A Toolkit for Efficient Computation of Sensitivities in Approximate Robust Optimal Control Problems

Abstract Efficient solution approaches for optimal control problems where the dynamics are described by uncertain differential equations are discussed in the present paper. Problems with uncertainties can be addressed by the robust worst-case formulation. In order to numerically solve the robust counterpart for the optimal control problem several approximation techniques can be employed. In this paper we use an approach based on linearization and solution of Lyapunov differential equations. We exploit the structure of the Lyapunov equation in the optimal control context providing an efficient numerical implementation. The capabilities and computational times of the new approach are demonstrated on two (bio)chemical examples.

[1]  T. Başar.  Feedback and Optimal Sensitivity: Model Reference Transformations, Multiplicative Seminorms, and Approximate Inverses , 2001 .

[2]  R. Kálmán.  LYAPUNOV FUNCTIONS FOR THE PROBLEM OF LUR'E IN AUTOMATIC CONTROL. , 1963, Proceedings of the National Academy of Sciences of the United States of America.

[3]  昌之 佐藤.  The 7th IFAC Symposium on Robust Control Designに参加して(国際会議の報告) , 2012 .

[4]  F. Schweppe,et al.  Control of linear dynamic systems with set constrained disturbances , 1971 .

[5]  Richard D. Braatz,et al.  Open-loop and closed-loop robust optimal control of batch processes using distributional and worst-case analysis , 2004 .

[6]  Fred C. Schweppe,et al.  Uncertain dynamic systems , 1973 .

[7]  Moritz Diehl,et al.  An approximation technique for robust nonlinear optimization , 2006, Math. Program..

[8]  Mi-Ching Tsai,et al.  Robust and Optimal Control , 2014 .

[9]  S. Bittanti,et al.  The Periodic Riccati Equation , 1991 .

[10]  J. Impe,et al.  Efficient deterministic multiple objective optimal control of (bio)chemical processes , 2009 .

[11]  K. R. Westerterp,et al.  Modeling of heat transfer in wall-cooled tubular reactors , 1999 .

[12]  Johannes P. Schlöder,et al.  Combined NMPC and MHE for a copolymerization process , 2006 .

[13]  Filip Logist,et al.  Multi-objective optimal control of chemical processes using ACADO toolkit , 2012, Comput. Chem. Eng..

[14]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[15]  Filip Logist,et al.  Fast Pareto set generation for nonlinear optimal control problems with multiple objectives , 2010 .

[16]  Z. Nagy,et al.  Distributional uncertainty analysis using power series and polynomial chaos expansions , 2007 .

[17]  Jan Van Impe,et al.  Robust multi-objective optimal control of uncertain (bio)chemical processes , 2011 .

[18]  Ilse Smets,et al.  Optimal design of dispersive tubular reactors at steady-state using optimal control theory , 2009 .

[19]  H. Bock,et al.  A Multiple Shooting Algorithm for Direct Solution of Optimal Control Problems , 1984 .

[20]  Moritz Diehl,et al.  ACADO toolkit—An open‐source framework for automatic control and dynamic optimization , 2011 .

[21]  Moritz Diehl,et al.  Robust nonlinear optimal control of dynamic systems with affine uncertainties , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.