Simultaneous design and nonlinear model predictive control under uncertainty: A back-off approach

Palma-Flores, Oscar; Ricardez‐Sandoval, Luis A.

doi:10.1016/j.jprocont.2021.12.007

Cited by 13 publications

(8 citation statements)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It can be the system output signal, control input signal, or a combination of these signals. When ( 1) z  δ is fixed, model ( 3) is simplified to a linear ARX model, which is a local linearization of the model at a working point of the system, and when ( 1) z  δ follows the system change, it can naturally switch to the next local linear ARX model. This feature decomposes the complexity of the model into the autoregressive parts of their respective variables and is helpful for the subsequent model-based predictive controller design.…”

Section: A Sd-arx Modelmentioning

confidence: 99%

“…Model predictive control (MPC) is an optimal control algorithm developed for industrial process control. Because its control mechanism has good adaptability to complex industrial processes, it has attracted the extensive attention of scholars and has achieved a lot of research results [1][2]. MPC algorithm uses a dynamic model to predict the future behavior of the system.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Deep Learning-Based State-Dependent ARX Modeling and Predictive Control of Nonlinear Systems

Kang

Peng

et al. 2023

IEEE Access

View full text Add to dashboard Cite

For many practical industrial objects with time-varying operating points, strong nonlinearity, and difficulty in obtaining analytical models, the data-driven identification method is usually used to model such nonlinear systems. However, it is difficult for traditional modeling algorithms to effectively extract the dynamic characteristics of nonlinear systems from data and obtain accurate mathematical models. In this paper, we consider using the deep learning network combined with the state-dependent exogenous variable autoregressive (SD-ARX) model framework to build the nonlinear system model, so as to effectively and accurately learn the space-time characteristics of the nonlinear system from the sample data. Based on the idea, the hybrid models, i.e., the RNN-ARX model, CNN-ARX model, and RNN-CNN-ARX model are built, which use recurrent neural networks (RNN), convolutional neural networks (CNN) and their combination to fit the function-type coefficients of SD-ARX model, respectively. SD-ARX model based on deep learning has the advantages of local linearity and global nonlinearity. Compared with the other two models, the RNN-CNN-ARX model has a stronger ability to extract the multidimensional spatiotemporal dynamic characteristics of nonlinear systems, because it combines the advantages of RNN in mining temporal features and CNN in extracting spatial features. According to the structural characteristics of these models, three model-based predictive control (MPC) strategies are designed, i.e., RNN-ARX-MPC, CNN-ARX-MPC, and RNN-CNN-ARX-MPC. The real-time control comparative experiment on an actual multiwater-tank object shows that the proposed modeling and MPC method is feasible and effective for the modeling and predictive control of the nonlinear system.

show abstract

Section: A Sd-arx Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Deep Learning-Based State-Dependent ARX Modeling and Predictive Control of Nonlinear Systems

Kang

Peng

et al. 2023

IEEE Access

View full text Add to dashboard Cite

show abstract

“…For example, Cannon et al 182 presented a framework where the optimization problem is reformulated in terms of the adjoint variables leading to a reduction of the online computational burden. A similar approach could be employed for integrated design and control problems 183 . Thus, the application of the PMP in MPC for chemical processes is still an area under development.…”

Section: Current Challenges and Perspectivesmentioning

confidence: 99%

“…A similar approach could be employed for integrated design and control problems. 183 Thus, the application of the PMP in MPC for chemical processes is still an area under development.…”

Section: Uncertaintymentioning

confidence: 99%

Optimal control and the Pontryagin's principle in chemical engineering: History, theory, and challenges

2022

View full text Add to dashboard Cite

In the mid‐1950s, Pontryagin et al. published a principle that became a fundamental concept in optimal control (OC) theory. The principle provides theoretical and practical methods to find the solution of OC problems, in particular, open‐loop control problems. In chemical engineering, the principle has played an important role as a decision making framework for more than 60 years. This study gathers the main contributions on the application of the Pontryagin's principle to the dynamic optimization of chemical processes. A concise overview of the optimality conditions for a wide class of constrained OC problems is provided. Numerical methods to solve the necessary conditions and strategies to address inequality constraints are summarized. The information and illustrative case study presented in this work can be used as a guide to implement the principle in different settings. Opportunities for further application of the principle in relevant chemical engineering problems are also discussed.

show abstract

“…However, this method cannot theoretically examine and ensure the feasibility of all scenarios over the whole uncertainty set. A third approach is the back-off method, [23][24][25][26] which approximates the largest deviation of the inequalities in the uncertainty set by appending a back-off term. This term can be calculated by Monte Carlo sampling 23,25 or the point-estimate method, 24 and is further updated to satisfy the convergence criterion.…”

Section: Introductionmentioning

confidence: 99%

Robust dynamic optimization for nonlinear chemical processes under measurable and unmeasurable uncertainties

Liang

Yuan

2022

AIChE Journal

View full text Add to dashboard Cite

We formulate an integrated framework for the robust dynamic optimization of nonlinear chemical processes under measurable and unmeasurable uncertainties. An affine decision rule is proposed to approximate the causal dependence of the wait‐and‐see decision variables on the gradually revealed measurable uncertainties. To overcome the computational intractability of the proposed model, a linearization technique based on the first‐order Taylor expansion is introduced around the nominal values of uncertainties to derive the robust dynamic counterpart, which can be discretized to a large‐scale nonlinear programming (NLP) formulation. Effects of first discretizing the dynamic models or introducing the affine decision rule are investigated. The proposed framework is also compared with the state‐of‐the‐art re‐optimization and traditional robust optimization approaches. An illustrative example and an industrial semi‐batch 2‐mercaptobenzothiazole production case are involved to demonstrate the advantages and applicability of the proposed framework.

show abstract

Simultaneous design and nonlinear model predictive control under uncertainty: A back-off approach

Cited by 13 publications

References 45 publications

Deep Learning-Based State-Dependent ARX Modeling and Predictive Control of Nonlinear Systems

Deep Learning-Based State-Dependent ARX Modeling and Predictive Control of Nonlinear Systems

Optimal control and the Pontryagin's principle in chemical engineering: History, theory, and challenges

Robust dynamic optimization for nonlinear chemical processes under measurable and unmeasurable uncertainties

Contact Info

Product

Resources

About