Direct heuristic dynamic programming based on an improved PID neural network

In this paper, an improved PID-neural network （IPIDNN） structure is proposed and applied to the critic and action networks of direct heuristic dynamic programming （DHDP）. As one of online learning algorithm of approximate dynamic programming （ADP）, DHDP has demonstrated its applicability to large st...

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Vydáno v:	Journal of control theory and applications Ročník 10; číslo 4; s. 497 - 503
Hlavní autoři:	Sun, Jian, Liu, Feng, Si, Jennie, Mei, Shengwei
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Heidelberg South China University of Technology and Academy of Mathematics and Systems Science, CAS 01.11.2012 Department of Electrical Engineering, Tsinghua University, Beijing 100084, China%Department of Electrical Engineering, Arizona State University, Tempe AZ 85287-5706, USA
Témata:	Algorithms Brief Paper Complexity Computational Intelligence Control Control and Systems Theory Control systems Dynamic programming Engineering Heuristic Learning Mathematical analysis Mechatronics Networks Neural networks Optimization PID神经网络 Robotics Systems Theory 启发式动态规划在线学习算法基础最优性方程状态反馈系统验证输出反馈控制 Approximate dynamic programming (ADP) Direct heuristic dynamic programming (DHDP) Improved PID neural network (IPIDNN)
ISSN:	1672-6340, 1993-0623
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Abstract	In this paper, an improved PID-neural network （IPIDNN） structure is proposed and applied to the critic and action networks of direct heuristic dynamic programming （DHDP）. As one of online learning algorithm of approximate dynamic programming （ADP）, DHDP has demonstrated its applicability to large state and control problems. Theoretically, the DHDP algorithm requires access to full state feedback in order to obtain solutions to the Bellman optimality equation. Unfortunately, it is not always possible to access all the states in a real system. This paper proposes a solution by suggesting an IPIDNN configuration to construct the critic and action networks to achieve an output feedback control. Since this structure can estimate the integrals and derivatives of measurable outputs, more system states are utilized and thus better control performance are expected. Compared with traditional PIDNN, this configuration is flexible and easy to expand. Based on this structure, a gradient decent algorithm for this IPIDNN-based DHDP is presented. Convergence issues are addressed within a single learning time step and for the entire learning process. Some important insights are provided to guide the implementation of the algorithm. The proposed learning controller has been applied to a cart-pole system to validate the effectiveness of the structure and the algorithm.
AbstractList	In this paper, an improved PID-neural network （IPIDNN） structure is proposed and applied to the critic and action networks of direct heuristic dynamic programming （DHDP）. As one of online learning algorithm of approximate dynamic programming （ADP）, DHDP has demonstrated its applicability to large state and control problems. Theoretically, the DHDP algorithm requires access to full state feedback in order to obtain solutions to the Bellman optimality equation. Unfortunately, it is not always possible to access all the states in a real system. This paper proposes a solution by suggesting an IPIDNN configuration to construct the critic and action networks to achieve an output feedback control. Since this structure can estimate the integrals and derivatives of measurable outputs, more system states are utilized and thus better control performance are expected. Compared with traditional PIDNN, this configuration is flexible and easy to expand. Based on this structure, a gradient decent algorithm for this IPIDNN-based DHDP is presented. Convergence issues are addressed within a single learning time step and for the entire learning process. Some important insights are provided to guide the implementation of the algorithm. The proposed learning controller has been applied to a cart-pole system to validate the effectiveness of the structure and the algorithm. In this paper, an improved PID-neural network (IPIDNN) structure is proposed and applied to the critic and action networks of direct heuristic dynamic programming (DHDP). As one of online learning algorithm of approximate dynamic programming (ADP), DHDP has demonstrated its applicability to large state and control problems. Theoretically, the DHDP algorithm requires access to full state feedback in order to obtain solutions to the Bellman optimality equation. Unfortunately, it is not always possible to access all the states in a real system. This paper proposes a solution by suggesting an IPIDNN configuration to construct the critic and action networks to achieve an output feedback control. Since this structure can estimate the integrals and derivatives of measurable outputs, more system states are utilized and thus better control performance are expected. Compared with traditional PIDNN, this configuration is flexible and easy to expand. Based on this structure, a gradient decent algorithm for this IPIDNN-based DHDP is presented. Convergence issues are addressed within a single learning time step and for the entire learning process. Some important insights are provided to guide the implementation of the algorithm. The proposed learning controller has been applied to a cart-pole system to validate the effectiveness of the structure and the algorithm. TL361; In this paper,an improved PID-neural network (IPIDNN) structure is proposed and applied to the critic and action networks of direct heuristic dynamic programming (DHDP).As one of online learning algorithm of approximate dynamic programming (ADP),DHDP has demonstrated its applicability to large state and control problems.Theoretically,the DHDP algorithm requires access to full state feedback in order to obtain solutions to the Bellman optimality equation.Unfortunately,it is not always possible to access all the states in a real system.This paper proposes a solution by suggesting an IPIDNN configuration to construct the critic and action networks to achieve an output feedback control.Since this structure can estimate the integrals and derivatives of measurable outputs,more system states are utihzed and thus better control performance are expected.Compared with traditional PIDNN,this configuration is flexible and easy to expand.Based on this structure,a gradient decent algorithm for this IPIDNN-based DHDP is presented.Convergence issues are addressed within a single learning time step and for the entire learning process.Some important insights are provided to guide the implementation of the algorithm.The proposed learning controller has been applied to a cart-pole system to validate the effectiveness of the structure and the algorithm.
Author	Jian SUN Feng LIU Jennie SI Shengwei MEI
AuthorAffiliation	Department of Electrical Engineering, Tsinghua University, Beijing 100084, China Department of Electrical Engineering, Arizona State University, Tempe AZ 85287-5706, USA
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Notes	Approximate dynamic programming （ADP）; Direct heuristic dynamic programming （DHDP）; ImprovedPID neural network （IPIDNN） In this paper, an improved PID-neural network （IPIDNN） structure is proposed and applied to the critic and action networks of direct heuristic dynamic programming （DHDP）. As one of online learning algorithm of approximate dynamic programming （ADP）, DHDP has demonstrated its applicability to large state and control problems. Theoretically, the DHDP algorithm requires access to full state feedback in order to obtain solutions to the Bellman optimality equation. Unfortunately, it is not always possible to access all the states in a real system. This paper proposes a solution by suggesting an IPIDNN configuration to construct the critic and action networks to achieve an output feedback control. Since this structure can estimate the integrals and derivatives of measurable outputs, more system states are utilized and thus better control performance are expected. Compared with traditional PIDNN, this configuration is flexible and easy to expand. Based on this structure, a gradient decent algorithm for this IPIDNN-based DHDP is presented. Convergence issues are addressed within a single learning time step and for the entire learning process. Some important insights are provided to guide the implementation of the algorithm. The proposed learning controller has been applied to a cart-pole system to validate the effectiveness of the structure and the algorithm. 44-1600/TP ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
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References_xml	– reference: YangL.Understanding and analyzing approximate dynamic programming with gradient-based framework and direct heuristic dynamic programmingA Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy2008Tempe, USAArizona State University6293 – reference: FerrariS.SteckJ. E.ChandramohanR.Adaptive feedback control by constrained approximate dynamic programmingIEEE Transactions on System, Man and Cybernetics200838498298710.1109/TSMCB.2008.924140 – reference: KirkD.Optimal Control Theory: An Introduction1970Englewood Cliffs, NJPrentice-Hall – reference: H. Shu, Y. Pi. PID neural networks for time-delay systems. Proceedings of the 7th International Symposium on Process Systems Engineering. Keystone, Colorado, USA, 2000: 859–862. – reference: RobbinsH.MonroS.LA stochastic approximation methodThe Annals of Mathematical Statistics1951223400407426680054.0590110.1214/aoms/1177729586 – reference: LewisF. L.VrabieD.Reinforcement learning and adaptive dynamic programming for feedback controlIEEE Transactions on Circuits and Systems Magazine2009933250283400110.1109/MCAS.2009.933854 – reference: SiJ.WangY.Reinforcement learning and adaptive dynamic programming for feedback controlIEEE Transactions on Neural Networks2001122264276185932110.1109/72.914523 – reference: BellmanR.DreyfusS.Applied Dynamic Programming1962Princeton, N JPrinceton University Press0106.34901 – reference: BorgersT.SarinR.Learning through reinforcement and replicator dynamicsEconomic Theory1997771117148429110.1006/jeth.1997.2319 – reference: EnnsR.SiJ.Apache helicopter stabilization using neuro-dynamic programmingAIAA Journal of Guidance, Control, and Dynamics2002251192510.2514/2.4870 – reference: ZhangH.WeiQ.LuoY.A novel infinite-time optimal tracking control scheme for a class of discrete-time nonlinear systems via the greedy HDP iteration algorithmIEEE Transactions on System, Man and Cybernetics200838493794210.1109/TSMCB.2008.920269 – reference: SiJ.BartoA. G.PowellW. B.Handbook of Learning and Approximate Dynamic ProgrammingScaling up to the Real World2004New YorkJohn Wiley & Sons10.1109/9780470544785 – reference: BalakrishnanS. N.DingJ.LewisF. L.Issues on stability of adp feedback controllers for dynamical systemsIEEE Transactions on Systems, Man and Cybernetics200838491391710.1109/TSMCB.2008.926599 – reference: ShuH.Study on the neural PID network cascade control systemAutomation & Instrumentation19975157 – reference: ShuH.PID neural network control for complex systemsProceedings of the International Conference on Computational Intelligence for Modeling, Control and Automation1999AmsterdamIOS Press166171 – reference: HuangY.Functional Analysis: An Introduction2009BeijingScience Press – reference: C. Lu, J. Si, X. Xie. Direct heuristic dynamic programming method for power system stability enhancement. IEEE Transactions on System, Man and Cybernetics, Part B, 2008 (8): 1008–1013. – reference: WangF.ZhangH.LiuD.Adaptive dynamic programming: an introductionIEEE Transactions on Computational Intelligence Magazine200942394710.1109/MCI.2009.932261 – reference: WerbosP.Advanced forecasting methods for global crisis warning and models of intelligenceGeneral System Yearbook19772222538 – reference: EnnsR.SiJ.Helicopter trimming and tracking control using direct neural dynamic programmingIEEE Transactions on Neural Networks200314492993910.1109/TNN.2003.813839 – reference: BartoA. G.SuttonR. S.AndersonC. W.Neuron like adaptive elements that can solve difficult learning control problemsIEEE Transactions on System, Man and Cybernetics198313583484710.1109/TSMC.1983.6313077 – reference: DaltonJ.BalakrishnanS. N.Learning through reinforcement and replicator dynamics: A neighboring optimal adaptive critic for missile guidanceMathmatics Computer Modeling199623117518810.1016/0895-7177(95)00226-X – volume: 22 start-page: 25 issue: 2 year: 1977 ident: 112_CR4 publication-title: General System Yearbook – volume: 4 start-page: 39 issue: 2 year: 2009 ident: 112_CR13 publication-title: IEEE Transactions on Computational Intelligence Magazine doi: 10.1109/MCI.2009.932261 – volume: 14 start-page: 929 issue: 4 year: 2003 ident: 112_CR11 publication-title: IEEE Transactions on Neural Networks doi: 10.1109/TNN.2003.813839 – volume: 22 start-page: 400 issue: 3 year: 1951 ident: 112_CR21 publication-title: The Annals of Mathematical Statistics doi: 10.1214/aoms/1177729586 – volume: 9 start-page: 32 issue: 3 year: 2009 ident: 112_CR8 publication-title: IEEE Transactions on Circuits and Systems Magazine doi: 10.1109/MCAS.2009.933854 – volume-title: Functional Analysis: An Introduction year: 2009 ident: 112_CR20 – ident: 112_CR18 doi: 10.1016/S0098-1354(00)00340-9 – volume: 13 start-page: 834 issue: 5 year: 1983 ident: 112_CR22 publication-title: IEEE Transactions on System, Man and Cybernetics doi: 10.1109/TSMC.1983.6313077 – start-page: 62 volume-title: A Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy year: 2008 ident: 112_CR19 – volume: 5 start-page: 5 issue: 1 year: 1997 ident: 112_CR16 publication-title: Automation & Instrumentation – volume-title: Applied Dynamic Programming year: 1962 ident: 112_CR1 doi: 10.1515/9781400874651 – volume: 25 start-page: 19 issue: 1 year: 2002 ident: 112_CR10 publication-title: AIAA Journal of Guidance, Control, and Dynamics doi: 10.2514/2.4870 – volume: 38 start-page: 913 issue: 4 year: 2008 ident: 112_CR7 publication-title: IEEE Transactions on Systems, Man and Cybernetics doi: 10.1109/TSMCB.2008.926599 – ident: 112_CR12 – volume: 77 start-page: 1 issue: 1 year: 1997 ident: 112_CR2 publication-title: Economic Theory doi: 10.1006/jeth.1997.2319 – volume: 12 start-page: 264 issue: 2 year: 2001 ident: 112_CR9 publication-title: IEEE Transactions on Neural Networks doi: 10.1109/72.914523 – volume-title: Optimal Control Theory: An Introduction year: 1970 ident: 112_CR5 – volume-title: Handbook of Learning and Approximate Dynamic ProgrammingScaling up to the Real World year: 2004 ident: 112_CR6 doi: 10.1109/9780470544785 – volume: 38 start-page: 982 issue: 4 year: 2008 ident: 112_CR15 publication-title: IEEE Transactions on System, Man and Cybernetics doi: 10.1109/TSMCB.2008.924140 – start-page: 166 volume-title: Proceedings of the International Conference on Computational Intelligence for Modeling, Control and Automation year: 1999 ident: 112_CR17 – volume: 38 start-page: 937 issue: 4 year: 2008 ident: 112_CR14 publication-title: IEEE Transactions on System, Man and Cybernetics doi: 10.1109/TSMCB.2008.920269 – volume: 23 start-page: 175 issue: 1 year: 1996 ident: 112_CR3 publication-title: Mathmatics Computer Modeling doi: 10.1016/0895-7177(95)00226-X
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SubjectTerms	Algorithms Brief Paper Complexity Computational Intelligence Control Control and Systems Theory Control systems Dynamic programming Engineering Heuristic Learning Mathematical analysis Mechatronics Networks Neural networks Optimization PID神经网络 Robotics Systems Theory 启发式动态规划在线学习算法基础最优性方程状态反馈系统验证输出反馈控制
Title	Direct heuristic dynamic programming based on an improved PID neural network
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