0Stabilization of Affine Nonlinear Systems with Input Constraints via Generalized Hamilton-Jacobi-Bellman Equation Approach
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- 英文论文题名：0Stabilization of Affine Nonlinear Systems with Input Constraints via Generalized Hamilton-Jacobi-Bellman Equation Approach
- 论文作者：Miao Zha ; Hanlin He
- 英文论文作者：Miao Zha ; Hanlin He ; College of Science ; Naval University of Engineering
- 年：2017
- 作者机构：College of Science,Naval University of Engineering;
- 英文论文关键词：Affine nonlinear systems ; Input saturation ; HJB ; optimal control
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（A）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（A）
- 语种：英文
- 分类号：O175;O231
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：5
- 文件大小：694k
- 原文格式：D
- 会议级别：全国
摘要
This paper deals with the stabilization of affine nonlinear systems with input saturation. We formulate the Hamilton–Jacobi–Bellman(HJB) equation corresponding to constrained control. A recursive algorithm for sequential improvement of the control which converges to the nearly optimal law is proposed by solving for a sequence of cost functions satisfying a sequence of generalized Hamilton–Jacobi–Bellman(GHJB) equations, and may provide a procedure for selecting effective controls for nonlinear systems with input constraints. The approach has been applied to a simple example to show the effectiveness of the proposed controller with input constraints.
This paper deals with the stabilization of affine nonlinear systems with input saturation. We formulate the Hamilton–Jacobi–Bellman(HJB) equation corresponding to constrained control. A recursive algorithm for sequential improvement of the control which converges to the nearly optimal law is proposed by solving for a sequence of cost functions satisfying a sequence of generalized Hamilton–Jacobi–Bellman(GHJB) equations, and may provide a procedure for selecting effective controls for nonlinear systems with input constraints. The approach has been applied to a simple example to show the effectiveness of the proposed controller with input constraints.
This paper deals with the stabilization of affine nonlinear systems with input saturation. We formulate the Hamilton–Jacobi–Bellman(HJB) equation corresponding to constrained control. A recursive algorithm for sequential improvement of the control which converges to the nearly optimal law is proposed by solving for a sequence of cost functions satisfying a sequence of generalized Hamilton–Jacobi–Bellman(GHJB) equations, and may provide a procedure for selecting effective controls for nonlinear systems with input constraints. The approach has been applied to a simple example to show the effectiveness of the proposed controller with input constraints.
引文
[1]C.Chauffaut,F.ois Defay,L.Burlion,H.de Plinval,UAV Obstacle Avoidance Scheme Using an Output to Input Saturation Transformation Technique,International Conference on Unmanned Aircraft Systems(ICUAS):227-234,2016
[2]L.G.Moreira,L.B.Groff,J.M.Gomes da Silva Jr.,S.Tar-bouriech Event-triggered PI control for continuous plants w-ith input saturation American Control Conference(AC-C)4251-4256,2016.
[3]Y.Chitour,M.Harmouche,S.Laghrouche,Lp-stabilization of integrator chains subject to input saturation using Lyapuno-v-based homogeneous design,1-23 2014
[4]X.Wang,A Saberi,A.A.Stoorvogel Stabilization of li-near system with input saturation and unknown constant delays Automatica(49):3632–3640,2013
[5]Yuto Yuasa,Noboru Sakamoto,Yoshio Umemura,Optimal Control Designs for Systems with Input Saturations and Rate Limiters,SICE Annual Conference:2042-2045,2010
[6]T.T.Tran,S.S.Ge,W.He,Adaptive Control for a Robotic Manipulator with Uncertainties and Input Saturations,IEEE Trans.on Mechatronics and Automation:1525-1530,2015
[7]T.T.Tran,S.S Ge,W.He,Adaptive control for an uncertain robotic manipulator with input saturations.Control Theory and Technology,2(14):113–121,2016
[8]Q.V.Dang,L.Vermeiren,A.Dequidt,M.Dambrine,Design of Stabilizing Controller for Uncertain Nonlinear Systems under Input Saturation,American Control Conference(ACC):5974-5979,2015
[9]M.Thiel,D.Schwarzmann,A.M.Annaswamy,M.Schultalbers,T.Jeinsch Improved Performance for Adaptive Control of Systems with Input Saturation.American Control Conference(ACC):6012-6017,2016
[10]S.Baldi,G.Valmorbida,A.Papachristodoulou,Elias B.Kosmatopoulos,Online Policy Iterations for Optimal Control of Input-Saturated Systems.American Control Conference(ACC):5734-5739,2016
[11]Y.Liu,Z.Zhao,F.Guo,Adaptive Lyapunov-based backstepping control for an axially moving system with input saturation,IET Control Theory&Applications:1-34;2016
[12]Z.Chen,Generalized Hamilton–Jacobi–Bellman Formulatio-n-Based Neural Network Control of Affine Nonlinear Discrete-Time Systems,IEEE Trans.on Neural Networks,1(19):90–106,2008.
[13]G.H.Chen,G.M.Chen,A numerical algorithm based on a variational iterative approximation for the dis-crete Hamilton–Jacobi–Bellman(HJB)equation,Computers and Mathematics with Applications,(61):901-907.2011
[14]G.H.Chen,G.M.Chen,Z.H.Dai,Modified domain decomposition method for Hamilton-Jacobi-Be-llman equations,Applied Mathematics and Mechanics(English Edition),31(12):1585–1592,2010.
[15]T.Cheng,Frank L.Lewis,Murad Abu-Khalaf,A neural network solution for fixed-final time optimal control of non-l-inear systems,Science Direct.Automatica,(43):482-490,200-7.
[16]M.Abu-Khalaf,Frank L.Lewis,J.Huang,Neuro dynamic Programming and Zero-Sum Games for Constrained Control Systems,IEEE Trans.on Neural Networks,7(19):1243-1252,2008.
[17]R.W.Beard and G.N.Saridis,“Approximate solutions to the time-invariant Hamilton-Jacobi-Bellman equation,”J.Optim.Theory Appl.3(96):589–626,1998.
[18]Y.S.Yang.Direct robust adaptive fuzzy control(DRAFC)for uncertain nonlinear systems using small gain theorem,Fuzzy Sets and Systems,151(2005)79–97.
[19]W.J.Liu.Nonlinear Robust control study on course and track for underactuated marine surface vessel,Ph.D Thesis,Shandong University,Jinan,China,2012.
[20]L.Zhou.Study of theory and application for control systems subject to actuator saturation,Ph.D Thesis,Harbin Engineering University,Harbin,China,2009.
[21]M.Abu-Khalaf,Frank L.Lewis,Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach,Automatica 41(2005)779-791.
[22]R.Beard,G.Saridis,,&J.Wen.Galerkin approximations of the generalized Hamilton–Jacobi–Bellman equation.Automatica,33(12)(1997),2159-2177.
[2]L.G.Moreira,L.B.Groff,J.M.Gomes da Silva Jr.,S.Tar-bouriech Event-triggered PI control for continuous plants w-ith input saturation American Control Conference(AC-C)4251-4256,2016.
[3]Y.Chitour,M.Harmouche,S.Laghrouche,Lp-stabilization of integrator chains subject to input saturation using Lyapuno-v-based homogeneous design,1-23 2014
[4]X.Wang,A Saberi,A.A.Stoorvogel Stabilization of li-near system with input saturation and unknown constant delays Automatica(49):3632–3640,2013
[5]Yuto Yuasa,Noboru Sakamoto,Yoshio Umemura,Optimal Control Designs for Systems with Input Saturations and Rate Limiters,SICE Annual Conference:2042-2045,2010
[6]T.T.Tran,S.S.Ge,W.He,Adaptive Control for a Robotic Manipulator with Uncertainties and Input Saturations,IEEE Trans.on Mechatronics and Automation:1525-1530,2015
[7]T.T.Tran,S.S Ge,W.He,Adaptive control for an uncertain robotic manipulator with input saturations.Control Theory and Technology,2(14):113–121,2016
[8]Q.V.Dang,L.Vermeiren,A.Dequidt,M.Dambrine,Design of Stabilizing Controller for Uncertain Nonlinear Systems under Input Saturation,American Control Conference(ACC):5974-5979,2015
[9]M.Thiel,D.Schwarzmann,A.M.Annaswamy,M.Schultalbers,T.Jeinsch Improved Performance for Adaptive Control of Systems with Input Saturation.American Control Conference(ACC):6012-6017,2016
[10]S.Baldi,G.Valmorbida,A.Papachristodoulou,Elias B.Kosmatopoulos,Online Policy Iterations for Optimal Control of Input-Saturated Systems.American Control Conference(ACC):5734-5739,2016
[11]Y.Liu,Z.Zhao,F.Guo,Adaptive Lyapunov-based backstepping control for an axially moving system with input saturation,IET Control Theory&Applications:1-34;2016
[12]Z.Chen,Generalized Hamilton–Jacobi–Bellman Formulatio-n-Based Neural Network Control of Affine Nonlinear Discrete-Time Systems,IEEE Trans.on Neural Networks,1(19):90–106,2008.
[13]G.H.Chen,G.M.Chen,A numerical algorithm based on a variational iterative approximation for the dis-crete Hamilton–Jacobi–Bellman(HJB)equation,Computers and Mathematics with Applications,(61):901-907.2011
[14]G.H.Chen,G.M.Chen,Z.H.Dai,Modified domain decomposition method for Hamilton-Jacobi-Be-llman equations,Applied Mathematics and Mechanics(English Edition),31(12):1585–1592,2010.
[15]T.Cheng,Frank L.Lewis,Murad Abu-Khalaf,A neural network solution for fixed-final time optimal control of non-l-inear systems,Science Direct.Automatica,(43):482-490,200-7.
[16]M.Abu-Khalaf,Frank L.Lewis,J.Huang,Neuro dynamic Programming and Zero-Sum Games for Constrained Control Systems,IEEE Trans.on Neural Networks,7(19):1243-1252,2008.
[17]R.W.Beard and G.N.Saridis,“Approximate solutions to the time-invariant Hamilton-Jacobi-Bellman equation,”J.Optim.Theory Appl.3(96):589–626,1998.
[18]Y.S.Yang.Direct robust adaptive fuzzy control(DRAFC)for uncertain nonlinear systems using small gain theorem,Fuzzy Sets and Systems,151(2005)79–97.
[19]W.J.Liu.Nonlinear Robust control study on course and track for underactuated marine surface vessel,Ph.D Thesis,Shandong University,Jinan,China,2012.
[20]L.Zhou.Study of theory and application for control systems subject to actuator saturation,Ph.D Thesis,Harbin Engineering University,Harbin,China,2009.
[21]M.Abu-Khalaf,Frank L.Lewis,Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach,Automatica 41(2005)779-791.
[22]R.Beard,G.Saridis,,&J.Wen.Galerkin approximations of the generalized Hamilton–Jacobi–Bellman equation.Automatica,33(12)(1997),2159-2177.