Abstract
This paper presents an extension of the recent multi-parametric (mp-)NCO-tracking methodology by Sun et al. [Comput. Chem. Eng. 92 (2016) 64–77] for the design of robust multi-parametric controllers for constrained continuous-time linear systems in the presence of uncertainty. We propose a robust-counterpart formulation and solution of multi-parametric dynamic optimization (mp-DO), whereby the constraints are backed-off based on a worst-case propagation of the uncertainty using either interval analysis or ellipsoidal calculus and an ancillary linear state feedback. We address the case of additive uncertainty, and we discuss approaches to dealing with multiplicative uncertainty that retain tractability of the mp-NCO-tracking design problem, subject to extra conservativeness. In order to assist with the implementation of these controllers, we also investigate the use of data classifiers based on deep learning for approximating the critical regions in continuous-time mp-DO problems, and subsequently searching for a critical region during on-line execution. We illustrate these developments with the case studies of a fluid catalytic cracking (FCC) unit and a chemical reactor cascade.
Highlights
On-line optimization and real-time control have received significant attention over the past few decades, driven by the need to improve performance and reduce economic costs in industrial processes
The focus is on developing robust formulations that are amenable to numerical solution at a similar computational effort as the nominal mp-necessary conditions for optimality (NCO)-tracking controllers in Sun et al [47], i.e. with Fw = 0 in (1)
Before presenting these two contributions, we provide an overview of multi-parametric dynamic optimization (mp-DO) and mp-NCO-tracking in the following subsections
Summary
On-line optimization and real-time control have received significant attention over the past few decades, driven by the need to improve performance and reduce economic costs in industrial processes. Sun et al [47] have introduced the multi-parametric (mp-)NCO-tracking approach, which combines mp-DO and NCOtracking into a unified framework for explicit MPC via the indirect mp-DO approach This approach has been demonstrated for constrained linear-quadratic optimal control problems. It provides a means for relaxing the invariant switching-structure and active-set assumptions that is typical of NCO-tracking by constructing critical regions for each switching structure. Similar applications of machine learning within explicit MPC have been proposed for approximating the solution of both linear and nonlinear MPC [16,28] Another feature of data classifiers lies in their ability to estimate the likelihood of a given parameter value to belong within a certain critical region, providing a basis for the point-location problem during the on-line execution of mp-NCO-tracking. A(·,i)]. ek ∈ Rn denotes the vector with a 1 in the ith coordinate and 0’s elsewhere
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