Cooperative And Optimal Control Of Multi-agent Systems With External Disturbances

With the rapid development of intelligent control technologies such as modern computer network and artificial intelligence,agent control technology has gradually become a hot research problem and has been widely used in all walks of life.As an important research direction of agent control technology,multi-agent system control has attracted the attention and interest of many research institutions and experts.In this paper,the problem of cooperative optimal control for multi-agent systems is considered when the multi-agent systems are affected by mismatched disturbances in different channels from the control input.The cooperative optimal control problem studied in this paper includes in-depth research on containment control and consensus.The main research work and innovation points are as follows:(1)The distributed consensus problem of second-order multi-agent systems with external disturbances is studied,in which the external disturbances include matched disturbances and mismatched disturbances.The state observers and disturbance observers are designed to estimate the unknown states and disturbances of the systems,and distributed cooperative control algorithms based on active anti-disturbance observers are constructed to make the states of the followers converge to the states of the leader.The simulation results show that the designed cooperative control protocols can achieve the state consistency of the systems.(2)The finite time containment control of second-order multi-agent systems with mismatched disturbances is studied.By applying modern control theory,nonlinear observers are designed to estimate the unknown states and disturbances in the systems.Based on state estimations and disturbance estimations,a finite time containment control algorithm is constructed.The finite time containment control of second-order multi-agent systems is analyzed by means of algebraic graph theory and homogeneous theory.The simulation results show that the finite-time containment control algorithm can effectively make the motion states of the followers converge to the target region surrounded by multiple leaders.(3)Leader-following optimal consensus of heterogeneous multi-agent systems is studied.A distributed leader-following control protocol with scaling factor is designed based on LQR(Linear Quadratic Regulator).There is an optimal scaling factor to minimize the cost function,so as to achieve the optimal consensus of the systems.The final simulation results show that the followers in the systems changes from the initial states to the states of the leader.And at the same time,there are the optimal scaling factor and the optimal control protocol,so that the cost function of the systems gets the minimum value,that is,the systems can achieve the optimal consensus,and the validity of the conclusions is verified.(4)The finite-time optimal consensus for heterogeneous multi-agent systems with matched and mismatched disturbances is studied.For the existence of external disturbances and the difficulty of obtaining the actual velocity information in the systems,by applying modern control theory and integral sliding-mode control method,the nonlinear finite time observers are designed to estimate the unknown states and disturbances of the agents in the systems.Based on the finite-time state observers,distributed finite-time active anti-disturbance optimal consensus control protocols of the first-order and the second-order agents in the heterogeneous systems are proposed.The simulation examples show that the proposed distributed finite time optimal consensus algorithms can not only minimize the cost function,but also make the states of each agent consistent in finite time,which is to realize the optimal consensus in finite time.