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

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


Diangelakis, N. A., Texas A&M University
Pistikopoulos, E. N., Texas A&M Energy Institute, Texas A&M University
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.


[1] S. Kameswaran, L.T. Biegler. Simultaneous dynamic optimization strategies: Recent advances and challenges. Computers & Chemical Engineering, 2006, 30(10-12): 1560-1575.

[2] E.N. Pistikopoulos, N.A. Diangelakis, R. Oberdieck, M.M. Papathanasiou, I. Nascu, M. Sun. PAROC-An integrated framework and software platform for the optimisation and advanced model-based control of process systems. Chemical Engineering Science, 2015, 136: 115-138.

[3] A. Cervantes, L.T. Biegler. Optimization Strategies for Dynamic Systems. Encyclopedia of Optimization, 2009, 4: 216-227.

[4] J. Fu, J.M. Faust, B. Chachuat, A. Mitsos. Local optimization of dynamic programs with guaranteed satisfaction of path constraints. Automatica, 2015, 62: 184-192.

[5] M.J. Mohideen, J.D. Perkins, E.N. Pistikopoulos. Towards an efficient numerical procedure for mixed integer optimal control. Computers & Chemical Engineering, 1997, 21: S457-S462.

[6] B. Beykal, S. Avraamidou, I.P.E Pistikopoulos, M. Onel, E.N. Pistikopoulos. DOMINO: Data-driven Optimization of bi-level Mixed-Integer NOnlinear problems. Journal of Global Optimization, 2020, 78: 1-36.

[7] B. Beykal, F. Boukouvala, C.A. Floudas, E.N. Pistikopoulos. Optimal design of energy systems using constrained grey-box multi-objective optimization. Computers & chemical engineering, 2018, 116: 488-502.

[8] B. Beykal, M. Onel, O. Onel, E.N. Pistikopoulos. A data‐driven optimization algorithm for differential algebraic equations with numerical infeasibilities. AIChE Journal, 2020, 66(10): e16657.

[9] B. Beykal, F. Boukouvala, C.A. Floudas, N. Sorek, H. Zalavadia, E. Gildin. Global optimization of grey-box computational systems using surrogate functions and application to highly constrained oil-field operations. Computers & Chemical Engineering, 2018, 114: 99-110.