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Implicit integration with adjoint sensitivity propagation for optimal control problems involving differential-algebraic equations

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Open access
Authors
Jiang, C.
Xie, K.
Guo, Z.
Teo, Kok Lay
Date
2017
Type
Conference Paper

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Jiang, C. and Xie, K. and Guo, Z. and Teo, K.L. 2017. Implicit integration with adjoint sensitivity propagation for optimal control problems involving differential-algebraic equations, in Proceedings of the 36th Chinese Control Conference, Jul 26-28 2017, pp. 2489-2494. Dalian, China: IEEE.
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Chinese Control Conference, CCC
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Department of Mathematics and Statistics
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Abstract

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.