Optimal Distributed Coordinated Controller Design For Linear Multi-agent Systems

The research on advanced control method for multi-agent systems is one of the hot issues that attract the domestic and foreign scholars in recent decades,and the optimal design method is an important branch of advanced control method for multiagent systems.Although a lot of achievements in development of the optimal control for multi-agent systems have been obtained,the research on it is still not perfect.Multi-agent systems,especially linear multi-agent systems with time delays,contain both the communication delays among multiple agents and input delay of single agent,which makes the existing feedback control methods for single system cannot effectively control this connected large-scaled system.The consensus tracking is the basis of the research on advanced control method for multi-agent systems.The other control objectives can be extended based on the theoretical approaches of consensus.Therefore,it has significant theory and practice values to adopt the optimal control methods to design advanced controllers with analytic form,aiming at the model of linear multi-agent systems with time delays,in order to make the whole multi-agent systems not only can achieve consensus tracking with superior control performance but also be convenient for engineering applications.Aiming at the linear multi-agent systems with time delays,this dissertation studies the advanced analytical control design problem for multi-agent systems using matrix theory,algebraic graph theory,frequency-domain method and optimal control theory.Firstly,a transfer function framework of multi-agent systems is established in frequency domain.And the sufficient and necessary conditions are given to achieve consensus tracking for both homogeneous and heterogeneous multi-agent systems.The stability analysis of the large-scaled system is decomposed into the control problem-s of finite independent systems.Subsequently,for homogeneous and heterogeneous multi-agent systems respectively,aiming at the optimization of reference signal tracking,input disturbance rejection performance indices and so on,through the rigorous theoretical derivations,the design method of analytical controller is given to optimize the performance indices of multi-agent systems.This type of controller design method has the following characteristics:1)the controller of single agent can be designed independently,which is fully-distributed and independent of global information;2)the proposed controller design can guarantee the optimization of performance index of linear multi-agent systems.It is given by specific analytical form,which is easy to use in real applications;3)the overall closed-loop system performance can be adjusted quantitatively by the adjustable parameters of each individual controller,to achieve the tradeoff between the nominal performance and robustness,which has a large practical significance in engineering applications.The main contributions can be concluded as follows:1.A multi-input multi-output framework based on transfer function is introduced in frequency domain to describe multi-agent systems.Single integrator,double integrator and general linear models can all be described by this framework.The block diagram can describe all kinds of linear multi-agent systems from a unified perspective,in which homogeneous system is only a special case.Besides,the sufficient and necessary conditions are accordingly deduced to achieve consensus tracking of linear multi-agent systems.The stabilization problem of multi-agent networked system can be converted into the zero steady-state error control problem of a set of independent subsystems.When the number of agents is too large,the stability of the multi-agent systems will become challenging to analyze.The decomposition scheme relaxes this difficulty significantly.2.For homogeneous multi-agent systems under undirected topology,a new analytic design method of the H2 optimal consensus tracking controllers is proposed.The decomposition method is utilized to simplify the analysis of internal stability and H2 performance index of the whole system to a set of independent optimization problems.Consequently,all of the controllers that can stabilize the decomposed subsystem and have a zero steady-state error for a step input are parameterized.Finally,the detailed analytical design formula of the optimal reference tracking controller is derived from the point of view of optimizing the system performance index.The proposed design method can optimize the performance index not only from the reference input to the system error but also from the output disturbance to the system output.3.For homogeneous multi-agent systems under undirected topology,a new analytic design method of the H2 optimal input disturbance rejection controllers is proposed.Aiming at the decomposed modal subsystems,the H2 optimal controller can be computed from all the stabilization controllers.Then the distributed coordinated controllers with the same type and structure can be unified.The proposed design method can optimize the performance index from the input disturbance to the system output.Based on the homogeneous systems of six unstable first order plus time delay agents,consensus controllers of multiple agents utilizing the proposed analytical design method are designed.Unexpected input disturbance and model uncertainties can be suppressed effectively.4.For homogeneous general integrator multi-agent systems under undirected topology,the new analytic design methods of H? and H2 optimal controllers are proposed.The basic feature of general integrator model is that the agent dynamic contains both integrator and time constant,which is a specific type of unstable process.Further development on the analytical design methods of control for the general integrator multi-agent systems is desirable and valuable.Aiming at the decomposed modal subsystems,both H? and H2 optimal controllers are computed analytically according to the corresponding performance indices.The proposed controllers not only can optimize the reference tracking performance but also has a simple tuning way to tradeoff the nominal performance and robustness.Finally,the H? and H2 steering autopilot are designed respectively in the formation control of autonomous surface vessels,in order to achieve the optimal consensus control of heading angle of multiple vessels.5.For heterogeneous multi-agent systems under directed topology,a new analytic design method of H2 optimal disturbance rejection controllers is proposed.Firstly,a sufficient and necessary condition is given to achieve consensus tracking of heterogeneous multi-agent systems based on the column diagonal dominance criterion.Once the controller structure has been designed,both the stability boundary to stabilize the diagonal closed-loop system and the column diagonal dominance region can be worked out.The intersection of the two regions is the conservative stability region.Secondly,for each subsystem without intercommunication,the optimal output,input and balancing output-input disturbance rejection controllers are designed independently.A filter is used to be in series with each controller to not only stabilize the whole systems but also achieve a tradeoff between nominal performance and robustness by adjusting a single tuning parameter.The proposed distributed H2 controllers calculated by alge-braic solution perform better capacity of disturbance attenuation than the conventional given-structured protocols.6.For heterogeneous multi-agent systems with unknown input load disturbance,a new analytic design method of H2 DOB-based optimal controllers is proposed.Firstly,a universal block diagram is established to describe the linear multi-agent systems based on transfer functions.A sufficient and necessary condition is accordingly deduced to impose on each controller.Secondly,based on the H2 performance index of each subsystem,both the optimal consensus controller and disturbance observer are derived analytically.The distributed H2 DOB-based consensus controller can not only achieve consensus tracking for the reference input,but also reject the effects of external disturbance and model uncertainty.