Consensus of Multi-agent Systems: Fixed-time Convergence and H infinity Performance

Abstract

In this thesis, we address the consensus of multi-agent systems in two different approaches. First, non-linear consensus protocol named fixed-time consensus is introduced in order to reduce the settling-time of the system and provide the upper bound of the settling-time. Second, robustness of the multi-agent consensus system under coupled disturbances is analyzed using H infinity approach by deriving LMI conditions that ensure consensus within a prescribed performance. Each approach is further analyzed after being applied to practical applications.

For fixed-time consensus protocol, we introduce orientation estimation and network localization problem in multi-agent system. The accuracy of the orientation and position information is crucial in formation control and therefore faster convergence of the state estimation system is required. The system is assumed to utilize only local measurements including relative orientation and relative distance. In the circumstance, fixed-time orientation estimation law and fixed-time orientation-aware network localization law are addressed showing faster convergence within the fixed settling-time. Further, integration of the two state estimation systems is provided. By assuming simultaneous operation of the two state estimation systems, the network localization system has the estimated orientation value as input and the uniform asymptotic stability of the system is proved. Lastly, simulation of a multi-agent system with 1 anchor node having global information is given confirming that the true orientation and position values could be obtained using the proposed state estimation system.

The robustness of the consensus system is studied upon the consensus problem in multi-agent systems under the influence of diffusively coupled disturbances. Two different types of systems are considered regarding the homogeneity of the disturbance coupling parameters. The main goal is to derive the conditions that guarantee the prescribed performance of the designed control system on disturbance attenuation. To estimate the disturbance attenuation performance of the controller, the H infinity norm of the transfer function from the redefined disturbance vector to the disagreement vector is measured. Then the sufficient conditions for the system to achieve consensus within the desired performance are derived in terms of linear matrix inequalities (LMI). Numerical examples of both one- and multi-dimensional consensus control systems are provided to check the validity of the derived LMI feasibility test along with the illustration of consensus behavior in time domain.