Distributed Estimation And Cooperative Control Of Multiple Lagrangian Systems

In the filed of cooperative control of multi-agent systems,intensive attentions have been paid to linear systems,which results in booming theoretical achievements.To extend the distributed control theory for linear system to nonlinear system,increasing researchers concentrate on Lagrangian system,which can represent a large class of mechanical systems.It is challenging to design distributed control algorithms for multiple Lagrangian systems due to their intrinsic nonlinearities and strong couplings.Hence,the research of distributed coordination of Lagrangian systems is of great significance theoretically and practically.Taking the cost of the whole system,the limitations of installing space,and the constraints on system's weight into consideration,it is not always possible to equip the system with sensors that used for measuring all the states.In addition,in the scenarios of complex and noisy working space,it is also difficult to obtain the precise values of the states through direct sensing.In this case,observers will facilitate the controller design,due to the facts that only position measurements are required to implement the observer-based control algorithms.Besides these,it is worth noting that the distributed estimation plays key role in fulfilling some complicated tasks,such as formation tracking,since none of the agents in the whole system has the access to the weighted centroid of the formation.However,the strong inner nonlinearity and couplings will definitely increase the difficulties of distributed estimation.Meanwhile,the structure change of the closed-loop system caused by estimators will also directly affect the system's stability,which simultaneously makes it more difficult when designing the cooperative controllers.Due to the reasons mentioned above,this dissertation will focus on the distributed estimation and cooperative control of multiple Lagrangian systems.The distributed tracking problem for multiple Lagrangian system with parameter uncertainties is first investigated under a directed graph.With the constraint that only a portion of the followers have access to the leader's information,sliding-mode estimators are developed to estimate the states of the dynamic leader in finite time.In addition,to cope with the absence of velocity measurements of each follower,a class of distributed observers using only position information is designed.Based on the outputs of the estimators and observers,distributed tracking control laws are proposed such that all the followers can track the dynamic leader.It is shown that the proposed control scheme can guarantee the locally asymptotical stability of the closed-loop system.We investigate the distributed tracking problem and leaderless consensus problem for multiple Lagrangian systems under a directed graph,respectively.For the problem of distributed tracking,a new kind of distributed observer is designed to estimate the velocity for each follower.The velocity observer is updated using only position information from the agent itself and its neighbors.Based on the outputs of the observer,the distributed control protocols are proposed,where no estimation for the dynamic leader is required any more,such that the tracking errors as well as the observation errors locally exponentially converge to zero.For distributed leaderless consensus,we develop distributed control protocols combined with the proposed velocity observers.It is also shown that with the proposed observercontroller framework,all the agents can achieve consensus locally exponentially under a directed graph that contains a directed spanning tree.We study the distributed tracking control problem for a class of Lagrangian systems that can not be linearized by output feedbacks.To begin with,we show the non-existence of the globally nonsingular coordinate transformation matrix that can fully linearize the specific Lagrangian system.By looking into the property of the inertia matrix,a class of nonsingular coordinate transformation matrix in upper triangular form is designed,such that the system model is partially linearized with respect to the unmeasurable states.Then the sub-systems are fully decoupled through state reconstruction.And,a new type of velocity observers is designed to estimate the unmeasurable velocities for each system.Then,based on the outputs of the velocity observers,we propose distributed control laws,with which the followers can track the leader globally uniformly asymptotically.The global stability of the closedloop system is proved by employing the properties of cascade systems,ISS(input-to-state stability),and Lyapunov stability analysis.The weighted centroid formation tracking problem is addressed for a group of mobile Euler-Lagrange agents.To cope with the constraint that no agent has the access to the weighted centroid of the formation,a class of novel estimators is developed for each agent.By applying the sig(·)function and the continuous approximation of unitary vector,the estimator turns to be continuous with the property of finite-time convergence.Then,the distributed distance-based control law is proposed based on the graph rigidity theory and artificial potential function,such that the weighted centroid of the formation is driven to track the prescribed time-varying trajectory,meanwhile maintaining the desired formation.