Neural-Dynamics-Based Time-Dependent Nonlinear Optimization Algorithms And Their Applications

Nonlinear optimization is one of the essential technologies frequently employed in modern science and engineering,which is widely used in various fields,such as machine learning,communication systems,optimal control,and pattern recognition.Many scientific research and industrial design problems are ultimately transformed into nonlinear optimization problems for solving,which has become a common solution.Traditional nonlinear optimization algorithms mostly solve the problem in the time-independent scenario,ignoring the time factor.They assume that the problem does not change with time in the computational interval,leading to the deviation between the actual and theoretical solutions.In recent years,algorithms for solving time-dependent nonlinear optimization problems have been extensively investigated and developed due to their applicability,and some achievements have been achieved.However,time-dependent nonlinear optimization algorithms also face some challenges,such as lagging errors,poor anti-interference ability,and inability to be distributed.As an improvement,this thesis conducts research from the following three aspects.Firstly,this thesis investigates and designs a class of neural dynamics(ND)algorithms to handle time-dependent infinity-norm optimization(TDINO)problems constrained by equality and inequality.Specifically,two improved ND algorithms are constructed by employing the simplified sign-bi-power(SBP)and the saturation activation functions(AFs)to accelerate the error convergence rate.Different from traditional algorithms,the proposed algorithms can monitor and control decision variables in realtime and minimize the maximum component of decision variables,which is easy to meet some specific practical application requirements.Subsequently,the results of theoretical analyses,the numerical simulation,and comparisons with existing algorithms exhibit that the proposed ND algorithms are capable of making errors converge in a short time and possesses a high accuracy.In addition,the ND algorithm with saturation AF is applied to robot motion generation to verify its efficacy.Secondly,by extending the variable constraint layer,a nonlinear optimization problem is investigated,which is transformed from a time-dependent system of linear equations(TDSLEs)with double-level constraints,i.e.,variables and their derivatives constraints.Concretely,by introducing a convex objective function,TDSLEs is equivalent to a time-dependent nonlinear optimization problem and unified into a variable derivative level for solving.Considering that the Hessian matrix pseudoinverse operation increases the extra computing burden,a pseudoinverse-free ND(PFND)algorithm is proposed to solve the above time-dependent nonlinear optimization in real-time and efficiently.The corresponding theoretical analysis and proof are given to prove its convergence.Besides,applications to motion generation of single and multiple robots further substantiate that target tracking tasks are effectively completed while guaranteeing that the change within the predetermined physical constraints of joint angles,joint velocities,and joint accelerations,which indicates that it is endowed with potential application prospects.Finally,to further improve the performance of the algorithm,a distributed-allowed noise-resistant ND(DANRND)algorithm is proposed to address the time-dependent quadratic programming(TDQP)problem constrained by inequality.Specifically,an error integral term is embedded in the proposed DANRND algorithm to enhance its noise suppression ability.Then,the global convergence of the DANRND algorithm with and without noise is proved by theoretical analyses and the numerical simulation.Moreover,the qualitative analysis and quantitative comparison with existing algorithms,as well as a multi-robot distributed coordinated application based on k-winner-take-all(k WTA)operation are supplied,which demonstrate the validity and applicability of the DANRND algorithm.