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Robust consensus for networked systems with negative imaginary properties

Skeik, Ola

[Thesis]. Manchester, UK: The University of Manchester; 2020.

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Abstract

This thesis investigates multi-agent systems problems for systems with negative imaginary dynamics. Via tools from negative imaginary theory and graph theory, this research addresses the following three multi-agent systems problems: (i) the distributed robust stabilization problem for networked multi-agent systems with strict negative imaginary uncertainties; (ii) the robust output consensus problem for homogeneous multi-agent systems with negative imaginary dynamics; and (iii) a rendezvous problem for multiple wheeled mobile robots, through the development of cooperative control strategies for integrator negative imaginary systems. The main results of this thesis are summarised as follows. Firstly, a solution to the distributed robust stabilization problem for networked multi-agent systems with strict negative imaginary uncertainties is proposed. The solution includes the derivation of sufficient conditions, in an LMI framework, for the existence of control protocol parameters such that the control protocol robustly stabilizes a networked multi-agent system in presence of strictly negative imaginary uncertainties of certain DC size; and guaranteeing that robust stability is achieved when variations in the network topology occur. Secondly, a solution to the robust output consensus problem for homogeneous multi-agent systems with negative imaginary dynamics is proposed. The solution includes relaxing the assumptions imposed in earlier literature thereby derive robust output consensus conditions under L2 external disturbances and model uncertainty which are not restricted and which simplify in the single-input single-output case to provide several insights not easily captured in the multi-input multi-output case. Finally, a solution to a rendezvous problem for nonholonomic wheeled mobile robots via the negative imaginary systems theory is proposed. The solution includes the derivation of necessary and sufficient conditions that guarantee output consensus and output tracking for strongly connected, balanced and directed networks of integrators subject to energy-bounded disturbances using the negative imaginary internal stability theorems and then utilize the results to achieve rendezvous of multiple wheeled mobile robot. Examples are provided in each of the three aforementioned research problems to demonstrate the effectiveness of the associated proposed results. Additionally, experimental results from real-robots are provided for the rendezvous research problem. This research contributes to the existing literature on cooperative control of multi-agent systems with negative imaginary properties. The research provides a timely and necessary study of the robust stabilization, output consensus and rendezvous problems for networked systems with negative imaginary properties. This current research is important since many practical systems can be modelled as negative imaginary systems and achieving a certain behaviour in multi-agent systems has potential real-world applications.