control problems of multi-agent systems;  addressing the distributed tracking and containment control problems for linear multi-agent systems with leaders of nonzero control inputs; studying the effects of measurement/communication errors and disturbances on consensus of multi-agent systems. These advances are summarized in one monograph which will be published by Taylor & Francis Press early 2015.

Figure 3.1: The relative velocities and positions of four near-earth satellites moving in a formation. (Li, et al., IEEE Transactions on Circuits and Systems I, 57, 213-224, 2010)
 
b)     Robust tracking control for hypersonic vehicles and design of integrated guidance and control for missiles
A novel nonsingular terminal sliding model control has been proposed for a class of nonlinear systems with disturbances and uncertainties and applied to integrated guidance and control design for missiles. The tracking controllers have been designed for a model of hypersonic vehicles in the presence of uncertain parameters, input constraints or actuator faults.

Figure 3.2: The three-dimensional interception geometry. (Wang and Wang, Journal of Guidance, Control, and Dynamics, 37, 644-657, 2014)
 
c)      Control of nonlinear systems with multiple equilibria
Analysis, synthesis and related algorithm design for global properties of a class of nonlinear systems with multiple equilibria have been made. The global properties which characterize the behavior of solutions for systems with multiple equilibria, including the Lagrange stability, the property of dichotomy, global asymptotic convergence, as well as different kinds of periodic and chaotic oscillations were investigated. Static or dynamic feedback controllers were constructed to ensure the existence or the nonexistence of some certain behavior of the system. The results are reported in one monograph published by World Scientific in 2009.
  

Figure 3.3: Left: The pendulum-like system without control; right: The states of the closed-loop pendulum-like system. (Wang, et al., Automatica, 42,145-150, 2006).
 
d)     Redundant control and dynamic control allocation
New problems from the redundant control on system performance have been studied. The necessary and sufficient condition of strict decreasing of the quadratic performance index when the columns of the input matrix are increased is established. Control allocation among redundant control inputs when there are uncertainties in the effective matrix or faults occur is presented.

Figure 3.4: The overall flight control system with control allocation. (Cui and Yang, Journal of Guidance, Dynamics, and Control, 34, 1632-1643, 2011).
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