A novel gain design method to improve the consensus performance of output-feedback multi-agent systems

关键词:  Consensus, output-feedback multi-agent systems, least mean square deviation, perturbation method

Key words:  Consensus, output-feedback multi-agent systems, least mean square deviation, perturbation method

摘要:

This paper considers the consensus problem of a group of homogeneous agents. These agents are governed by a general linear system and can only directly measure the output, instead of the state. In order to achieve the consensus goal, each agent estimates its state through a Luenberger observer, exchanges its estimated state with neighbors, and constructs the control input with the estimated states of its own and neighbors. Due to the existence of observation and process noises, only practical consensus, instead of asymptotical consensus, can be achieved in such multi-agent systems. The performance of the achieved practical consensus can be measured by the ultimate mean square deviation of the states of agents. That performance is closely related to the observation gains of the state observers and the control gains of agents. This paper proposes a method to optimize such performance with respect to the concerned observation and control gains. That method starts with a set of feasible observation and control gains and formulates a group of linear matrix inequalities (LMIs). Solving these LMIs gives some intermediate matrix variables. By perturbing observation and control gains, and the intermediate matrix variables, the original LMIs yield another group of LMIs, which can be solved to provide a descent direction of observation and control gains. Moving along that descent direction, observation and control gains can be improved to yield better performance and work as the starting point of the next iteration. By iteratively repeating this procedure, we can hopefully improve the consensus performance of the concerned multi-agent system. Simulations are done to demonstrate the effectiveness of the proposed method.

Abstract:

This paper considers the consensus problem of a group of homogeneous agents. These agents are governed by a general linear system and can only directly measure the output, instead of the state. In order to achieve the consensus goal, each agent estimates its state through a Luenberger observer, exchanges its estimated state with neighbors, and constructs the control input with the estimated states of its own and neighbors. Due to the existence of observation and process noises, only practical consensus, instead of asymptotical consensus, can be achieved in such multi-agent systems. The performance of the achieved practical consensus can be measured by the ultimate mean square deviation of the states of agents. That performance is closely related to the observation gains of the state observers and the control gains of agents. This paper proposes a method to optimize such performance with respect to the concerned observation and control gains. That method starts with a set of feasible observation and control gains and formulates a group of linear matrix inequalities (LMIs). Solving these LMIs gives some intermediate matrix variables. By perturbing observation and control gains, and the intermediate matrix variables, the original LMIs yield another group of LMIs, which can be solved to provide a descent direction of observation and control gains. Moving along that descent direction, observation and control gains can be improved to yield better performance and work as the starting point of the next iteration. By iteratively repeating this procedure, we can hopefully improve the consensus performance of the concerned multi-agent system. Simulations are done to demonstrate the effectiveness of the proposed method.