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Consensus Control of a Class of Nonlinear Systems

Mohd Isira, Ahmad Sadhiqin Bin

[Thesis]. Manchester, UK: The University of Manchester; 2016.

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Abstract

This dissertation aims at solving the consensus control problem of multi-agent systems with Lipschitz nonlinearity. This depends on the design of the controller that enables each agent or subsystem in multi-agent systems with Lipschitz nonlinearity to reach consensus; using the understanding of the agents' connection network from the knowledge of graph theory as well as the control system design strategy. The objective is achieved by designing a type of distributed control, namely the consensus control, which manipulates the relative information of each agent in a multi-agent systems in order to arrive at a single solution. In addition, containment control is also developed to solve containment problem. It is an extension of consensus control via leader-follower configuration, aimed at having each agent contained by multiple leaders in a multi-agent systems with Lipschitz nonlinearity.Four types of controllers are proposed - state-feedback consensus controller, observer-based consensus controller, state-feedback containment controller and observer-based containment controller; each provides the stability conditions based on Lyapunov stability analysis in time domain which enabled each agent or subsystem to reach consensus. The observer-based controllers are designed based on the consensus observer that is related to Luenberger observer. Linear Matrix Inequality (LMI) and Algebraic Riccati Equation (ARE) are utilized to obtain the solutions for the stability conditions. The simulation results of the proposed controllers and observers have been carried out to prove their theoretical validity. Several practical examples of flexible robot arm simulations are included to further validate the theoretical aspects of the thesis.