For future research, the distributed stabilization problem needs to be studied for multi-input multi-output (MIMO) nonlinear MASs. However, this problem should be easy to solve since the result for MIMO linear MASs indicates that distributed stability holds as long as condition (3.14) is replaced by (3.17).
In many practical MASs, the state information is usually not available for feedback. In that case, output feedback can be applied and distributed observers have to be employed to estimate the states of individual agents. It is mentioned at the end of Chapter 4 that direct output feedback stabilizes the closed-loop MAS if the N individual agents in the network are all strictly passive. However, how to stabilize the MAS using output feedback control laws remains to be a difficult problem when the N agents are not necessarily strictly passive, especially since the design of observers for nonlinear systems are much more complex than the case of linear systems.
Just as we claimed before, the distributed stabilization is just a fundamental part in the consensus problem. Our final goal is to find a distributed control law such that the outputs of the heterogeneous nonlinear MAS asymptotically synchronize to some desired
common trajectory. In [6], coupling control laws are derived for the output synchronization of homogeneous nonlinear MAS with relative degree one and weakly minimum phase, while the results are limited to the case when the interconnection graph is balanced. In [11], the author considers the output regulation problem for regular nonlinear systems and proposes to embed an internal model to the controller, which happens to be quite similar to the internal model principle introduced in Chapter 2.
Future work can also be focused on some more complex consensus problems of geneous nonlinear MASs, such as heterogeneous nonlinear MASs with time-delays, hetero-geneous nonlinear MASs under time-varying topologies or random networks, discrete-time heterogeneous nonlinear MASs, etc.
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VITA
Jianming Zhou was born in Shanghai, China. He is the son of Zemin Zhou and Wenying Zhang. He completed his undergraduate program of Automation and obtained his Bachelor’s Degree of Science in Engineering from Shanghai Jiao Tong University, Shanghai, China, in June 2013. In Fall 2013, he came to the United States and joined the Department of Electrical and Computer Engineering at Louisiana State University, Baton Rouge, in pursuit of his graduate study, focusing on Systems Control. He anticipates being awarded the Master’s Degree of Science in Electrical Engineering in May 2015.