Research On Optimal Containment Control Of Multi-agent Systems

Multi-agent systems are large-scale networked control systems which are made up of some intelligent units,and they through the exchange of local information to complete a given group task.With the rapid development of wireless communication,modern control theory and technology,network control of multi-agent systems has become a hot topic in the field of distributed control.The containment control and the optimal consensus are one of the fundamental problems in cooperative control of multi-agent systems,the objective of containment control is to design the distributed protocol for each follower to make sure the states of followers asymptotically converges to the convex hull spanned by the leaders;and the objective of 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.Currently,the results about these two problems are very abundant,but few scholars pay attention to optimal containment control of multi-agent systems.In practice of engineering,we always want to minimize the cost to accomplish a goal,so the obtained results have theoretical value and practical significance for the development of the theory of network systems.The main results are listed as follows in the order of chapters:1.The optimal containment control of linear dynamics for multiple leaders and followers with single-integrator dynamics in continuous-time setting is considered.A global cost function,namely,interaction-related cost function is proposed.Based on the linear-quadratic-regulator(LQR)theory,the optimal scaling factor for a pre-specified symmetric Laplacian matrix associated with the interaction graph is given.The results of simulation show the validity of the proposed method.2.The optimal containment control of linear dynamics with multiple leaders and fixed information topology is studied.A distributed protocol with optimal feedback and a optimal coupling gain is proposed based on the linear-quadratic-regulator(LQR)theory.By solving the Riccati equation,the sufficiency condition for the all followers converge to the stationary convex hull spanned by the stationary leaders for arbitrary initial conditions is obtained.The results of simulation verify the validity of the proposed method.3.The optimal leader-follower consensus problem of heterogeneous multi-agent system is investigated,which consists of one static leader,first-followers,and second-order followers.Under the conditions that the position digraph contains a spanning tree and at least one second-order follower takes the static leader as a neighbor,the necessary and sufficient condition is presented for the considered system to achieve the optimal consensus by employing the liner-quadratic regulator(LQR)theory and inverse optimization method.In this sense,the proposed control protocols for each follower is optimal for the obtained linear quadratic performance index function.The results of simulation show the validity of the proposed method.