Distributed Tracking Control For Multiple Euler-Lagrange Systems With Error Constraints

Multi-agent systems can describe many practical systems,such as multiple manipulators,formation flying satellites,autonomous underwater vehicles,and sensor networks,to name a few.For multi-agent systems,the agents communicate with each other in a certain way so that they are able to accomplish the assigned tasks.The distributed control for multi-agent systems means that each agent can calculate its required control input independently by using the local information of the systems.By adopting distributed control strategies,the multi-agent systems possess higher flexibility,robustness,and environmental adaptability.Euler-Lagrange(EL)equation is can describe many systems with inherent nonlinearities,such as robotic manipulators,autonomous vehicles,and walking robots.The multi-agent systems modeled by EL equations are named as multiple EL systems.When there eixsts one leader in the systems,the objective of distributed tracking control for multiple EL systems is that all the followers can track the leader by distributed control schemes.The convergence rate of the systems can be improved by adopting the finite-time control or fixed-time control methods.The systems can be stable before a certain time when finite-time or fixed-time controllers are used so that the convergence rate of the systems is accelerated.The function of error constrained control is to ensure that the related variables do not exceed the prescribed bounds during the whole control process.By combining the finite/fixed-time control with error constrained control methods,we can improve the overall performances of the control systems.From the above statements,this dissertation is focused on the distributed finite/fixed-time tracking control for multiple EL systems with error constraints.The main contents of this study are listed as follows.The distributed finite-time tracking control for multiple EL systems with error constraints is investigated under directed communication topology.When the nominal system models are known,a distributed finite-time tracking controller is designed by backstepping scheme.It is demonstrated that the tracking error of each follower can converge to a neighborhood of zero in finite time.Besides,a tan-type barrier Lyapunov function is utilized to guarantee that the error variables will not exceed the prescribed bounds.When there exist nonlinear uncertainties for multiple EL systems,a model-independent distributed finite-time tracking control algorithm is developed with radial basis function neural networks being used to estimate and compensate for the uncertain terms.Based on the above researches and considering that there exist input saturations for the agents,a novel distributed finite-time error constrained tracking control protocol is then put forward.The distributed fixed-time tracking control problem for multiple EL systems with error constraints is addressed.When the nominal system models are known,a distributed fixed-time tracking controller is designed by the adding a power integrator technique under directed topology.It is proved that the tracking error of each follower can converge to a neighborhood of zero in a fixed time.An improved exponential-type barrier Lyapunov function is employed to guarantee that the error constraints will not be violated.Based on this result,the case that there exist system uncertainties and the acceleration information is unmeasurable is further considered.A distributed fixed-time observer is firstly proposed to estimate the leader's generalized velocity and position for the followers.Then,a distributed fixed-time tracking control strategy is given by the adding a power integrator method for the multiple EL systems whose inertia matrices are in the diagonal forms.The radial basis function neural networks are utilized to approximate the uncertain terms of the systems.Theoretical analysis and numerical simulations show that the tracking error of each follower will converge to a neighborhood of zero in a fixed time while the error constraints will be satisfied during the whole control process.