Title: Direct Transcription Solution of Inequality Constrained Optimal Control Problems: Theory vs Practice

Direct transcription is a popular way of solving the complex optimal control problems that arise in industry. With a direct transcription approach the problem is fully discretized and then the discrete problem is solved numerically. Recently it has been shown that the theory for direct transcription differs in several key ways from the theory for other approaches. These differences have implications for numerical algorithms and the interpretation of solutions to practical problems. This talk examines some of those differences.
Two different examples where the theory needs to be reinterpreted will be given. One involves the theory of Differential Algebraic Equation (DAE) integrators. The other involves the necessary conditions for optimal control problems. Needed terminology and background information will be provided and the presentation will try to avoid excessive technical detail. The talk should be accessible to a range of graduate students, faculty, and researchers in engineering, applied mathematics, and computer science.