Coordinated Control Of Partial Differential Multi-agent Systems Based On Iterative Learning Algorithm

Coordination control of multi-agent systems(MASs)is a hot research topic in the control field,which mainly involves the consensus control of systems without leader,the tracking control of systems with one leader,and the containment control of systems with multiple leaders.Compared with ordinary differential MASs,the state space of the partial differential MASs is related to infinite dimensional space,and the state variables of the systems at every moment are functions,so the application areas of the partial differential MASs are wider and the used mathematical tools are more complex.Iterative learning control algorithm,as an emerging control technology,considers to find the control torque,and improves the information of the current round by repeatedly using the information obtained from the previous round,so that the robot can follow the desired trajectory exactly over a finite time interval.Owing to its simplicity and effectiveness,iterative learning control algorithm has become one of the most active fields in intelligent control and system control.In this paper,we study the coordination control of partial differential MASs based on iterative learning control algorithm.Firstly,the iterative learning control algorithm is applied to the non-classical(degenerate equations)partial differential MASs,and the consensus control is considered,which expands the research scope.Then,the iterative learning control algorithm is applied to the classical(the second-order parabolic or hyperbolic equations)partial differential MASs,and the containment control is considered(tracking control is included).Furthermore,this algorithm is applied to the high order(the fourth-order hyperbolic equations)partial differential MASs,so as to show the universality of this method.On the other hand,the boundary control of a class of hyperbolic partial differential systems is considered.A method,which is different from the commonly used Backstepping design,is given to achieve a breakthrough in research methods,.Concrete research contents are as follows:1.The consensus control of degenerate partial differential MASs is studied,and the consensus conclusions based on iterative learning stability are achieved;2.The containment control(tracking control is included)of the second-order parabolic or hyperbolic partial differential MASs is studied,and the containment conclusions in the sense of iterative learning stability are obtained;3.The boundary control of the hyperbolic partial differential systems is studied,and the convergence conclusions are obtained based on Lypaunov stability;4.The containment control(tracking control is included)of the fourth-order hyperbolic partial differential MASs is studied,and the containment conclusions in the sense of iterative learning stability are achieved.Finally,the results of this study are summarized,and some problems to be further studied are put forward.