(371m) The Development of Multiparametric Model Predictive Controllers Via the Argonaut Framework

Authors: 
Katz, J., Texas A&M University
Beykal, B., Texas A&M University
Pappas, I. S., Texas A&M University
Diangelakis, N. A., Texas A&M University
Pistikopoulos, E. N., Texas A&M Energy Institute, Texas A&M University
The use of model-based optimization for the advanced control of chemical processes is a proven methodology [1]. In these advanced control formulations, the model development stage is crucial, where the process at hand is approximated by a reduced, but representative linear model. Many strategies exist in the literature to develop these representative linear models in open loop to great success [2]. Although, when these linear models are cast in an optimization formulation, it is difficult to ascertain the effectiveness of the resulting model based controller in closed loop. Currently, research directions are exploring alternatives to optimization formulations based on approximate models. With the emergence of data-driven techniques, strategies are employed which directly formulate the relationship between the states of the system and the optimal control action [3]. However, there is still a benefit in maintaining the optimization formulation that implicitly defines the optimal control action at a given state of the system.

In this work, a nonlinear dynamic optimization control scheme is directly approximated using the data-driven framework ARGONAUT. In contrast to (i) standard approaches which utilize an approximate linear model of the nonlinear dynamic system as the basis of a model predictive control scheme, and (ii) data-driven approaches which identify the relationship between the current state and the manipulated action, the proposed methodology treats the original nonlinear optimization problem as a black box to develop an approximate quadratic optimization formulation. In this way, ARGONAUT can explicitly build approximate surrogate formulations for the objective function and the feasible space of the original nonlinear optimization formulation separately. To ensure the developed objective function and constraint set that define the quadratic formulation are satisfactory, ARGONAUT utilizes optimal sampling strategies, global parameter estimation, and model validation [4, 5]. The constructed model predictive controller is then recast as its multiparametric counterpart and solved using the Parametric Optimization (POP) toolbox, providing the explicit set of optimal control laws as an affine function of bounded uncertain parameters [6, 7]. The proposed methodology is tested on a continuously stirred tank reactor and a distillation column.

References

[1] Qin, S. J.; Badgwell, A. A Survey of Industrial Model Predictive Control Technology. Control Engineering Practice 2003, 11, 733-764.

[2] Ljung, L. System Identification: Theory for the User. Prentice-Hall, 1999.

[3] Ma, Y; Zhu. W; Benton, M.G; Romagnoli, J. Continuous control of a polymerization system with deep reinforcement learning. Journal of Process Control 2019, 75, 40-47.

[4] Boukouvala, F; Floudas, C.A. ARGONAUT: AlgoRithms for Global Optimization of coNstrAined grey-box compUTational problems. Optimization Letters 2017, 11, 895-913.

[5] Beykal, B.; Boukouvala, F.; Floudas, C.A.; Sorek, N.; Zalavadia, H.; Gildin, E. 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.

[6] Oberdieck, R.; Diangelakis, N. A.; Papathanasiou, M. M.; Nascu, I.; Pistikopoulos, E. N. POP - Parametric Optimization Toolbox. Industrial & Engineering Chemistry Research 2016, 55, 8979-8991.

[7] Bemporad, A.; Morari, M.; Dua, V.; Pistikopoulos, E. N. The explicit linear quadratic regulator for constrained systems. Automatica 2002, 38, 3-20.