基于FPAA模拟神经网络的快速预测控制算法
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摘要
针对模型预测控制(model predictive control,MPC)优化求解中占用资源较多、实时性较低且实现相对复杂的问题,该文提出了一种基于现场可编程模拟阵列(field programmable analog array,FPAA)模拟神经网络的快速模型预测控制算法。通过FPAA模拟电路来实现基于连续神经网络的二次规划求解,有效规避了离散神经网络的收敛性问题,具有求解速度快、占用资源小、简单易实现的特点;通过平移变换和尺度变换方法,解决FPAA模拟电路的信号限制。最后该文给出了FPAA模拟神经网络预测控制软硬件设计方案并通过实验验证了该算法的有效性。
A fast predictive control algorithm was developed for simpler,faster MPC optimization based on an FPAA analog neural network. An FPAA analog circuit provides the quadratic programming using a continuous neural network which avoids the convergence problem of discrete neural networks in a fast,simple and flexible algorithm that uses less computational resources than previous methods.The signal constraint of the FPAA analog circuit is solved by translation and scaling.The software and hardware design of the FPAA analog neural network predictive control is presented and verified in tests that show that the algorithm is effective.
A fast predictive control algorithm was developed for simpler,faster MPC optimization based on an FPAA analog neural network. An FPAA analog circuit provides the quadratic programming using a continuous neural network which avoids the convergence problem of discrete neural networks in a fast,simple and flexible algorithm that uses less computational resources than previous methods.The signal constraint of the FPAA analog circuit is solved by translation and scaling.The software and hardware design of the FPAA analog neural network predictive control is presented and verified in tests that show that the algorithm is effective.
引文
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[6]HU X L,ZHANG B.A new recurrent neural network for solving convex quadratic programming problems with an application to the k-winners-take-all problem[J].IEEE Transactions on Neural Networks,2009,20(4):654-664.
[7]XIA Y S,FENG G,WANG J.A recurrent neural network with exponential convergence for solving convex quadratic program and related linear piecewise equations[J].Neural Networks,2004,17(7):1003-1015.
[8]ZHANG Y N,WANG J.A dual neural network for convex quadratic programming subject to linear equality and inequality constraints[J].Physics Letters A,2002,298(4):271-278.
[9]LIU S B,WANG J.A simplified dual neural network for quadratic programming with its KWTA application[J].IEEE Transactions on Neural Networks,2006,17(6):1500-1510.
[10]DENNIS J B.Mathematical programming and electrical networks[D].Cambridge,USA:Massachusetts Institute of Technology,1959.
[11]CHUA L,LIN G N.Nonlinear programming without computation[J].IEEE Transactions on Circuits and Systems,1984,31(2):182-188.
[12]VICHIK S,BORRELLI F.Solving linear and quadratic programs with an analog circuit[J].Computers&Chemical Engineering,2014,70:160-171.
[13]TANK D W,HOPFIELD J J.Simple“neural”optimization networks:An A/D converter,signal decision circuit,and a linear programming circuit[J].IEEE Transactions on Circuits and Systems,1986,33(5):533-541.
[14]VICHIK S,ARCAK M,BORRELLI F.Stability of an analog optimization circuit for quadratic programming[J].Systems&Control Letters,2016,88:68-74.
[15]JIAN L,LI D W,XI Y G.Implementation of dynamic matrix control on FPGA[C]//Proceedings of the 29th Chinese Control Conference(CCC).Beijing,China:IEEE,2010:5970-5974.
[2]KENNEDY M P,CHUA L O.Neural networks for nonlinear programming[J].IEEE Transactions on Circuits and Systems,1988,35(5):554-562.
[3]RODRIGUEZ-VAZQUEZ A,DOMINGUEZ-CASTRO R,RUEDA A,et al.Nonlinear switched capacitor“neural”networks for optimization problems[J].IEEE Transactions on Circuits and Systems,1990,37(3):384-398.
[4]ZHANG S,CONSTANTINIDES A G.Lagrange programming neural networks[J].IEEE Transactions on Circuits and Systems II:Analog and Digital Signal Processing,1992,39(7):441-452.
[5]HAM F M,KOSTANIC I.Principles of neurocomputing for science and engineering[M].New York,USA:McGraw-Hill Higher Education,2000.
[6]HU X L,ZHANG B.A new recurrent neural network for solving convex quadratic programming problems with an application to the k-winners-take-all problem[J].IEEE Transactions on Neural Networks,2009,20(4):654-664.
[7]XIA Y S,FENG G,WANG J.A recurrent neural network with exponential convergence for solving convex quadratic program and related linear piecewise equations[J].Neural Networks,2004,17(7):1003-1015.
[8]ZHANG Y N,WANG J.A dual neural network for convex quadratic programming subject to linear equality and inequality constraints[J].Physics Letters A,2002,298(4):271-278.
[9]LIU S B,WANG J.A simplified dual neural network for quadratic programming with its KWTA application[J].IEEE Transactions on Neural Networks,2006,17(6):1500-1510.
[10]DENNIS J B.Mathematical programming and electrical networks[D].Cambridge,USA:Massachusetts Institute of Technology,1959.
[11]CHUA L,LIN G N.Nonlinear programming without computation[J].IEEE Transactions on Circuits and Systems,1984,31(2):182-188.
[12]VICHIK S,BORRELLI F.Solving linear and quadratic programs with an analog circuit[J].Computers&Chemical Engineering,2014,70:160-171.
[13]TANK D W,HOPFIELD J J.Simple“neural”optimization networks:An A/D converter,signal decision circuit,and a linear programming circuit[J].IEEE Transactions on Circuits and Systems,1986,33(5):533-541.
[14]VICHIK S,ARCAK M,BORRELLI F.Stability of an analog optimization circuit for quadratic programming[J].Systems&Control Letters,2016,88:68-74.
[15]JIAN L,LI D W,XI Y G.Implementation of dynamic matrix control on FPGA[C]//Proceedings of the 29th Chinese Control Conference(CCC).Beijing,China:IEEE,2010:5970-5974.