Sensitivity-based adaptive mesh refinement collocation method for dynamic optimization of chemical and biochemical processes

Collocation on finite element (CFE) is an effective simultaneous method of dynamic optimization to increase the profitability or productivity of industrial process. The approach needs to select an optimal mesh of time interval to balance the computational cost with desired solution. A new CFE approach with non-uniform refinement procedure based on the sensitivity analysis for dynamic optimization problems is, therefore, proposed, where a subinterval is further refined if the obtained control parameters have significant effect on the performance index. To improve the efficiency, the sensitivities of state parameters with respect to control parameters are derived from the solution of the discretized dynamic system. The proposed method is illustrated by testing two classic dynamic optimization problems from chemical and biochemical engineering. The detailed comparisons among the proposed method, the CFE with uniform mesh, and other reported methods are also carried out. The research results reveal the effectiveness of the proposed approach.

[1]  L. Biegler.  An overview of simultaneous strategies for dynamic optimization , 2007 .

[2]  Filip Logist,et al.  Multi-objective optimal control of dynamic bioprocesses using ACADO Toolkit , 2013, Bioprocess and Biosystems Engineering.

[3]  M. Dehghan,et al.  Distributed optimal control of the viscous Burgers equation via a Legendre pseudo‐spectral approach , 2016 .

[4]  M. Shamsi,et al.  Gauss pseudospectral and continuation methods for solving two-point boundary value problems in optimal control theory , 2015 .

[5]  Anil V. Rao,et al.  Algorithm 902: GPOPS, A MATLAB software for solving multiple-phase optimal control problems using the gauss pseudospectral method , 2010, TOMS.

[6]  Junfeng Li,et al.  Pseudospectral Methods for Trajectory Optimization with Interior Point Constraints: Verification and Applications , 2013, IEEE Transactions on Aerospace and Electronic Systems.

[7]  William W. Hager,et al.  Pseudospectral methods for solving infinite-horizon optimal control problems , 2011, Autom..

[8]  Anil V. Rao,et al.  Direct Trajectory Optimization Using a Variable Low-Order Adaptive Pseudospectral Method , 2011 .

[9]  K. Teo,et al.  The control parameterization enhancing transform for constrained optimal control problems , 1999, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[10]  Eva Balsa-Canto,et al.  Dynamic optimization of bioprocesses: efficient and robust numerical strategies. , 2005, Journal of biotechnology.

[11]  Stephen L. Campbell,et al.  Solving optimal control problems with control delays using direct transcription , 2016 .

[12]  Nasser Sadati,et al.  Hierarchical optimal control of large-scale nonlinear chemical processes. , 2009, ISA transactions.

[13]  P. Tsiotras,et al.  Mesh Refinement Using Density Function for Solving Optimal Control Problems , 2009 .

[14]  Günter Wozny,et al.  An efficient sparse approach to sensitivity generation for large-scale dynamic optimization , 2011, Comput. Chem. Eng..

[15]  Liang Ma,et al.  An effective pseudospectral method for constraint dynamic optimisation problems with characteristic times , 2018, Int. J. Control.

[16]  K. Teo,et al.  Numerical solution of an optimal control problem with variable time points in the objective function , 2002, The ANZIAM Journal.

[17]  J. Betts.  Survey of Numerical Methods for Trajectory Optimization , 1998 .

[18]  P. Tsiotras,et al.  Trajectory Optimization Using Multiresolution Techniques , 2008 .

[19]  Xinggao Liu,et al.  An effective simultaneous approach with variable time nodes for dynamic optimization problems , 2017 .

[20]  Xinggao Liu,et al.  An effective pseudospectral optimization approach with sparse variable time nodes for maximum production of chemical engineering problems , 2017 .

[21]  William W. Hager,et al.  Adaptive mesh refinement method for optimal control using nonsmoothness detection and mesh size reduction , 2015, J. Frankl. Inst..

[22]  Xinggao Liu,et al.  Optimal control problems with incomplete and different integral time domains in the objective and constraints , 2014 .

[23]  Ping Wang,et al.  The Combination of Adaptive Pseudospectral Method and Structure Detection Procedure for Solving Dynamic Optimization Problems with Discontinuous Control Profiles , 2014 .

[24]  William W. Hager,et al.  A unified framework for the numerical solution of optimal control problems using pseudospectral methods , 2010, Autom..

[25]  Debasis Sarkar,et al.  Genetic algorithms with filters for optimal control problems in fed-batch bioreactors , 2004, Bioprocess and biosystems engineering.

[26]  Xinggao Liu,et al.  An iterative multi-objective particle swarm optimization-based control vector parameterization for state constrained chemical and biochemical engineering problems , 2015 .

[27]  Ping Liu,et al.  Novel non-uniform adaptive grid refinement control parameterization approach for biochemical processes optimization , 2016 .

[28]  D. Himmelblau,et al.  Optimization of Chemical Processes , 1987 .

[29]  Wolfgang Marquardt,et al.  Dynamic optimization using adaptive control vector parameterization , 2005, Comput. Chem. Eng..

[30]  Feng Qian,et al.  Dynamic optimization of chemical engineering problems using a control vector parameterization method with an iterative genetic algorithm , 2013 .

[31]  R. Luus.  Application of dynamic programming to high-dimensional non-linear optimal control problems , 1990 .

[32]  Geoffrey Todd Huntington,et al.  Advancement and analysis of Gauss pseudospectral transcription for optimal control problems , 2007 .

[33]  Pu Li,et al.  An Analytical Hessian and Parallel-Computing Approach for Efficient Dynamic Optimization Based on Control-Variable Correlation Analysis , 2015 .

[34]  Daim-Yuang Sun,et al.  Using Dynamic Optimization Technique to Study the Operation of Batch Reactors , 2008 .

[35]  J. E. Cuthrell,et al.  On the optimization of differential-algebraic process systems , 1987 .

[36]  R. Jaczson.  Optimal use of mixed catalysts for two successive chemical reactions , 1968 .

[37]  Zhihua Xiong,et al.  Optimal Control of Fed-Batch Processes Based on Multiple Neural Networks , 2005, Applied Intelligence.

[38]  Liwei Wang,et al.  A new sensitivity-based adaptive control vector parameterization approach for dynamic optimization of bioprocesses , 2016, Bioprocess and Biosystems Engineering.

[39]  Vassilios S. Vassiliadis,et al.  Inequality path constraints in optimal control: a finite iteration ε-convergent scheme based on pointwise discretization , 2005 .

[40]  R. B. Martin,et al.  Optimal control drug scheduling of cancer chemotherapy , 1992, Autom..

[41]  Debasis Sarkar,et al.  ANNSA: a hybrid artificial neural network/simulated annealing algorithm for optimal control problems , 2003 .

[42]  Remko M. Boom,et al.  Control vector parameterization with sensitivity based refinement applied to baking optimization , 2008 .

[43]  Helen H. Lou,et al.  A probability distribution estimation based method for dynamic optimization , 2007 .