Research On Shape Asymptotic Tracking Control For Continuous Dynamic Systems

Shape is a geometric concept to describe the curved profile of a curve.It is generally used to describe the states trajectories and control targets of the system in the research of control theory.The existing research results show that the research of system control issue from the perspective of shape is helpful to intuitively understand and improve the concept and method of control theory,thus,it has important theoretical and practical significance.Since there is no unified quantitative description of shape at present,thus,there is no general method on how to use the shape concept to explore the system control issue,and there are few system control methods involving shape.Therefore,it is still a new research topic to research the system con-trol problem by means of the shape concept.In this dissertation,the system trajectory's shape is described by the rigid body motion,and the shape asymptotic tracking of the continuous dynamic system is emphatically researched.The specific contents are shown as follows:1.Considering shape asymptotic tracking issue of two-dimensional linear system,a syn-thetic method of shape asymptotic tracking controller is proposed.The definition of shape asymptotic tracking for two-dimensional linear system is given.The model refer-ence adaptive method is extended,and the sufficient and necessary condition of model matching condition is also given.Based on this,an effective two-dimensional shape asymptotic tracking controller is synthesized by applying the Lyapunov stability theory,such that the shape asymptotic tracking of two-dimensional linear system is achieved.2.Following consideration of shape asymptotic tracking problem of high dimensional lin-ear system,a design method of shape asymptotic tracking controller is given.Shape asymptotic tracking is defined by the concept of system shape variables.By construct-ing a partitioned matrix with the orthogonal matrix and enlargement the dimensional of constant vector,the general method of synthesizing the high dimensional shape asymp-totic tracking controller is given.It can ensure that the shape asymptotic tracking of the high dimensional linear system is achieved meanwhile the other states are asymptotically uniformly bounded.3.Considering the shape asymptotic tracking issue of nonlinear system,a shape asymptotic tracking control method with the ability of compensating the influence of nonlinear terms is proposed.Following a review of the nonlinear terms' impact,the model reference adaptive method is extended.An effective shape asymptotic tracking control method with the ability of compensating the influence of nonlinear terms is proposed.It can ensure that all signals in the closed-loop system are bounded while achieving the shape asymptotic tracking.4.Following consideration of the shape asymptotic tracking issue of multi-agent system,the shape asymptotic tracking control protocol of multi-agent system is proposed.Multi-agent system' definitions of shape variables and shape asymptotic tracking are given.By combining model reference adaptive method and algebraic graph theory,a leader-following based shape asymptotic tracking control protocol is proposed,such that the shape asymptotic tracking of multi-agent system can be realized.