Applications, Modeling Tools, and Parallel Solution Algorithms for Dynamic Optimization

Dynamic optimization problems directly incorporate detailed dynamic models as constraints within an optimization framework. Model predictive control, state estimation, and parameter estimation are all common applications of dynamic optimization which can lead to significant improvements in process efficiency, reliability, safety, and profitability. This dissertation deals with dynamic optimization from three perspectives. We begin with an application of dynamic optimization. State estimation is a crucial part of the monitoring and/or control of all chemical processes. We make use of a state estimation technique called moving horizon estimation (MHE) which can be formulated as a dynamic optimization problem. However, large-scale MHE formulations may require non-negligible computational time to solve limiting its application for real-time state estimation. An extension of MHE, called Advanced Step Moving Horizon Estimation (asMHE), eliminates this computational delay. Both MHE and asMHE perform well under the assumption of Gaussian measurement noise. We consider the case where this assumption does not hold and measurements are contaminated with large errors. Standard least squares based estimators generate biased estimates even with relatively few gross measurement errors. We therefore extend MHE and asMHE formulations using robust M-Estimators in order to mitigate the bias of these errors on the state estimates. We demonstrate this approach on dynamic models of a CSTR and a distillation column and find that our approach produces fast and accurate state estimates even in the presence of many gross measurement errors. A well-established method to solve dynamic optimization problems is direct transcription where the differential equations are replaced with algebraic approximations using some numerical method such as a finite-difference or Runge-Kutta scheme. In the second part of this work we present pyomo.dae, an open-source modeling framework that enables high-level abstract representations of optimization problems with differential and algebraic equations. A key distinctive feature of pyomo.dae is that it does not adhere to standard, predefined formats of optimal control and estimation problems. This enables high modeling flexibility and the consideration of constraints and objective functions in non-standard forms that cannot be easily handled by traditional solution methods and cannot be expressed in other modeling frameworks. pyomo.dae also enables the specification of optimization problems with high-order differential equations and partial differential equations on restricted domain types and it provides automatic discretization capabilities to transcribe high-level abstract models into finite-dimensional algebraic problems that can be solved with off-the-shelf optimization solvers. However, for problems with thousands of state variables and discretization points, direct transcription may result in nonlinear optimization problems that exceed memory and speed limits of most serial computers. In particular, when applying interior point optimization methods, the computational bottleneck and dominant computational cost lies in solving the linear systems resulting from the Newton steps that solve the discretized optimality conditions. To overcome these limits, we exploit the parallelizable structure of the linear system to accelerate the overall interior point algorithm. We investigate two algorithms which take advantage of this property, cyclic reduction and Schur complement decomposition and study the performance of these algorithms when applied to dynamic optimization problems.