Improved Two-Stage Gauss Pseudospectral Collocation Approach for Engineering Optimal Control Problems

To improve the optimization performance of Gauss pseudospectral method for bang-bang optimal control problems, a two-stage mesh refinement Gauss pseudospectral method based on the sensitivity is proposed. In the first stage, the state and control vector are approximated by global interpolation polynomials. The differential equations are approximated by orthogonal polynomials and the optimal control problem is then transformed into an NLP problem. In the second stage, the relative sensitivity is calculated and the mesh is refined by merging and subdividing collocation points. Finally a new NLP problem is obtained with refined Gauss collocation points. Simulation tests are carried out on two classical bang-bang optimal control problems. The test results show that this method is better than the traditional Gauss pseudo-spectral method in both accuracy and time.