Exploitation of the control switching structure in multi-stage optimal control problems by adaptive shooting methods

•Exploitation of the control switching structure for multi-stage problems.•Exploitation of the control switching structure for multiple-shooting problems.•Wavelet-based grid refinement of nested multi-stage/multiple-shooting problem.•A new measure to evaluate the intermediate constraint violation.

The adaptive switching structure approach is generalized from single-stage problems and single-shooting to multi-stage problems and multiple-shooting. This generalization is based on previous work on the exploitation and detection of the control switching structure and wavelet-based control grid refinement for single-stage problems. Here, single-shooting is employed to transcribe the multi-stage optimal control problem (OCP) into a nonlinear programming problem. The proposed multi-stage formulation is also capable to represent the transcription of single-stage OCP stemming from multiple-shooting. Thus, the previously reported adaptive multiple-shooting approach is extended by an adaptation of the switching structure. Finally, a new stopping criterion is introduced that measures the intermediate constraint violation at the optimal solution.The proposed adaptive switching structure detection is illustrated for a multi-stage and a multiple-shooting problem using the Williams–Otto semi-batch reactor. A solution of user-specified accuracy in the objective and the path-constraints can be obtained using only few decision variables.