Inequality path constraints in optimal control: a finite iteration ε-convergent scheme based on pointwise discretization

This paper presents a new result in the analysis and implementation of path constraints in optimal control problems (OCPs). The scheme uses the well-known concept of discretizing path constraints on a finite number of points, yielding a set of interior-time point constraints replacing the original path constraints. The approach replaces the original OCP by a sequence of OCPs which is shown to converge in a finite number of steps to the solution of the original path constrained problem with ε-accuracy. Numerical results, verifying the theoretical analysis, are presented. The method is shown to be effective and promising for future applications, particularly in control vector parameterization implementations.