Design,Analysis And Application Of Recurrent Neural Network Algorithms For Time-varying Problems

In scientific computing,mathematical theory,and practical engineering problems,there exist a large number of time-varying problems that require real-time computation,such as timevarying optimization decisions,economic scheduling,portfolio optimization,robot motion planning,and so on.A real-time easy-to-implement solver with global stability,fast calculation speed,high accuracy,strong anti-disturbance ability,and low computational complexity is very necessary for time-varying problems.How to design and construct such a time-varying solver has become one of the directions that many researchers in this field have been trying to explore.Traditional numerical computation methods often require more computational time and resources for time-varying problems due to their high computational complexity and high frequency of iteration.Furthermore,numerical computation methods focus more on time-invariant problems.In recent years,recurrent neural networks have been proven to have faster computation speed and higher accuracy than traditional numerical methods,and are therefore more frequently used for solving time-varying problems.Recurrent neural networks not only can solve time-varying problems but also can analyze their stability,convergence,and robustness by using the theory of stability.Such an advantage also gives recurrent neural networks more interpretability.Based on these advantages,more and more recurrent neural networks with high performance are proposed and applied to various practical scenarios.In this paper,some recurrent neural network algorithms for obtaining real-time solutions of time-varying problems will be designed.Furthermore,the effectiveness of recurrent neural networks in robot motion planning and control systems will be investigated.The main research works are as follows.1.A varying-parameter neural network with a time-varying parameter function is proposed,studied,and applied to the time-varying linear equation problem.Based on the theory of stability and differential equation,this paper will prove that the varying-parameter neural network has global stability,super-exponential convergence rate,and strong anti-disturbance ability.Furthermore,this paper will analyze the computational performance of the varying-parameter neural network under different activation functions and time-varying parameter functions.By incorporating the time-varying parameter function into the network structure,the ability to solve time-varying problems of the varying-parameter neural network is improved.Furthermore,the varying-parameter neural network can eliminate the influence of noise theoretically.2.Different from the traditional recurrent neural network design ideas based on differential equation structure,this paper proposes a recurrent neural network based on a purely integral equation.Due to its inherent integral equation structure,this neural network can effectively suppress the influence of noise,achieve monotone convergence,and does not cause overshoot,which is not possible with the current noise-tolerant recurrent neural network.Meanwhile,according to the analysis method of integral equation and stability theory,this integral-equationdriven neural network is proved to be exponentially stable.3.Although the above two methods have good performance in solving time-varying problems,the time-varying parameter function of the varying-parameter neural network and the purely integral equation structure are not conducive to iterative computation,which can easily increase the computational burden of the computer.In this paper,an error redefinition neural network by combining two design ideas(differential equation structure and integral equation structure)is proposed.Furthermore,the convergence and robustness of this neural network are analyzed.This method redefines the error function as an integral equation and constructs a recurrent neural network by the differential equation structure.This method also inherits the advantages of these two design ideas.Furthermore,the error redefinition neural network has the advantages of fast convergence,strong anti-disturbance ability,no overshoot,and easy computer implementation.4.By discretization,a discrete error redefinition neural network method is proposed in this paper.According to the stability theory of discrete systems,this discrete recurrent neural network is globally stable and has the same performance as the continuous error redefinition neural network.In addition,since the stability of the discrete system is related to the selection of the step size and parameters,the actual parameters and step size selection conditions for this network are also given.5.Recurrent neural network methods for time-varying equation problems are often ineffective in solving some motion planning problems of redundant manipulators with inequality constraints.Unlike the traditional collision-avoidance inequality constraint,this paper describes the collision-avoidance problem as the optimization criterion of the motion planning scheme through the design idea of collision repulsion force.This collision-avoidance criterion further deals with the motion planning problem with collision-avoidance inequalities that cannot be efficiently solved by recurrent neural networks.At the same time,the traditional scheme does not consider the maximization of collision avoidance,while the collision-avoidance optimization criterion proposed in this paper can achieve the maximization of obstacle avoidance and further solve the constraint conflict problem that often occurs in the original motion planning scheme.In addition,by combining the kinematic model of the mobile platform and the weight factor based on spatial distance,a bi-criteria collision-avoidance repetitive-motion-planning scheme using spatial weight factor for mobile redundant manipulators is proposed.6.By combining the design idea of defining the error function multiple times in the error redefinition neural network,an adaptive multi-layer neural dynamics controller for the timevarying trajectory tracking task is proposed and analyzed.By constructing the error function and using the neural dynamics method multiple times,the proposed controller can control the target system to achieve the effective tracking of time-varying trajectories.In addition,the combination of adaptive control further improves the anti-disturbance performance of this controller and gives the controller the ability to estimate external disturbances and uncertain parameters online.In addition,the application in a real-world multi-rotor UAV demonstrates the effectiveness and reliability of the controller design method.