Towards Pseudospectral Control and Estimation

Abstract: This thesis covers different topics related to the application of pseudospectral optimization methods in the field of automatic control. Pseudospectral optimization methods solve dynamic optimization problems by discretizing the state-space, creating a discretized version of a continuous problem. The resulting discretized optimization problems are solved by standard software for nonlinear optimization. An evaluation of pseudospectral optimal control in a model predictive control (MPC) setting is presented, as a double-tank process is controlled from one set point to another. The method quite often experiences divergence, which makes its use in a real setting limited. The thesis proposes a way to use pseudospectral optimization as a nonlinear state estimator together with Out-Of-Sequence-Measurements(OOSM). The main idea is outlined; however, it represents future work as a lot remains to be done. The thesis also evaluates possible performance gains when solving optimization problems governed by ODE system dynamics in parallel. For large systems, with very many discretization points, substantial speedups are possible. However, the application is shown only on randomly generated systems, as real world examples of such large sizes are elusive.