10 - Robust cooperative control of networked negative-imaginary systems

Abstract

This chapter mainly focuses on the robust consensus algorithms on networked NI systems, which can be regarded as a class of special systems with negative imaginary (NI) frequency response. NI systems applications include aerospace, large space structures, multi-link robotic arms usually with co-located position sensors and force actuators [137], nano-positioning [83], etc. Toward this end, NI system theory is adopted to first derive conditions for robust output feedback consensus and then transport the proposed results to cooperative tracking to obtain a robust output feedback cooperative control framework for a wide class of LTI systems. The outline of this chapter is as follows: Section 10.1 introduces the definition and typical results of NI systems; in Sections 10.2 and 10.3, robust consensus problem of both homogeneous and heterogeneous NI systems will be introduced separately; Section 10.4 extends to the robust cooperative control framework and Section 10.5 concludes this chapter.