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| Received:November 10, 2010Revised:March 24, 2011 |
| 基金项目:This work was supported by the Natural Science Foundation of China (No. 60974039) and the National Science and Technology Major Project (No.2008ZX05011). |
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| Optimization method for solving bang-bang and singular control problems |
| Shurong LI,Ruiyan ZHAO,Qiang ZHANG |
| (College of Information and Control Engineering, China University of Petroleum) |
| Abstract: |
| In this paper we study optimal control problems with the control variable appearing linearly. A novel method for optimization with respect to the switching times of controls containing both bang-bang and singular arcs is presented. This method transforms the control problem into a finite-dimensional optimization problem by reformulating the control problem as a multi-stage optimization problem. The optimal control problem is partitioned as several stages, with each stage corresponding to a particular control arc. A control vector parameterization approach is applied to convert the control problem to a static nonlinear programming (NLP) problem. The control profiles and stage lengths act as decision variables. Based on the Pontryagin maximal principle, a multi-stage adjoint system is constructed to calculate the gradients required by the NLP solvers. Two examples are studied to demonstrate the effectiveness of this strategy. |
| Key words: Bang-bang control Singular control Multi-stage problem Nonlinear programming problem |
