Fully Distributed Robust Adaptive Learning Control Protocols For Several Classes Of Nonlinear Multi-agent Systems

Nowadays,the research of multi-agent systems attracts more and more attention from scholars in various fields,especially the research of nonlinear multi-agent systems.In addition,learning control,as an intelligent control method which can achieve higher precision tracking through the repeated operation of the system,has been used to study the coordination problem of nonlinear multi-agent systems(the consensus and formation problem),and has made a breakthrough progress,but there are still some problems worth exploring.In this paper,under the framework of learning control theory and with the method of adaptive control,the completely distributed robust adaptive learning control protocols are studied for several classes of nonlinear multi-agent systems with repeatable operations,considering input saturation,state constraints,unknown control directions and nonlinear parametrization and other practical problems.The main research results of this paper are as follows:1.For the first-order nonlinear multi-agent systems with input saturation,when the systems contain nonparametric uncertain functions,under the framework of iterative learning control,a time-varying gain with fully saturated difference adaptive updating law is designed in combination with adaptive control,and the completely distributed robust iterative learning control protocols are obtained.Although the input saturation function is included in the dynamic of each follower,by constructing Lyapunov-Krasvoskii functional with time-varying weighting factors,on the interval [0,T ],it is proved that the consensus error approaches uniformly to zero as the iteration number increases indefinitely,that is,the perfect leaderfollower consensus of the state on [0,T ] is realized.Then,the formation problem is transformed into the consensus problem and solved based on the designed consensus algorithm,and the boundedness of all the signals in the closed-loop systems can be guaranteed in both two cases.2.For the second-order nonlinear multi-agent systems with input saturation and nonparametric uncertain functions,a distributed filtering error is defined.By using the adaptive iterative learning control method,the time-varying gain with fully saturated difference adaptive updating law is designed,and the completely distributed robust adaptive iterative learning control protocols are obtained.By reconstructing Lyapunov-Krasvoskii functional and using Schur's complement lemma,it is proved that the consensus errors of displacement and velocity of each follower tend uniformly to zero on [0,T ] as the iteration number increases indefinitely,i.e.,the perfect leader-follower consensus of the positions and velocities of agents is achieved on [0,T ];and the formation problem is transformed into the consensus problem and resolved by the designed consensus scheme,so that the displacement between each follower and the leader keeps the desired distance,and the velocity reaches the perfect consensus.3.For the second-order nonlinear multi-agent systems subjected to displacement constraints and partially unknown control directions,where the unknown nonlinear function is smooth and time-varying,and the system contains bounded external disturbances.Firstly,define some auxiliary variables for the design of completely distributed control protocols and the analysis of consensus;secondly,the time-varying neural network is used to approximate the unknown time-varying smooth nonlinear function,and the adaptive iterative learning control method is used to design the time-varying gains with differential adaptive updating laws,the fully saturated difference and differential parameter adaptive updating laws,and the completely distributed robust adaptive iterative learning control protocols are obtained;finally,by constructing a new barrier Lyapunov-Krasvoskii functional,selecting a piecewise Nussbaum gain function,and using Barbalat-like lemma,it is proved that all the agents can achieve the perfect consensus of displacement and velocity on [0,T ],that is,the the perfect leaderless consensus of displacement and velocity on [0,T ] is obtained.4.For a class of high-order nonlinear multi-agent systems with nonlinear parametrization,the dynamics of agents contain the nonlinear parametrization function with unknown timevarying parameters,and the leader has unknown the bounded input.First of all,the unknown time-varying parameters are separated by the parameter separation technique.By using the method of adaptive iterative learning control,the time-varying gains with differential adaptive updating laws,the fully saturated difference and differential parameter adaptive updating laws are designed,and the completely distributed robust adaptive iterative learning control protocols are yielded.By constructing an appropriate Lyapunov-Krasvoskii functional and using Barbalat-like lemma,on [0,T ],it is proved that the components of the consensus error vector tend uniformly to zero with the iteration number increases indefinitely,and the perfect leader-follower consensus of the state vectors of agents is achieved on [0,T ].5.For a class of high-order nonlinear multi-agent systems with linear parametrization,the followers contain unknown periodic time-varying parameters and the leader contains unknown dynamics.Under the framework of repetitive learning control,combined with the method of adaptive control,the time-varying gain with differential adaptive updating laws,the fully saturated difference and differential parameter adaptive updating laws are designed,and the completely distributed robust adaptive repetitive learning control protocols are obtained.By constructing a suitable Lyapunov-Kravoskii functional and based on Barbalat-like lemma,it is proved that the components of the consensus error vector approach approximately to zero as the time increases indefinitely,and the asymptotic leader-follower consensus of state vectors of agents on [0,+?)is gained.