Simultaneous design and NMPC control under uncertainty and structural decisions: A discrete-steepest descent algorithm

In this article, we address the integration of design and nonlinear model-based control under uncertainty and structural decisions for naturally ordered structures. We propose an algorithmic framework to determine the optimal location of process units or streams over an ordered discrete set that operates in closed-loop with a model-based controller. The formulation corresponds to a mixed-integer bilevel problem (MIBLP) that is transformed into a single-level mixed-integer nonlinear problem (MINLP) using a KKT transformation strategy. In our methodology, the integer decisions are partitioned into subsets called external variables, such that the MINLP is decomposed into an integer-based master problem and primal subproblems with fixed discrete variables. The master and primal problems are solved using a Discrete-Steepest Descent Algorithm (D-SDA). We illustrate the discrete-based methodology in a case study for a binary distillation column. The D-SDA showed an improved performance compared to a benchmark continuous-based formulation using differentiable distribution functions (DDFs).

Automated summary

In this article, the integration problem of design and nonlinear model-based control under uncertainty and structural decisions is addressed. An algorithmic framework is proposed to determine the optimal location of process units or streams in closed-loop with a model-based controller. The problem is formulated as a mixed-integer bilevel problem (MIBLP) and transformed into a single-level mixed-integer nonlinear problem (MINLP) using a KKT transformation strategy. The methodology decomposes the MINLP into an integer-based master problem and primal subproblems, which are solved using a Discrete-Steepest Descent Algorithm (D-SDA). The discrete-based methodology is illustrated in a case study for a binary distillation column, where D-SDA outperforms the benchmark continuous-based formulation using differentiable distribution functions (DDFs).