Numerical Regularization for Singular Optimal Control Problems

Singular control problems arise naturally in chemical process control and are often solved using methods based on Lie algebra. However, these become cumbersome for large problems. As an alternative, we present a Radau collocation strategy for the solution of singular control problems that is based on indirect methods. Our solution strategy realizes that singular OCPs are inherently ill-conditioned, and attempts to regularize the problem instead of resorting to the conventional index-reformulation strategy. The problem is regularized through the construction of a simple objective function that attempts to enforce continuity conditions on the derivative of the Hamiltonian, while monitoring certain error residuals. This approach is demonstrated on several process examples that are singular over the entire time domain. Extensions of this approach to problems involving switches and singular arcs, as well as the incorporation of this approach within a direct transcription NLP strategy will also be presented.