A novel adaptive grid refinement algorithm for dynamic optimization with guaranteed feasibility of path constraints

This article proposes an adaptive grid refinement algorithm based on a novel joint density function to solve a kind of dynamic optimization problem subject to inequality path constraints. Different from the existing work, the dynamic optimization problem with inequality path constraints is transformed into a semi-infinite programming problem by parameterizing control vectors with a uniform grid first, and a novel joint density function based on the changing rate of control input and the degree of constraint violation is constructed at each iteration to adaptively adjust the grid distribution such that grid points are dynamically redistributed to avoid redundancy in non-critical regions while maintaining fulfillment of inequality path constraints. The proposed algorithm can not only reduce computational time but also effectively balance optimization accuracy with computational efficiency compared to the existing results. A numerical example is presented to verify the advantages of our proposed method.