Hierarchical Distributed Optimization Of Nonlinear Cluster Lagrange Dynamical System

With the application of automatic control technology in practical engineering,the control method of nonlinear cluster system has gradually come into people’s research field.Due to nonlinear cluster system consists of multiple intelligent individuals,it can complete more complex and difficult work.The increase of the number of individuals in the system will inevitably bring a lot of resource consumption,so the optimization control research of nonlinear cluster system is of great significance.In addition,for some nonlinear cluster systems with more complex models such as task-space trajectory and attitude equation transformation,the optimal control method is of great significance.In this thesis,a mathematical model of nonlinear cluster system is constructed,and three hierarchical optimization control methods are designed based on the gradient optimization control technology.The objectives of task-space bipartite coordination optimization control,finite-time attitude multi-objective formation tracking control,and fixed-time consensus optimization control are achieved.The main work is as follows:(1)A fully distributed hierarchical optimization control algorithm based on optimization estimator is proposed for bipartite coordination optimization control of nonlinear cluster systems in task space,considering dynamic uncertainty,co-existence of cooperative and competitive individuals,high communication pressure and high resource consumption.The monotonous bilateral adaptive gain is used to avoid the use of global information and reduce the communication pressure.At the same time,the cost function is minimized and the resource consumption is reduced by relying on the optimization estimator.The bipartite coordination optimization control in task space of nonlinear cluster system is achieved by using the symbol of communication weight to deal with the competing and cooperating individuals.(2)To solve the multi-formation tracking optimization control problem of nonlinear cluster systems with attitude equation,a finite time hierarchical optimization control algorithm based on optimization estimator is proposed considering the time varying anchor trajectory,multi-formation tracking,one-way network communication and high resource consumption.Based on finite time optimization estimator,the cost function representing resource consumption in the control process is minimized.Meanwhile,formation information is introduced into the optimization function to realize multiformation tracking.A new energy storage function is constructed to ensure that the proposed algorithm is suitable for the system with unidirectional network communication.The nonlinear cluster system with attitude equation can achieve the optimal control of multi-formation tracking for the trajectory of time-varying anchor in finite time.(3)In order to solve the fixed-time optimization control problem of nonlinear cluster systems,a fixed-time coordination optimization control algorithm based on optimization estimator is proposed considering the convergence time of system state,optimization with equality constraints,high resource consumption and coordination of system state.Based on the fixed-time optimization estimator,the cost function related to the output state of the system is minimized when the estimator results are in coordination,and the equality constraint is satisfied.The adaptive sliding mode control technology is used to design the local fixed-time controller to ensure the state of the system is in coordination in optimal way in fixed time.The convergence time can be calculated and is independent of the initial state of the system.