Summary: This paper describes the ANSI C/C++ computer program dsoa, which implements an algorithm for the approximate solution of dynamics system optimization problems. The algorithm is a direct method that can be applied to the optimization of dynamic systems described by index-1 differential-algebraic equations (DAEs). The types of problems considered include optimal control problems and parameter identification problems. The numerical techniques are employed to transform the dynamic system optimization problem into a parameter optimization problem by: (i) parameterizing the control input as piecewise constant on a fixed mesh, and (ii) approximating the DAEs using a linearly implicit Runge-Kutta method. The resultant nonlinear programming (NLP) problem is solved via a sequential quadratic programming technique. The program dsoa is evaluated using 83 nontrivial optimal control problems that have appeared in the literature. Here we compare the performance of the algorithm using two different NLP problem solvers, and two techniques for computing the derivatives of the functions that define the problem.

##### MSC:

90-08 | Computational methods for problems pertaining to operations research and mathematical programming |

49M37 | Numerical methods based on nonlinear programming |

65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |

90C30 | Nonlinear programming |

##### Keywords:

dynamic system optimization; nonlinear optimal control; parameter identification; nonlinear programming
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\textit{B. C. Fabien}, Optim. Control Appl. Methods 31, No. 3, 231--247 (2010; Zbl 1200.90010)

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##### References:

[1] | Hairer, Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems (1996) · Zbl 1192.65097 |

[2] | Agrawal, Optimization of Dynamic Systems (1999) |

[3] | Betts, Survey of numerical methods for trajectory optimization, AIAA Journal Guidance, Control, and Dynamics 21 pp 193– (1998) · Zbl 1158.49303 |

[4] | Bhattacharya R. OPTRAGEN: a MATLAB toolbox for optimal trajectory generation. Forty-Fifth IEEE Conference on Decision and Control, San Diego, CA, U.S.A., 2006; 6832-6836. |

[5] | Bauer, Numerical methods for optimum experimental design in DAE systems, Journal of Computational and Applied mathematics 120 pp 1– (2000) · Zbl 0998.65083 |

[6] | Cuthrell, On the optimization of differential-algebraic process systems, AIChE Journal 33 pp 1257– (1987) |

[7] | Gerdts, Direct shooting method for the numerical solution of higher-index DAE optimal control problems, Journal of Optimization Theory and Applications 117 pp 267– (2003) · Zbl 1033.65046 |

[8] | Schulz V. Reduced SQP methods for large-scale optimal control problems in DAE with application to path planning problems for satellite mounted robots. Ph.D. Thesis, University of Heidelberg, 1996. · Zbl 0848.49021 |

[9] | Serban, COOPTA software package for optimal control of large-scale differential-algebraic equation systems, Mathematics and Computers in Simulation 56 pp 187– (2001) |

[10] | Fabien, Direct optimization of dynamic systems described by differential-algebraic equations, Optimal Control Applications and Methods 29 pp 445– (2008) |

[11] | Fabien, Parameter optimization using the L exact penalty function and strictly convex quadratic programming problems, Applied Mathematics and Computation 198 pp 834– (2008) · Zbl 1138.65045 |

[12] | Fabien, Implementation of a robust SQP algorithm, Optimization Methods and Software 23 pp 827– (2008) |

[13] | Stengel, Optimal Control and Estimation (1994) |

[14] | Bock HG, Plitt KJ. A multiple shooting algorithm for direct solution of optimal control problems. IFAC 9-th Triennial World Congress, Budapest, Hungary, 1984; 1603-1608. |

[15] | Goh, MISER: a FORTRAN program for solving optimal control problems, Advances in Engineering Software 10 pp 319– (1988) |

[16] | Kraft, Algorithm 733: TOMP-Fortran modules for optimal control calculations, ACM Transactions on Mathematical Software 20 pp 262– (1994) · Zbl 0888.65079 |

[17] | Teo, A Unified Computational Approach to Optimal Control Problems (1991) · Zbl 0747.49005 |

[18] | Steinebach, Adaptive Method of Lines (2001) |

[19] | Lang, ROS3P-An accurate third-order Rosenbrock solver designed for parabolic problems, BIT 41 pp 731– (2001) · Zbl 0996.65099 |

[20] | Jacobson, A transformation technique for optimal control problems with state variable inequality constraints, IEEE Transactions on Automatic Control 14 pp 457– (1969) |

[21] | Dadebo, Dynamic optimization of constrained chemical engineering problems using dynamic programming, Computers and Chemical Engineering 19 pp 513– (1995) · Zbl 0833.65063 |

[22] | Fabien, Dynamic modelling and identification of a waterjet cutting machine, Mathematical and Computer Modelling of Dynamical Systems 9 pp 45– (2003) · Zbl 1038.93504 |

[23] | Available from: http://abs-5.me.washington.edu/dsoa/dsoa.zip. |

[24] | Rall, Differentiation in Pascal-SC: Type GRADIENT, ACM Transactions on Mathematical Software 10 pp 161– (1984) · Zbl 0564.65010 |

[25] | Dissanayake, Time-optimal trajectories for robot manipulators, Robotica 9 pp 131– (1991) |

[26] | Buskens, SQP-methods for solving optimal control problems with control and state constraints: adjoint variables, sensitivity analysis and real-time control, Journal of Computational and Applied Mathematics 120 pp 84– (2000) |

[27] | Balsa-Canto, Dynamic optimization of chemical and biochemical processes using restricted second-order information, Computers and Chemical Engineering 25 pp 539– (2001) |

[28] | Dolan, Benchmarking optimization software with performance profiles, Mathematical Programming, Series A 91 pp 201– (2002) · Zbl 1049.90004 |

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