(57e) Model Reduction Based Optimization for Distributed Parameter Systems
A model reduction-based optimization framework is presented, to be used with input/output dynamic simulators in order to perform both steady state and dynamic optimisation. This is the case when a black-box code (e.g. a commercial package) is used to model a process, and the system Jacobians and Hessians cannot be directly computed. Therefore, it is in general, computationally inefficient to perform gradient-based optimization and parameter estimation using such codes.
For steady state optimization a two-step projection approach is presented : In the first projection, the state variables are projected to the low-dimensional subspace of the dominant eigenmodes identified adaptively by the Recursive Projection Method (RPM). The second projection is performed onto the subspace of the few decision variables without the need to compute any large-scale matrices. Furthermore, a methodology is discussed that is used to perform stable, efficient dynamic optimization/optimal control by discretizing the time domain in a number of subintervals and performing reduced Hessian SQP-type optimization to the resulting problem . We again adopt a two-step projection strategy exploiting a Newton-Picard based scheme that is used for the stabilization of multiple shooting procedures . We use illustrative distributed parameter systems including the tubular reactor and large-scale CFD codes to demonstrate our optimization methodologies.
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