Research On Coordinated Control Of Discrete-time Descriptor Multi-Agent Systems With Input Saturation

In the field of engineering control,the coordinated control of descriptor multi-agent systems has been received attractions gradually due to its applications in such areas as power system,robot system and support system.However,most of the current literatures still focuse on the cooperative control of linear multi-agent systems described by differential equations or difference equations,and a dearth of study on descriptor multi-agent systems.Due to descriptor systems have many characteristics which are different from normal systems,it will be more difficult to study coordinated control of descriptor multi-agent systems.Although some achievements have been made in coordinated control of descriptor multi-agent systems,input saturation has still not taken into account in these researches.The input signal received by the controller may not match the real input if the system has a saturation constraints,it will result in poor stability of the closed-loop system.Based on the above analysis,this thesis studies the coordinated control problem of discrete-time descriptor multi-agents with input saturation under fixed digraph topology and symbolic digraph topology,respectively.The main research contents include:The problem of the semi-global output consensus of descriptor multi-agent systems with input saturation under a fixed directed communication topology.Firstly,the original problem is transformed into an output regulation problem with distributed observers.Secondly,the explicit solution of the descriptor system is obtained by a parametric discrete-time Riccati equation,which avoids the constrained equivalent decomposition of a descriptor system.Thirdly,the semi-global output consensus control protocols are constructed based on the distributed state observers and an output regulator,and the sufficient conditions for the stability of the system are given by selecting an appropriate Lyapunov function.It is proved that the system can achieve semi-global output consensus control under the control protocols.Finally,the obtained results are verified by numerical simulation examples.The semi-global bipartite consensus problem for descriptor multi-agent systems with cooperative-adversarial relations with input saturation constraints is considered under a fixed sign directed graph topology.By using the modified parametric discrete-time Riccati equation method and the relative output information between agents,the distributed control protocols based on descriptor observers are designed,and the related design steps are given.Secondly,by using matrix-theoretic,graph-theoretic tools and related lemmas about stability of discrete-time linear descriptor systems,some sufficient conditions for the system to achieve bipartite consensus are obtained.It is verified that the system reaches semi-global bipartite consensus if the structure of symbolic digraph is balanced.If the structure of symbolic digraph is unbalanced,all state components of the intelligent agent tends to zero.Finally,the correctness of the results are verified by a MATLAB numerical simulation.The problem of semi-global bipartite containment control for descriptor multi-agent systems with input saturation is studied under a weakly connected symbolic directed graph topology.Based on the assumption that the follower system is asymptotically zero controllable and each follower has at least one reachable leader,the distributed semi-global bipartite containment control protocols are designed by using the modified parametric discrete-time Riccati equation and the state errors of adjacent agents.The sufficient condition for the system to achieve semiglobal bipartite containment control is that the independent strongly connected branches of the symbolic directed graph are structurally balanced.The corresponding conclusions are proved by the theory of symbolic directed graph and descriptor Lyapunov stability theory.Finally,a MATLAB simulation example is used to illustrate the results.