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Method for Solving State-Path Constrained Optimal Control Problems Using Adaptive Radau Collocation
  • Cale Byczkowski,
  • Anil Rao
Cale Byczkowski
University of Florida
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Anil Rao
University of Florida

Corresponding Author:[email protected]

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A new method is developed for accurately approximating the solution to state-variable inequality path constrained optimal control problems using a multiple-domain adaptive Legendre-Gauss-Radau collocation method. The method consists of the following parts. First, a structure detection method is developed to estimate switch times in the activation and deactivation of state-variable inequality path constraints. Second, using the detected structure, the domain is partitioned into multiple-domains where each domain corresponds to either a constrained or an unconstrained segment. Furthermore, additional decision variables are introduced in the multiple-domain formulation, where these additional decision variables represent the switch times of the detected active state-variable inequality path constraints. Within a constrained domain, the path constraint is differentiated with respect to the independent variable until the control appears explicitly, and this derivative is set to zero along the constrained arc while all preceding derivatives are set to zero at the start of the constrained arc. The time derivatives of the active state-variable inequality path constraints are computed using automatic differentiation and the properties of the chain rule. The method is demonstrated on two problems, the first being a benchmark optimal control problem which has a known analytical solution and the second being a challenging problem from the field of aerospace engineering in which there is no known analytical solution. When compared against previously developed adaptive Legendre-Gauss-Radau methods, the results show that the method developed in this paper is capable of computing accurate solutions to problems whose solution contain active state-variable inequality path constraints.
12 Apr 2023Submitted to Optimal Control, Applications and Methods
12 Apr 2023Submission Checks Completed
12 Apr 2023Assigned to Editor
12 Apr 2023Review(s) Completed, Editorial Evaluation Pending
30 Apr 2023Reviewer(s) Assigned
24 Jul 2023Editorial Decision: Revise Minor
09 Sep 20231st Revision Received
12 Sep 2023Assigned to Editor
12 Sep 2023Submission Checks Completed
12 Sep 2023Review(s) Completed, Editorial Evaluation Pending
17 Sep 2023Reviewer(s) Assigned
20 Nov 2023Editorial Decision: Revise Minor
22 Nov 20232nd Revision Received
22 Nov 2023Assigned to Editor
22 Nov 2023Submission Checks Completed
22 Nov 2023Review(s) Completed, Editorial Evaluation Pending