(Pre-given)Finite Time Control Of Multi-Agent Systems

Large-scale networked systems have complex dynamic characteristics, making it important and challenging to control such systems. The traditional centralized control method cannot fulfill the requirements to guarantee the coordinated, stable and efficient operation of the complicated multiple systems. Different from the traditional centralized control method, distributed control method, dedicated to achieving a global common objective by using only local communication in the absence of central coordination, is more promising due to the advantages such as limited communication/sensing range, cooperative fashion, flexibility, and scalability. Thus it is the ideal control of the large-scale networked systems, and has been extensively applied to various fields such as attitude control of satellites, intelligent transportation systems, large-scale power dispatching. Cooperative consensus is known as the most fundamental issue in the distributed control of networked multi-agent systems(NMAS), which is the basis for solving other distributed control problems. How to ensure multi-agent systems to achieve high-stability, high-precision and high-speed convergence under the weakest communication topology condition is the important and difficult point of the consensus control research. The finite time consensus control of nonlinear multi-agent systems with complicated uncertainties and the pre-given finite time control of multi-agent systems are studied in this thesis and the following innovative achievements have been accomplished:Finite time control(1) Regarding to the finite-time consensus control problem of second-order nonlinear MAS under single-way communication topology, a distributed adaptive control scheme is established by introducing the newly constructed Laplacian matrix into the properly chosen Lyapunov function candidate, in which the rigorous theoretical analysis and proof verifying an important property of the new Laplacian matrix are given. The proposed method relieves a bottleneck in the finite-time control for NMAS under one-way directed topology in which the modern finite-time control theory cannot analyze it analytically. In addition, the finite-time stability analysis method is further extended to the formation-containment control of this class of nonlinear NMAS. This work provides a solution to the continuous finite-time formation-containment problem for second-order nonlinear NMAS under one-way topology.(2) The problem of finite time consensus for a class of second-order uncertain nonlinear NMAS, which involves unknown time-varying control gain, non- parametric system uncertainties, and undetectable actuation failures, is investigated under singe-way directed communication topology. By using the adding integrator technology, core function theory, and adaptive control method, a fault-tolerant finite-time consensus control scheme based on fraction state feedback and fraction adaptive law is proposed. The rigorous theoretical analysis and proof verifying the effectiveness of the proposed control scheme are given by introducing the concept of the virtual parameter estimation error and the local filtered error and incorporating them into a skillfully chosen Lyapunov function candidate, which breaks through a dilemma in the distributed finite-time control of NMAS in the presence of uncertain time-varying control gain and undetectable actuator faults. In addition, the stability analysis method is further extended to a class of high-order non-affine NMAS, and a finite-time consensus algorithm is established by using backstepping control design method, inductive argument, adding an integrator technology in high-order case, core function theory and adaptive control method, which solves the finite-time consensus control problem for the nonlinear NMAS with high-order non-affine dynamics.(3) In order to solve the problem of finite-time consensus for a class of high-order pure-feedback NMAS with mismatched non-parametric uncertainties, a distributed neural adaptive control scheme based on fraction state feedback is developed. Such finite time feature is made possible by the fraction dynamic surface control(F-DSC) design technique based upon the concept of virtual fraction filter. The rigorous stability analysis and proof are given by using the Lyapunov stability theory, backstepping control method, and packaged function technique, through which the finite-time consensus tracking control problem of such complicated NMAS with mismatched uncertainties is resolved. In addition, the stability analysis method is extended successfully to the finite-time containment control of such class of NMAS.Pre-given finite-time control(4) A new finite-time control theory with new analysis method is proposed, which is not the usual one that is based on the signum function or fractional power feedback. The finite convergence time with this method does not depend on any initial conditions and any other design parameters such that it can be uniformly pre-specified. With this finite time control theory, the results of cooperative consensus achieved within a uniformly pre-specified finite time are derived under both bidirectional and unidirectional interactions for first-order NMAS, which breaks through the control dilemma that the finite convergence time cannot be pre-assigned uniformly and also the dilemma that the control input signals are not continuous or non-smooth among the existing finite-time methods. Furthermore, this theory is extended to apply to the finite-time leader-follower consensus problem of high-order NMAS, in which the dilemmas that both the design of the controller and the stability analysis are too complex to be applicable to the practical systems and that the finite convergence time is hard to pre-given uniformly are removed.