The Cooperative Optimal Control Of Multi-Agent Systems

In this paper,cooperative optimal control of multi-agent systems(MAS)is considered.Two goals are intended to be achieved:(1)the consensus of multi-agent systems is guaranteed;(2)obtain the optimality of performance index insist of control input and state information.Three kinds of problems in cooperative optimal control of MAS are studied in this paper: distributed inverse optimal control of second order MAS under independent position and velocity topologies,distributed optimal control problem for second-order MAS under topology related performance index and distributed approximately optimal control of discrete time linear MAS.Firstly,linear quadratic regulator(LQR)theory is applied to solve the inverse optimal consensus problem for a second-order linear multi-agent systems under independent position and velocity topology.The existing work on consensus problem of second order multi-agent systems almost based on the assumption that the position and velocity states interact on the same topology.In this paper,a second order MAS under independent position and velocity topologies is considered.A distributed controller contained position and velocity topologies is given based on the literatures studying on consensus problem of second order MAS.The optimal Laplacian matrices related to the topologies of position and velocity are derived by solving the algebraic Riccati equation(ARE).Theoretically,we obtain the optimal Laplacian matrices,which correspond to the directed strongly connected graphs,for the second-order multi-agent systems.Finally,two simulation examples are provided to verify the theoretical analysis of this paper.Secondly,interaction-related performance index for second-order linear multi-agent systems is considered.A consensus protocol consist of the scaling factor is designed for the second-order MAS.The optimal scaling factor is derived during minimizing the interaction-related performance index.The consensus of second-order MAS is reached under the optimal scaling factor.Illustrative example is given as a proof of concept.Finally,distributed approximately optimal control of discrete-time high order linear multi-agent systems consist of the other main result in this paper.There are two defects in the existing work on the cooperative optimal control of discrete time MAS: individual performance index and the specific dynamic form of MAS.In this paper,the general dynamic multi-agent systems under global performance index is considered.The multi-agent systems can be considered as a lump system under the assumption that each agent can obtain the states of all the other agents.The cooperative optimal control of MAS in this situation can be solved as a standard LQR problem.This section investigates distributed approximately optimal controllers for linear discrete-time high-order multi-agent systems.The estimators of others agents are established for each fixed agent to estimate the states of the non-neighbor agents.The distributed estimator-based optimal controllers are designed by using LQR under the communication graph of the MAS being strongly connected.The states of each agent for the closed-loop system can be guaranteed to converge to the corresponding system with centralized optimal controllers.Simulation results show effectiveness of the proposed controllers.Furthermore,the cooperative optimal control problems considered in this paper are both based on the global performance index,which guarantees the global optimality.