Research On Optimal Consensus Of Multi-agent Systems

With the rapid development of Wireless communication,modern control theory and technology,networking technology,network control of multi-agent systems has become a hot topic in the field of distributed control.Currently,the results about consensus of multi-agent systems are very abundant,but few scholars pay attention to optimal consensus of multi-agent systems.In practice of engineering,control input of multi-agent systems is always bounded and we always want to minimize the cost to accomplish a goal;so research on optimal consensus of multi-agent systems is very important.For a multi-gent systems,optimal consensus is optimizing the edge weigh of the interaction topology or designing a protocol or an interaction topology so as to minimize a given cost function.The study mainly focuses on linear systems of multi-agent systems,systematic study is carried out mainly in the following three aspects:1.The optimal output tracking of a class of heterogeneous linear multi-agent systems is considered.A suitable performance function is first introduced by employing the nonzero desired trajectory linear quadratic regulator theory.Then,the sufficient and necessary conditions are derived such that the output variables of all agents converge to the desired value.Further,It is noted that the optimal output tracking problem is equivalent to the optimal state tracking problem as the output matrices of all agents are taken as the identity matrix.On this basis,the obtained results are extended to the case where the state time-delay of each agent exists and the similar condition are also proposed.Meanwhile,the upper bound of time-delay is determined,The obtained results give a tool to design the information topology of a heterogeneous linear multi-agent system and its controller based on the individuals,by which the performance index function can be minimized.The results of simulation revealed the validity of the proposed method.2.The optimal average consensus problem of multi-agent systems based on the state space decomposition method is considered.By introducing two control parameters named global scaling factor and local scaling factor,the topology conditions is given for the considered system to achieve the average consensus by employing the bipartite connected digraph.On this basis,two reduced-order cost functions that depend on the global scaling factor are proposed for the continuous and discrete time case,respectively.Further,the sufficient conditions are obtained such that the proposed system not only achieves the average consensus but also makes the corresponding cost function minimized.3.An optimal consensus problem of second-order leader-follower multi-agent systems is considered by using inverse optimality and LMI method.For a given control input,under the condition that the communication topology among followers is undirected connected and at least one follower can received information of leader,a positive definite matrix in a linear quadratic performance index function is got,which makes the linear quadratic performance index function to obtain the minimum value.