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This book introduces models and methodologies that can be employed towards making the Industry 4.0 vision a reality within the process industries, and at the same time investigates the impact of uncertainties in such highly integrated settings. Advances in computing power along with the widespread availability of data have led process industries to consider a new paradigm for automated and more efficient operations. The book presents a theoretically proven optimal solution to multi-parametric linear and mixed-integer linear programs and efficient solutions to problems such as process scheduling and design under global uncertainty. It also proposes a systematic framework for the uncertainty-aware integration of planning, scheduling and control, based on the judicious coupling of reactive and proactive methods. Using these developments, the book demonstrates how the integration of different decision-making layers and their simultaneous optimisation can enhance industrial process operations and their economic resilience in the face of uncertainty.

### Chapter 1. Thesis Background

Abstract
The process manufacturing industry is confronted nowadays, more than ever before, with several factors that threaten its economic stability, such as market globalisation, fluctuation in the products’ demand and increased cost of raw material, to name a few. Under the light of this ever-increasingly uncertain socioeconomic environment, the need to safeguard process profitability, sustainability and reliability becomes progressively urgent.
Vassilis M. Charitopoulos

### Chapter 2. Parametric Optimisation: 65 years of developments and status quo

Abstract
In this chapter, a histogram of the theoretical and algorithmic developments that led the current status of multi-parametric programming is drawn. For conceptual and organisational purposes, three distinct eras are identified and the related findings are discussed while key limitations in the state of the art are outlined. Based on these, the main developments in the field of multi-parametric programming presented in the thesis are motivated.
Vassilis M. Charitopoulos

### Chapter 3. Multi-parametric Linear and Mixed Integer Linear Programming Under Global Uncertainty

Abstract
In this chapter, two algorithms for the exact explicit solution of mp-(MI)LPs under global uncertainty are presented. The algorithms comprise of two key steps: (i) analytical solution of the problem’s KKT system with the uncertain parameters and the integer variables treated as symbols using $$Gr\ddot{o}bner$$ Bases and (ii) the computation of the related possibly non-convex and discontinuous CRs using Cylindrical Algebraic Decompositions on the parametric space. Problems related to process synthesis and scheduling highlight the potential of the proposed work while for the first time the functional nature of the explicit solution is theoretically characterised and proven.
Vassilis M. Charitopoulos

### Chapter 4. Towards Exact Multi-setpoint Explicit Controllers for Enterprise Wide Optimisation

Abstract
In this chapter, the applicability of the algorithm presented in the previous chapter, is showcased for the solution of a special class of multi-parametric programming nonlinear problems. The main focus of the chapter, however is not the algorithmic advances themselves, but the study of the concept of “multi-setpoint explicit controller” and their potential use in problems of enterprise wide optimisation in which the grade of control is involved.
Vassilis M. Charitopoulos

### Chapter 5. Open-Loop Integration of Planning, Scheduling and Optimal Control: Overview, Challenges and Model Formulations

Abstract
Traditionally, planning, scheduling and optimal control problems are solved in a decoupled way, neglecting their strong interdependence. Integrated Planning, Scheduling and optimal Control (iPSC) aims to address this issue. In this chapter, current developments on the topic of integrating control with process operations are reviewed and a new approach for the iPSC of continuous processes aiming to reduce model and computational complexity is proposed. The resulting problem is a mixed integer program for which different solution strategies are employed and analysed.
Vassilis M. Charitopoulos

### Chapter 6. Closed-Loop Integration of Planning, Scheduling and Multi-parametric Nonlinear Control

Abstract
In this chapter, motivated by the need for efficient closed-loop implementation of the control objectives set within the integrated planning, scheduling and control (iPSC) problem a novel framework that enables its online solution under dynamic disturbances is presented. Utilising the concept of multi-setpoint explicit controllers, from Chap. 4, a rigorous rescheduling mechanism that mitigates the impact of the dynamic disruptions on the operational decisions of planning and scheduling is developed. The overall closed-loop problem is formulated as mixed integer linear program with the control problem integrated via an outer loop. The benefits of the proposed framework are highlighted through two case studies and the results indicate the importance of considering dynamic disruptions within the scope of the integrated problem.
Vassilis M. Charitopoulos

### Chapter 7. A Hybrid Framework for the Uncertainty-Aware Integration of Planning, Scheduling and Explicit Control

Abstract
In this chapter the integrated planning, scheduling and control (iPSC) of process systems under uncertain conditions throughout the three levels of decision making is examined. The planning problem is explored in a rolling horizon fashion coupled with demand forecasts. Proactive and reactive approaches are employed to handle the effect of stochastic variations. Depending on the nature of the uncertain parameters robust optimisation and chance constrained programming are employed. For the closed-loop implementation of the control, multi-setpoint explicit controllers are designed. The proposed framework is tested on the iPSC of a polymerisation process.
Vassilis M. Charitopoulos

### Chapter 8. Conclusions and Future Work

Abstract
In this final chapter, the main contributions of the thesis are summarised and future research directions are drawn for each of the two topics that were discussed, i.e. multi-parametric programming and uncertainty-aware integration of process operations with control.
Vassilis M. Charitopoulos