Analytical sensitivity computation using collocation method with non-uniform mesh discretisation for numerical solutions of optimal control problems

ABSTRACT

A numerical computational method based on the orthogonal collocation on finite element with sparse variable time points is proposed for the optimal control problems (OCPs). This approach generates a non-uniform mesh in the whole time horizon to obtain a better approximation than the uniform discretisation methods. The original problem is converted to a nonlinear programming problem, where only the discretised control parameters and the interval parameters used for the jumps of control are treated as optimisation variables. To improve the convergence rate and the efficiency, the analytical first-order and second-order sensitivities of state at collocation points with respect to the control, as well as the variable interval parameters are derived, respectively. The proposed method is illustrated by testing two OCPs with different complexities. The detailed comparisons between the proposed method and other methods are also carried out. The research results reveal the effectiveness of proposed approach.

Keywords:

• Optimal control
• analytical sensitivity computation
• collocation on finite element
• non-uniform discretisation

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant numbers 61590921, 61603336], Zhejiang Province Natural Science Foundation [LY18D060002], Shanghai Aerospace Science and Technology Innovation Fund [E11501] and Aerospace Science and Technology Innovation Fund of China Aerospace Science and Technology Corporation [E11601], and their supports are thereby acknowledged.