The Interal Dynamic Learning Network For Solving Constrained Time-varying Convex QP Problem

The convex quadratic programming(QP)problem is always the focus of engineering research.Many scientific and engineering problems,such as system analysis and combinatorial optimization,can be expressed as QP problems to solve.In general,QP problem which has been converted to Lagrange form can be solved by using neural network.However,the traditional differential neural network such as the gradient neural network(GNN),zeroing neural network(ZNN),varying-parameter convergent differential neural network(VP-CDNN)can't perform well so that convergence time is too long when facing the large-scale real-time QP problem.Based on this,this paper proposes a novel integral dynamic learning network(IDLN)and varying-parameter integral dynamic learning network(VP-IDLN).The simulation results verify the effectiveness and high-accuracy of the IDLN and VP-IDLN for solving time-varying convex QP problem with linear equality constraints.The main work of this paper includes the following two parts:1.Aiming at the disadvantage that the convengence time of the traditional differential neural network for solving time-varying convex QP problem is too long,a novel integral dynamic learning network(IDLN),based on the error integral equation,is proposed and analysied.Firstly,Lyapunov stability theory proves that IDLN has good global convergence property and flexible control strategy.Secondly,the theoretical analysis verifys that the convergence rate of the network can reach exponential and IDLN has good robustness when the activation function is monotone increasing odd function.Finally,the simulation results prove that when using different activation functions,the IDLN has faster convergence rate and shorter convergence time than the GNN,ZNN and VP-CDNN.2.In order to solve the problem that the convergence rate of IDLN with linear activation function is similar to the traditional differential neural network,a varying-parameter integral dynamic learning network(VP-IDLN)is proposed by adding time-varying exponential design parameter on the basis of IDLN.Firstly,the IDLN can improve the flexible control and adaptive adjustment ability by adding exponential parameter.Secondly,the theoretical analysis proves that the convergence rate of the network can reach super-exponential and VP-IDLN has good robustness when the activation function is monotone increasing odd function.Finally,the simulation results verify that compared with the traditional differential neural network and IDLN,the VP-IDLN has faster convergence rate and shorter convergence time when different activation functions are selected.To sum up,be different from the traditional differential neural networks with long convergence time,the proposed IDLN and VP-IDLN can efficiently solve the time-varying convex QP problem and the convergence time is tens of thousands of traditional differential neural networks.