Research On Model Predictive Control Approach Based On Alternating Direction Method Of Multipliers

The controlled systems in the field of industrial control enjoy generally multi-input,multi-output and high-dimensional complex systems.It is difficult to establish accurate mathematical models,and there are lots of physical constraints in systems.Among many advanced control theories,the Model Predictive Control(MPC)has many advantages when dealing with complex large system control problems such as multiple input,output and time-varying characteristics,so it has been applied to transportation,robots,and aircraft.However,Model predictive control needs to repeatedly solve the optimization problem online at each sampling time.Therefore,the time delay is a key problem that plagued the application of model predictive control.In order to improve the online calculation speed of linear MPC,this paper first reviews the development of MPC,introduces the basic principles and characteristics of MPC,analyzes the difficulties encountered by MPC in practical system applications,and summarizes research advances in methods for solving optimization problems in MPC and increasing the speed of online computation of MPC.The main contributions of this research are as follows:Firstly,in order to improve the online speed of the model predictive control,the Alternating Direction Method of Multipliers is applied to the rolling optimization of model predictive control.The Alternating Direction Method of Multipliers uses the idea of divide and conquer,which decomposes the high-dimensional overall online optimization problem of a multivariable system into multiple low-dimensional sub-problems,and performs distributed optimization on the decomposed sub-problems,thereby speeding up the solution.Secondly,in order to reduce the sensitivity of ADMM to the initial value of the penalty parameter,this paper continues to analyze the principle of the algorithm and explore to speed up the algorithm's convergence speed.Among them,the principle of residual balance is to adjust the penalty parameter by keeping the original and dual residuals at similar sizes,thereby accelerating the convergence speed of the algorithm.We draw on the ideas of this method to alleviate the sensitivity of ADMM to the initial value of penalty parameters,in order to further improve the speed of solving optimization problems.Finally,in order to verify the effectiveness of the adaptive ADMM algorithm in model predictive control problems,a simulation experiment platform is established,and the convergence performance of various optimization algorithms in model predictive control problems is experimentally compared in this simulation platform.Specifically,this study uses numerical modeling of the drone's motion laws.Based on this,this study implements a variety of optimization algorithms.Finally,this study uses different optimization algorithms to solve the model predictive control problem of UAVs trajectory tracking.Experimental results show that the adaptive ADMM algorithm can significantly reduce the number of iterations of the model predictive controller,improve its convergence efficiency,and greatly reduce the time delay.