Synchronization Control For Multi-agent Systems With Positivity Constraint

Positive systems are the kind of systems whose states and outputs are always non-negative whenever the system initial conditions and the inputs are non-negative.Such type of systems are frequently encountered in science and technology fields such as the social ecology,industrial engineering and so on.Recently,the dynamics of positive systems are widely concerned and many significant achievements have been achieved.As is well-known,multi-agent system is composed by a set of agents with simple dynamics,which belong to one of the important branches of the artificial intelligence with distributed collaboration manner,where complex dynamics are realized due to the communication and co-ordination among these agents.Such kind of systems are often encountered in our daily life,for example,the wireless sensor network system detecting the temperature in the greenhouse,where the states of these systems or the final state they all achieve are also always required to be non-negative.At the present stage,the researches on the multi-agent systems under positive constraint are still insufficiency.In this paper,the distributed synchronization control problem is addressed for the multi-agent systems with positivity constraint.The main works are summarized as follows.(1)Synchronization control of linear multi-agent systems under the positivity constraint.Firstly,for the network with undirected topology,necessary and sufficient conditions are presented which guarantee the coupled multi-agent system to be not only positive but also achieve synchronization.Then,according to the properties of Metzler matrices and the theory on Riccati equations,special design scheme is given for the gain matrix,which depends only on algebraic connectivity of the communication topology and the system matrices.Finally,a numerical example is given to illustrate the effectiveness of the obtained theoretical results.(2)Fixed-time synchronization control of nonlinear multi-agent systems under the positivity constraint.Firstly,necessary and sufficient criteria are given to assure the multi-input(MI)systems to be positive.Secondly,based on the network with undirected topology,a novel control protocol is designed for the MI nonlinear multi-agent system such that the coupled network achieves synchronization in fixed time.Moreover,the synchronization convergence value is not only positive but also independent on the initial conditions taken.Finally,a numerical example is provided to demonstrate the effectiveness of the results derived.