Improvements And Applications Of KWTA Network Models Based On Nonlinear Optimization

Winner-take-all(WTA)refers to the process of identifying the most important input from a given set of inputs,and it is widely used in recognition and classification tasks.k-winners-take-all(k WTA)is an extension of WTA that can identify the top k most important inputs from a set of m inputs.This extension broadens the scope of k WTA,making it applicable to a wider range of scenarios,such as data analysis,feature selection,and decision systems.Specifically,in multi-robot systems,k WTA problems can be used for task allocation,path planning,and resource management.However,solving k WTA problems is often a performance bottleneck in these applications.To address this,three recurrent neural network(RNN)models are proposed in this thesis to solve the k WTA problem,each with different characteristics and good accuracy for identifying the most important inputs.Firstly,we explore the solution to time-variant nonlinear optimization with equality and inequality constraints(TVNOEIC)problems.The Lagrange multiplier method and nonlinear complementarity function are used to transform the optimization problem into an equivalent time-variant nonlinear system of equations.Based on this,a noisesuppressing discrete-time(NSDT)neural network model that can efficiently solve such optimization problems is designed.Theoretical analysis and simulation experiments demonstrate that the proposed model has several advantages,such as fast convergence,high accuracy,strong robustness,and ease of hardware implementation.Furthermore,this thesis shows that the k WTA problem can be equivalently transformed into a TVNOEIC problem.Based on this fact and the properties of the k WTA problem,this thesis obtains an equivalent optimization problem form of the k WTA problem through a series of transformation operations and verifies the feasibility of the proposed NSDT model on the k WTA problem through simulations.Subsequently,a gradient-based k WTA(G-k WTA)model is introduced for the k WTA problem.To meet the requirements of real-time and robustness,the velocity compensation and the error integration term are introduced to improve the model and obtain a gradient-based differential k WTA(GD-k WTA)model.Theoretical analysis and simulation results demonstrate that this model not only performs well in solving the k WTA problem but also effectively suppresses various noise interferences in the environment.In addition,this thesis applies the model to a multi-robot system to model the competitive behavior among multiple robots,demonstrating its broad applicability and practicality.Finally,since optimizing convergence parameters is a crucial operation in neural networks,this thesis introduces the fuzzy control theory and proposes a new RNN model to effectively solve the k WTA problem.This model has adaptive fuzzy parameters,and thus is referred to as the fuzzy k WTA(F-k WTA)model.By more effectively controlling the convergence parameters,this model can better adapt to different environments and tasks.Theoretical analysis and simulation results demonstrate the feasibility and effectiveness of the model in solving the k WTA problem.Furthermore,the model is applied to a multi-robot system,successfully achieving more efficient task allocation,further proving its applicability.