(345c) Data-Driven Dynamic Optimization Using Continuous-Time Surrogate Models

Time-varying systems are ubiquitous in the chemical process industry and their systematic control is essential for a feasible and safe operation of any process [1]. Derivation of the appropriate optimal control strategies is key to ensure each system is operated at the desired settings while avoiding undesirable outcomes. A typical approach for solving such problems follows approximations which may include uniform/non-uniform discretization and the solution of large-scale linear/nonlinear/linearized problems, depending on the original problem structure and accuracy implications [2,3]. Seldom is the calculus of variations employed for these problems due to the complexity that this approach may pose and its limited applicability to linear ODE problems [4,5]. In highly nonlinear systems, the full discretization of the time-varying problem such that a manipulated action is taken at each discrete time point is computationally expensive, while the linear control schemes are often insufficient to delineate an appropriate nonlinear control strategy for a given nonlinear process. Recently, data-driven modeling and optimization is shown to be an effective methodology for addressing such challenging classes of optimization problems [6-9], however, their applicability has not been fully extended to time-varying and dynamic optimization problems.

In this work, we address the control optimization of time-varying chemical systems without the full discretization of the underlying high-fidelity models and derive optimal control trajectories using surrogate modeling and data-driven optimization. We postulate nonlinear continuous-time control action trajectories and derive the parameters of these functional forms using data-driven optimization. We test exponential and polynomial functional forms as well as various data-driven optimization strategies (local vs. global and sample-based vs. model-based) to test the consistency of each approach for controlling dynamic systems. Path constraints are also considered in the formulation and are handled as grey-box constraints. We demonstrate the applicability of our approach on a motivating example and a CSTR control case study.

References

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