Implicit Integration with Adjoint Sensitivity Propagation for Optimal Control Problems Involving Differential-Algebraic Equations
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- 英文论文题名：Implicit Integration with Adjoint Sensitivity Propagation for Optimal Control Problems Involving Differential-Algebraic Equations
- 论文作者：Canghua Jiang ; Kun Xie ; Zhiqiang Guo ; Kok Lay Teo
- 英文论文作者：Canghua Jiang ; Kun Xie ; Zhiqiang Guo ; Kok Lay Teo ; School of Electrical Engineering and Automation ; Hefei University of Technology ; Department of Mathematics and Statistics ; Curtin University
- 年：2017
- 作者机构：School of Electrical Engineering and Automation,Hefei University of Technology;Department of Mathematics and Statistics,Curtin University;
- 英文论文关键词：Differential-algebraic equation ; Implicit Runge-Kutta method ; Adjoint sensitivity ; Optimal control ; Delta robot
- 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（B）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（B）
- 语种：英文
- 分类号：O232
- 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：6
- 文件大小：314k
- 原文格式：D
- 会议级别：全国
摘要
For the solution of optimal control problem involving an index-1 differential-algebraic equation, an efficient function evaluation algorithm is proposed in this paper. In the evaluation procedure, the state equation is propagated forwards, then,adjoint sensitivity is propagated backwards. Thus, it is computationally more efficient than forward sensitivity propagation when the number of constraints is less than that of optimization variables. In order to reduce Newton iterations, the adjoint sensitivity is derived utilizing the implicit function theorem, and the integration procedure is accelerated by incorporating a predictor-corrector strategy. This algorithm is integrated with a nonlinear programming solver Ipopt to solve sequentially the point-to-point optimal control for a Delta robot with constrained motor torque. Numerical experiments demonstrate the efficiency of this algorithm.
For the solution of optimal control problem involving an index-1 differential-algebraic equation, an efficient function evaluation algorithm is proposed in this paper. In the evaluation procedure, the state equation is propagated forwards, then,adjoint sensitivity is propagated backwards. Thus, it is computationally more efficient than forward sensitivity propagation when the number of constraints is less than that of optimization variables. In order to reduce Newton iterations, the adjoint sensitivity is derived utilizing the implicit function theorem, and the integration procedure is accelerated by incorporating a predictor-corrector strategy. This algorithm is integrated with a nonlinear programming solver Ipopt to solve sequentially the point-to-point optimal control for a Delta robot with constrained motor torque. Numerical experiments demonstrate the efficiency of this algorithm.
For the solution of optimal control problem involving an index-1 differential-algebraic equation, an efficient function evaluation algorithm is proposed in this paper. In the evaluation procedure, the state equation is propagated forwards, then,adjoint sensitivity is propagated backwards. Thus, it is computationally more efficient than forward sensitivity propagation when the number of constraints is less than that of optimization variables. In order to reduce Newton iterations, the adjoint sensitivity is derived utilizing the implicit function theorem, and the integration procedure is accelerated by incorporating a predictor-corrector strategy. This algorithm is integrated with a nonlinear programming solver Ipopt to solve sequentially the point-to-point optimal control for a Delta robot with constrained motor torque. Numerical experiments demonstrate the efficiency of this algorithm.
引文
[1]K.E.Brenan,S.L.Campbell,and L.R.Petzold,Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations.Philadelphia:SIAM,1996.
[2]L.Petzold,S.Li,Y.Cao,and R.Serban,Sensitivity analysis of differential-algebraic equations and partial differential equations,Computers&Chemical Engineering,30:1553–1559,2006.
[3]R.Quirynen,M.Vukov,and M.Diehl,Auto generation of implicit integrators for embedded NMPC with microsecond sampling times,in Proceedings of 4th IFAC nonlinear model predictive control conference,2012:175–180.
[4]B.Houska,H.J.Ferreau,and M.Diehl,ACADO Toolkit—an open source framework for automatic control and dynamic optimization,Optimal Control Applications and Methods,32(3):298–312,2011.
[5]R.Quirynen,S.Gros,and M.Diehl,Lifted implicit integrators for direct optimal control,in Proceedings of 2015 IEEE54th Annual Conference on Decision and Control,2015:3212–3217.
[6]R.Pytlak,Runge-Kutta based procedure for the optimal control of differential-algebraic equations,Journal of Optimization Theory and Applications,97(3):675–705,1998.
[7]R.Pytlak,Numerical procedure for optimal control of higher index DAEs,Discrete and Continuous Dynamical Systems—Series A(DCDS-A),29(2):647–670,2011.
[8]R.Pytlak and T.Zawadzki,On solving optimal control problems with higher index DAEs,Optimization Methods&Software,29:1139–1162,2014.
[9]L.T.Biegler,Nonlinear Programming:Concepts,Algorithms,and Applications to Chemical Processes.Philadelphia:SIAM,2010.
[10]R.Quirynen,S.Gros,B.Houska,and M.Diehl,Lifted collocation integrators for direct optimal control in ACADO Toolkit,http://www.optimization-online.org/DB_FILE/2016/05/5468.pdf
[11]A.W?chter and L.T.Biegler,On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming,Mathematical Programming,Ser.A,106:25–57,2006.
[12]E.Hairer and G.Wanner,Solving Ordinary Differential Equations:II Stiff and Differential-Algebraic Problems.Berlin:Springer-Verlag,1991.
[13]A.Griewank,Evaluating Derivatives,Principles and Techniques of Algorithmic Differentiation.Philadelphia:SIAM,2000.
[14]A.Codourey,Dynamic modeling of parallel robots for computed-torque control implementation,The International Journal of Robotics Research,17(12):1325–1336,1998.
[15]R.Quirynen,S.Gros,and M.Diehl,Inexact Newton based lifted implicit integrators for fast nonlinear MPC,in Proceedings of 5th IFAC nonlinear model predictive control conference,2015:32–38.
[2]L.Petzold,S.Li,Y.Cao,and R.Serban,Sensitivity analysis of differential-algebraic equations and partial differential equations,Computers&Chemical Engineering,30:1553–1559,2006.
[3]R.Quirynen,M.Vukov,and M.Diehl,Auto generation of implicit integrators for embedded NMPC with microsecond sampling times,in Proceedings of 4th IFAC nonlinear model predictive control conference,2012:175–180.
[4]B.Houska,H.J.Ferreau,and M.Diehl,ACADO Toolkit—an open source framework for automatic control and dynamic optimization,Optimal Control Applications and Methods,32(3):298–312,2011.
[5]R.Quirynen,S.Gros,and M.Diehl,Lifted implicit integrators for direct optimal control,in Proceedings of 2015 IEEE54th Annual Conference on Decision and Control,2015:3212–3217.
[6]R.Pytlak,Runge-Kutta based procedure for the optimal control of differential-algebraic equations,Journal of Optimization Theory and Applications,97(3):675–705,1998.
[7]R.Pytlak,Numerical procedure for optimal control of higher index DAEs,Discrete and Continuous Dynamical Systems—Series A(DCDS-A),29(2):647–670,2011.
[8]R.Pytlak and T.Zawadzki,On solving optimal control problems with higher index DAEs,Optimization Methods&Software,29:1139–1162,2014.
[9]L.T.Biegler,Nonlinear Programming:Concepts,Algorithms,and Applications to Chemical Processes.Philadelphia:SIAM,2010.
[10]R.Quirynen,S.Gros,B.Houska,and M.Diehl,Lifted collocation integrators for direct optimal control in ACADO Toolkit,http://www.optimization-online.org/DB_FILE/2016/05/5468.pdf
[11]A.W?chter and L.T.Biegler,On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming,Mathematical Programming,Ser.A,106:25–57,2006.
[12]E.Hairer and G.Wanner,Solving Ordinary Differential Equations:II Stiff and Differential-Algebraic Problems.Berlin:Springer-Verlag,1991.
[13]A.Griewank,Evaluating Derivatives,Principles and Techniques of Algorithmic Differentiation.Philadelphia:SIAM,2000.
[14]A.Codourey,Dynamic modeling of parallel robots for computed-torque control implementation,The International Journal of Robotics Research,17(12):1325–1336,1998.
[15]R.Quirynen,S.Gros,and M.Diehl,Inexact Newton based lifted implicit integrators for fast nonlinear MPC,in Proceedings of 5th IFAC nonlinear model predictive control conference,2015:32–38.