Review of Pure State-Path Inequality Constraint Enforcement Methods Within the Indirect Method

Incorporation of pure state-path inequality constraints (PSPICs) is an important step of formulating and solving practical optimal control problems (OCPs). Traditionally, PSPICs can be difficult to enforce within the indirect formalism of optimal control theory, since a priori knowledge of the sequence of active constraint arcs is required to enforce additional boundary conditions through interior point constraints, potentially introducing discontinuities in the costates and Hamiltonian. Recent developments and use of penalty- and barrier-based techniques has facilitated the enforcement of PSPICs, but each method has its pros and cons. In this work, we review a few of these recent techniques to compare and assess different methods to deal with PSPICs. To demonstrate the utility of the proposed methods, we solve two OCPs: 1) the well-known Breakwell problem, which is a double-integrator system subject to a second-order state-path inequality constraint and 2) a constrained planar spacecraft trajectory optimization problem with a PSPIC on the minimum semiparameter. A general-purpose pseudospectral-based OCP solver is used to verify the accuracy and optimality of the solutions.